There are 100 dears within a circular area with a radius of 10. Find the density of deer for 400 square miles.

Answers

Answer 1

The density of deer for 400 square miles is around 1:4 based on stated number of deers.

The density of deer will be given by the formula -

Population density of deer = number of deer/ area

Population density is the amount or number of individuals of a population on land per unit area.

Keep the value in formula to find the population density

Population density = 100/400

Cancelling zero as common in both numerator and denominator

Population density = 1:4

Thus, there is 1 deer for every 4 square mile.

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Related Questions

Manuel the trainer has two solo workout plans that he offers his clients: plan a and plan b. each client does either one or the other (not both). on monday there were 3 clients who did plan a and 8 who did plan b. manuel trained his monday clients for a total of 7 hours and his tuesday clients for a total of 6 hours. how long does each workout plans last?​

Answers

Plan a lasts 1/5 of an hour (or 12 minutes) and plan b lasts 29/5 hours (or 5 hours and 48 minutes).

Let's denote the length of plan a by 'a' and the length of plan b by 'b' (measured in hours).

From the problem, we know that:

- On Monday, 3 clients did plan a and 8 clients did plan b. Therefore, the total time spent on plan a on Monday was 3a and the total time spent on plan b on Monday was 8b.

- On Tuesday, we don't know how many clients did each plan, but we do know that the total time spent on both plans was 6 hours.

Putting these together, we can create a system of two equations:

3a + 8b = 7  (total time spent on Monday)

a + b = 6    (total time spent on Tuesday)

We can solve this system by using substitution. Rearranging the second equation, we get:

b = 6 - a

Substituting this expression for b into the first equation, we get:

3a + 8(6 - a) = 7

Simplifying and solving for a, we get: a = 1/5

Substituting this value back into the expression for b, we get:

b = 6 - a = 29/5

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Differentiate between absolute and relative measure of dispersion

Answers

Absolute measures of dispersion give the actual spread or variability in the original units of measurement, while relative measures of dispersion express the dispersion relative to the mean or some other characteristic of the data.

Measures of dispersion are used to describe the spread or variability of a set of data. There are two common types of measures of dispersion: absolute measures and relative measures.

Absolute measures of dispersion, such as the range, interquartile range (IQR), and standard deviation, give an actual value or measurement of the spread in the original units of measurement.

For example, the range is simply the difference between the maximum and minimum values in a data set, while the standard deviation is a measure of how far each value is from the mean.

Relative measures of dispersion, such as the coefficient of variation (CV), express the dispersion relative to the mean or some other characteristic of the data. These measures are useful when comparing the variability of different sets of data that have different units of measurement or different means

For example, the CV is the ratio of the standard deviation to the mean, expressed as a percentage, and it can be used to compare the variability of different data sets that have different means.

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4. Let A be a 3 x 4 matrix and B be a 4 x 5 matrix such that ABx = 0 for all x € R5. a. Show that R(B) C N(A) and deduce that rank(B) < null(A) b. Use the Rank-Nullity theorem to prove that rank(A) + rank(B) < 4.

Answers

a. To show that R(B) is a subset of N(A), let y be any vector in R(B):

This means that there exists a vector x in R4 such that Bx = y.

Now, since ABx = 0 for all x in R5, we can write:

A(Bx) = 0

But we know that Bx = y, so we have:

Ay = 0

This shows that y is in N(A), and therefore R(B) is a subset of N(A).

To deduce that rank(B) is less than null(A), recall that by the Rank-Nullity theorem, we have:

rank(B) + null(B) = dim(R5) = 5

rank(A) + null(A) = dim(R4) = 4

Since R(B) is a subset of N(A), we have null(A) >= rank(B).

Therefore, using the above equations, we get:

rank(B) + null(A) <= null(B) + null(A) = 5

which implies:

rank(B) <= 5 - null(A) = 5 - (4 - rank(A)) = 1 + rank(A)

This shows that rank(B) is less than or equal to 1 plus the rank of A.

Since the rank of A can be at most 3 (since A is a 3 x 4 matrix),

we conclude that:

rank(B) < null(A)

b. To use the Rank-Nullity theorem to prove that rank(A) + rank(B) < 4

We simply add the equations:

rank(A) + null(A) = 4

rank(B) + null(B) = 5

to get:

rank(A) + rank(B) + null(A) + null(B) = 9

But since R(B) is a subset of N(A), we know that null(A) >= rank(B), and therefore:

rank(A) + rank(B) + 2null(A) <= 9

Using the first equation above, we can write null(A) = 4 - rank(A), so we get:

rank(A) + rank(B) + 2(4 - rank(A)) <= 9

which simplifies to:

rank(A) + rank(B) <= 1

Since rank(A) is at most 3,

we conclude that:

rank(A) + rank(B) < 4

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Consider the line segment defined by the points A(0, 1) and B(4,6). How does a


reflection across the x-axis affect AB?


Select all that apply.


A. The x-values of the reflection are the opposite values of the x-values of the


original segment.


B. The y-values of the endpoints become their opposites.


C• The length of the reflection of AB is greater than the length of AB.


DThe length of the reflection of AB is less than the length of AB.


E. The length of the reflection of AB is the same as the length of AB.

Answers

Considering "line-segment" defined by points A(0, 1) and B(4,6), then  effects of reflection across the "x-axis" are :

(b) The "y-coordinate" of "end-points" become opposites in sign.

(e) The length of reflection of AB is same as length of line-segment AB.

When reflecting a line segment across the x-axis, the x-coordinates of all points remain the same, but the y-coordinates become their opposites.

So, for the line segment AB, the x-coordinate of point A remains 0, and the x-coordinate of point B remains 4. However, the y-coordinate of point A becomes -1, and the y-coordinate of point B becomes -6. This results in a new line segment A'(0, -1) and B'(4, -6).

Since the reflection is across a horizontal line, the length of the reflection is the same as the length of the original segment.

Therefore, the correct options are (b) and (e).

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Three vertices of parallelogram wxyz are w(-5,2), x(2,4), and z(-7, -3). find the coordinates of vertex y.
the coordinates of vertex y are

Answers

Coordinates of vertex y are (-12,-1).

How to find the coordinates of vertex Y?

To find the coordinates of vertex y in parallelogram WXYZ, we can use the fact that opposite sides of a parallelogram are parallel. We can use this property to find the coordinates of y by first finding the vector between points X and Z, and then adding that vector to the coordinates of point W.

The vector between points X and Z is (-7-2,-3-4)=(-9,-7). Adding this vector to the coordinates of point W gives (-5-9, 2-7)=(-14,-5). Therefore, the coordinates of vertex Y are (-14,-5).

Hence, the coordinates of vertex Y in the parallelogram WXYZ are (-14, -5).

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A trapezoid has an area of 24 in. 2. If the lengths of the bases are 5. 8 in. And 2. 2 in. , what is the height?

Answers

Answer: 6

Step-by-step explanation: Area = 1/2 (a+b) x h, divide both side by 1/2(a+b), we have Area : (1/2 (a+b)) = h. Now, replace A = 24, a=5.8, b= 2.2. We got h = 6.

Guadalupe models the volume of a popcorn box as a right rectangular prism and the box can hold 46 cubic inches of popcorn when it is full. Its length is 2 3 4 2 4 3 ​ in and its height is 7 1 2 7 2 1 ​ in. Find the width of the popcorn box in inches. Round your answer to the nearest tenth if necessary.

Answers

The width of the rectangular prism popcorn box is approximately 2.27 inches when rounded to the nearest tenth.

How to Find the Width of a Rectangular Prism?

The volume of a right rectangular prism is given by:

V = lwh

where V is the volume, l is the length, w is the width, and h is the height.

We are given that the box can hold 46 cubic inches of popcorn, the length is 2¾ inches, and the height is 7½ inches. Let's use w to represent the width we are trying to find.

So we have:

46 = (2¾)w(7½)

To solve for w, we can divide both sides of the equation by (2¾)(7½):

46 / ((2¾)(7½)) = w

Simplifying the right-hand side, we get:

w ≈ 2.27

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Complete Question:

Guadalupe models the volume of a popcorn box as a right rectangular prism and the box can hold 46 cubic inches of popcorn when it is full. Its length is 2¾ inches and its height is 7½ inches. Find the width of the popcorn box in inches. Round your answer to the nearest tenth if necessary.

A cat falls from a tree (with zero initial velocity) at time t = 0. How far does the cat fall between t = 0.5 s and t=1.4 s? Use Galileo's formula u(t) = -32t ft/s.
Answer = _______

Answers

The distance is negative because it's a fall, so the cat falls 27.36 ft between t = 0.5 s and t = 1.4 s.

To find the distance the cat falls between t = 0.5 s and t = 1.4 s, we need to use the formula for velocity and distance.
we first need to find the position at each of these times using the given formula u(t) = -32t ft/s.

The formula for distance fallen is:
distance(t) = initial position + initial velocity × t + (1/2) × acceleration × t²

Since the cat falls with zero initial velocity and starts from the tree, we can simplify the formula:
distance(t) = (1/2) × acceleration × t²

First, let's find the velocity of the cat at t = 0.5 s and t = 1.4 s using Galileo's formula:
u(0.5) = -32(0.5) = -16 ft/s
and, u(1.4) = -32(1.4) = -44.8 ft/s

Now, we can use the formula for distance:
distance = (velocity at t = 0.5 s + velocity at t = 1.4 s) / 2 x (t = 1.4 s - t = 0.5 s)
⇒ distance = (-16 ft/s + (-44.8 ft/s)) / 2 x (1.4 s - 0.5 s)
⇒ distance = (-60.8 ft/s) / 2 x (0.9 s)
⇒ distance = -27.36 ft/s x s

Therefore, the cat falls 27.36 feet between t = 0.5 s and t = 1.4 s.

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find the distance between each pair of points. (5 1/2, -7 1/2) and (5 1/2, -1 1/2)

Answers

Answer:

6

Step-by-step explanation:

The distance between both those points are 6

Set up the partial fraction decomposition for a given function. Do not evaluate the coefficients. f(x) = 16x3 + 12x2 + 10x + 2 / (x4 – 4x2)(x2 + x + 1)2(x2 – 3x + 2)(x4 + 3x2 + 2)

Answers

We can decompose the given rational function as follows:

f(x) = (16x^3 + 12x^2 + 10x + 2) / [(x^4 – 4x^2)(x^2 + x + 1)^2(x^2 – 3x + 2)(x^4 + 3x^2 + 2)]

To find the partial fraction decomposition, we first factor the denominator completely:

x^4 – 4x^2 = x^2(x^2 – 4) = x^2(x – 2)(x + 2)

x^2 + x + 1 = (x + 1/2)^2 + 3/4

x^2 – 3x + 2 = (x – 1)(x – 2)

x^4 + 3x^2 + 2 = (x^2 + 1)(x^2 + 2)

Substituting these factorizations into the denominator, we get:

f(x) = (16x^3 + 12x^2 + 10x + 2) / [x^2(x – 2)(x + 2)(x + 1/2)^2(3/4)^2(x – 1)(x – 2)(x^2 + 1)(x^2 + 2)]

We can now write the partial fraction decomposition as:

f(x) = A/x + Bx + C/(x – 2) + D/(x + 2) + E/(x + 1/2) + F/(x + 1/2)^2 + G/(x – 1) + H/(x^2 + 1) + I/(x^2 + 2)

where A, B, C, D, E, F, G, H, and I are constants to be determined.

Note that the term E/(x + 1/2) has a repeated linear factor (x + 1/2)^2, so we need to include a second term F/(x + 1/2)^2 in the decomposition.

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Lines AC←→
and DB←→
intersect at point W. Also, m∠DWC=138°
.

Answers

The measure of the angles are m∠DWC=138°, ∠AWB = 138°, ∠AWD = 42°, ∠BWC = 42°

How do we calculate?

The Vertical angle theorem states that if two lines intersect at a point then vertically opposite angles are congruent.

To find the measure of all the angles:

∠AWB and ∠DWC are vertically opposite angles.

Therefore, ∠AWB = ∠DWC

⇒ ∠AWB = 138°

we know that the Sum of all the angles in a straight line = 180°

⇒ ∠AWD + ∠DWC = 180°

⇒ ∠AWD + 138° = 180°

⇒ ∠AWD = 180° – 138°

⇒ ∠AWD = 42°

Since ∠AWD and ∠BWC are vertically opposite angles.

Therefore, ∠AWD = ∠BWC

⇒ ∠BWC = 42°

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#complete question:

Lines AC←→ and DB←→ intersect at point W. Also, m∠DWC=138° .

Enter the angle measure for the angle shown.

see attached image:

Use this data set, which shows how many miles Tisha ran each week for 10 weeks

4,9,8,6,14,8,16,12

Find the statistical measures that you need tomake a box plot of Tisha's running distances.

(what’s a statistical measure)

Answers

Statistical measures, you can construct a box plot that shows the range, median, and quartiles of Tisha's running distances over the 10 weeks.

A statistical measure is a numerical value that provides information about a specific aspect of a dataset's distribution, such as its central tendency, spread, or variability. Box plots require several statistical measures to be constructed, including:

Minimum: The smallest value in the dataset. In this case, the minimum value is 4.

Maximum: The largest value in the dataset. In this case, the maximum value is 16.

Median: The middle value of the dataset when it is arranged in numerical order. In this case, the median is the average of the two middle values, which are 8 and 9. The median is therefore (8 + 9) / 2 = 8.5.

First Quartile (Q1): The value below which 25% of the data falls. In this case, the first quartile is the median of the first half of the data, which is 6.

Third Quartile (Q3): The value below which 75% of the data falls. In this case, the third quartile is the median of the second half of the data, which is 14.

With these statistical measures, you can construct a box plot that shows the range, median, and quartiles of Tisha's running distances over the 10 weeks.

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An italian ice shop sells italian ice in four flavors: lime, cherry, blueberry, and
watermelon. the ice can be served plain, mixed with ice cream, or as a drink.
using an organized list or table, what is the sample space of possible
outcomes?

Answers

The possible outcomes of sample space is 12.

To calculate the total number of outcomes in a sample space, multiply the number of serving options with the number of flavors.

There are 4 flavors that are lime, cherry, blueberry, and  watermelon and 3 serving options that are served plain, mixed with ice cream, or as a drink.

Hence, the possible outcomes will be:

4 x 3 = 12

The outcomes can be represented as lime Italian ice mixed with ice cream, cherry Italian ice served as a drink, Watermelon Italian ice mixed with ice cream, Blueberry Italian ice served plain and likewise.

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Tim jones bought 100 shares of mutual fund abc at $4.25 with no load and sold them for $850. and 100 shares of def at $6.00 which had a load of $375 dollars, and sold them for $1,200.

*this is one where you finish the table, i looked it up and couldn't find the answer so i guessed and got a 100. so this is for yall who can't just guess it perfectly on the 1st try*
<<<<< on odyssey ware >>>>>

purchase price load total cost sales price sales price ÷ total cost
abc = $425 0 $425 ? ? % (nearest 1%)
def = $600 $375 ? ? ? % (nearest 1%)

---answers---

purchase price load total cost sales price sales price ÷ total cost
abc = $425 0 $425 $850 200 % (nearest 1%)
def = $600 $375 $975 $1200 123 % (nearest 1%)

Answers

The sales price divided by total cost is 123%.

Based on the information provided, I can help you complete the table:

Purchase Price | Load | Total Cost | Sales Price | Sales Price ÷ Total Cost (nearest 1%)
ABC = $425     |   0  |   $425     |   $850      |        200%
DEF = $600     | $375 |   $975     |   $1,200    |        123%

For mutual fund ABC, there was no load, so the total cost is equal to the purchase price. The sales price ÷ total cost is 200% (nearest 1%). For mutual fund DEF, the total cost includes the $375 load, resulting in a total cost of $975. The sales price ÷ total cost is 123% (nearest 1%).

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Let P be the parallelogram with vertices (-1, -1), (1, -1), (2, 2), (0, 2). Compute S'p xy dA.

Answers

Answer:Area = 2 * 3 = 6 square units

Explanation:

Given:vertices (-1, -1), (1, -1), (2, 2), (0, 2)

 we can use the formula for the area of a parallelogram:Area = 2 * 3 = 6 square units



Area = base * height

First, let's find the base and height of the parallelogram.

The base can be represented by the distance between vertices (-1, -1) and (1, -1), which is 2 units.

The height can be represented by the distance between vertices (1, -1) and (2, 2), which is 3 units.

Now, we can compute the area of the parallelogram:

Area = 2 * 3 = 6 square units

Finally, the integral S'P xy dA represents the double integral of the function xy over the region P.

My office is 10 ft by 12 ft. I want to buy border for the top of my wall. I have a 3ft door on a 10 ft wall and a 3 ft window directly across from it. How much wallpaper border should I buy?



a. 24


b. 44


c. 38

Answers

You should buy 38 feet of wallpaper that cover the border for the top of the wall using the perimeter of the room. Thus, option C is correct.

Length of office = 10 feets

width of office  = 12 feets

Door length = 3 feet

Wall length = 10 feet

Window length = 3 feet

To estimate the length of the wallpaper border needed, we need to calculate the perimeter of the room that needs the bordering of wallpaper. It is given that only the top of the roof needs bordering.

We need to add the lengths of all 4 sides of the walls and subtract the lengths of the door and window.

Mathematically,

The perimeter of the room =(sum of the length of sides of the room) - (length of the window) - (length of the door)

Perimeter of room = (10 + 12 + 10 + 12) - 3 - 3

Perimeter of room = 38 ft

Therefore, we can conclude that we need to buy 38 feet of the wallpaper border.

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Work out the size of an exterior angle of a regular hexagon

Answers

The size of an exterior angle of a regular hexagon is 60 degrees.

Working out the size of an exterior angle

In a regular hexagon, all the interior angles are equal and are given by the formula:

Interior angle = (n-2) x 180 / n

where n is the number of sides of the polygon.

For a hexagon, n = 6, so the interior angle is:

Interior angle = (6-2) x 180 / 6 = 120 degrees

An exterior angle is the supplement of an interior angle, which means it is the angle that when added to the interior angle, will equal 180 degrees.

So, exterior angle = 180 - interior angle = 180 - 120 = 60 degrees.

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What are the Actual dimensions of the house(in ft)

Answers

The house's real measurements are 18 feet by 20 feet.

What do we mean by dimensions?

In everyday speech, a dimension is a measurement of an object's length, width, and height, such as a box.

The idea of dimension in mathematics is an expansion of the concepts of one-dimensional lines, two-dimensional planes, and three-dimensional space.

Examples of dimensions include width, depth, and height.

One dimension is that of a line, two dimensions are those of a square, and three dimensions are those of a cube. (3D).

So, scaling is the process of changing a figure's size to produce a picture.

Considering that a scale of 6 cm equals 12 ft.

Hence:

9 cm = 9 cm * (12 ft. per 6 cm) = 18 feet

10 cm = 10 cm * (12 ft. per 6 cm) = 20 feet

Therefore, the house's real measurements are 18 feet by 20 feet.

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Correct question:

A scale drawing of a house shows 9cm x10cm. If 6cm=12 ft, what are the actual dimensions?

7. quentin has 45 coins, all dimes and quarters. the total value of the coins is $9.15.
how many of each coin does he have?
number of dimes =
number of quarters =

Answers

Quentin has 14 dimes and 31 quarters.

Let x be the number of dimes, and y be the number of quarters. According to the problem, we have two equations: x + y = 45 (equation 1) 0.10x + 0.25y = 9.15 (equation 2)

To solve for x and y, we can use substitution or elimination method. Here, we'll use the elimination method:

Multiplying equation 1 by 0.10, we get: 0.10x + 0.10y = 4.50 (equation 3)

Subtracting equation 3 from equation 2, we get: 0.15y = 4.65, y = 31

Substituting y=31 in equation 1, we get: x + 31 = 45, x = 14

Therefore, Quentin has 14 dimes and 31 quarters.

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find the next three terms in the sequence 3/4, 1/2, 1/4, 0​

Answers

Answer:

[tex]\sf \bf \dfrac{-1}{4} \ ; \ \dfrac{-1}{2} \ ; \ \dfrac{-3}{4}[/tex]

Step-by-step explanation:

Arithmetic sequence:

     Each term in the arithmetic sequence is obtained by adding or subtracting a common number with the previous term.

To find the next three terms, we need to find the common difference.

         Common difference = second term - first term

                                            [tex]\sf = \dfrac{1}{2}-\dfrac{3}{4}\\\\=\dfrac{2-3}{4}\\\\=\dfrac{-1}{4}\\\\\\\text{Each term is obtained by adding $\dfrac{-1}{4} $ with the previous term}[/tex]

Next three terms are,

           [tex]\sf 0 + \left(\dfrac{-1}{4}\right)= 0 - \dfrac{1}{4}=\dfrac{-1}{4}\\\\\\\dfrac{-1}{4}+\left(\dfrac{-1}{4}\right)=\dfrac{-1}{4}-\dfrac{1}{4}=\dfrac{-2}{4}=\dfrac{-1}{2}\\\\\\\dfrac{-1}{2}+\left(\dfrac{-1}{4}\right)=\dfrac{-1}{2}-\dfrac{-1}{4}=\dfrac{-2-1}{4}=\dfrac{-3}{4}[/tex]

The current student population of the Brentwood student Center is 2500. The enrollment at center increases at a rate of 6% each year. To the nearest whole number, what will the student population closest to seven years?

Answers

In seven years, the student population at the Brentwood Student Center will be approximately 4,174.

Using the given terms, the current student population at the Brentwood Student Center is 2,500 and the enrollment increases at a rate of 6% each year. To find the student population closest to seven years from now, we'll use the formula for exponential growth:

Future Population = Current Population × (1 + Growth Rate)^Number of Years

In this case, the future population will be:

Future Population = 2,500 × (1 + 0.06)^7

After calculating, we get:

Future Population ≈ 4,174

So, to the nearest whole number, the student population at the Brentwood Student Center will be approximately 4,174  in seven years.

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Which of these contexts describes a situation that is an equal chance or 50-50?
A. Rolling a number between 1 and 6 (including 1 and 6) on a standard six-sided die, numbered from 1 to 6.

B. Spinning a spinner divided into four equal-sized sections colored red/green/yellow/blue and landing on yellow or blue or green.

C. Winning a raffle that sold a total of 100 tickets if you bought 50 tickets.

D. Reaching into a bag full of 5 strawberry chews and 15 cherry chews without looking and pulling out a strawberry chew. ​

Answers

option B  describes a situation that is an equal chance or 50-50

Option A describes a situation that is not 50-50 because there are six possible outcomes and only one of them is desired, so the probability of rolling a particular number is 1/6.

Option B describes a situation that is 50-50 because there are four possible outcomes and two of them are desired, so the probability of landing on a desired color is 2/4 or 1/2.

Option C does not describe a situation that is 50-50 because the probability of winning depends on the number of tickets sold and the number of tickets purchased by the individual.

Option D describes a situation that is not 50-50 because there are 5 strawberry chews and 15 cherry chews, so the probability of pulling out a strawberry chew is 5/20 or 1/4.

Therefore, the only option that describes a situation that is an equal chance or 50-50 is option B.

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The foutain in the of a park is circular with a diameter of 16 feet. There is a walk way that is 3 feet wide that goes around the fountain what is the approximate are of the walkway?

Answers

The approximate area of the walkway is 179 square feet.

To find the area of the walkway, we need to subtract the area of the inner circle (fountain) from the area of the outer circle (walkway + fountain).

The radius of the fountain is half the diameter, which is 16/2 = 8 feet.

The radius of the outer circle is the radius of the fountain + the width of the walkway, which is 8 + 3 = 11 feet.

The area of a circle is πr², where π (pi) is approximately 3.14.

So, the area of the fountain is:

π(8)² ≈ 201 square feet

And the area of the walkway plus fountain is:

π(11)² ≈ 380 square feet

To find the area of just the walkway, we subtract the area of the fountain from the area of the walkway plus fountain:

380 - 201 ≈ 179 square feet

So, the approximate area of the walkway is 179 square feet.

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. let u = <4,8>, v = <-2, 6>. find u + v. (1 point)


how to find find u+v?

Answers

The sum of vectors u  = <4,8>,and v = <-2, 6>  i.e. (u+v) is <2, 14>

To find the sum of vectors u and v (u+v), you need to perform the following steps:

1. Identify the components of vectors u and v: u = <4, 8> and v = <-2, 6>.

2. Add the corresponding components of both vectors: To find the sum (u+v), add the x-components (4 and -2) and the y-components (8 and 6) separately.

3. Calculate the sum of the x-components: 4 + (-2) = 2.

4. Calculate the sum of the y-components: 8 + 6 = 14.

5. Combine the results to form the new vector (u+v): <2, 14>.

So, the sum of vectors u and v (u+v) is <2, 14>.

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Among 130 pupils, 30 liked both biscuits and chocolates, 10 liked neither and twice as many as liked biscuits liked chocolates.
I) How pupils liked: chocolates, biscuits and exactly one of the two.

Answers

The number of pupils who liked both biscuits and chocolates is 30.

The number of pupils who liked neither biscuits nor chocolates is 10.

Let's assume that the number of pupils who liked only biscuits is x, and the number of pupils who liked only chocolates is y.

According to the problem, twice as many pupils liked chocolates as those who liked biscuits. Mathematically, we can write this as:

y = 2x

Now, let's find the total number of pupils who liked at least one of the two:

Total = P(Biscuits) + P(Chocolates) - P(Biscuits and Chocolates)

Total = x + y + 30

Total = x + 2x + 30

Total = 3x + 30

We know that the total number of pupils is 130, and the number of pupils who liked neither is 10. Therefore,

Total = P(All pupils) - P(Neither)

130 = x + y + 30 + 10

130 = x + y + 40

130 - 40 = x + y

90 = x + y

We can now solve these two equations to get the values of x and y:

3x + 30 = 90

3x = 60

x = 20

y = 2x = 40

Therefore, 20 pupils liked only biscuits, 40 pupils liked only chocolates, and 30 pupils liked both biscuits and chocolates. And, 40 pupils liked exactly one of the two.

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Christine has 5 coloured sweets in a bag. 1 of the sweets are red and 4 are green. She removes a sweet at random from the bag, notes the colour, and does not replace the sweet in the bag. She then chooses a second sweet at random. P(double green) P(Red | green) P( ∪) P(Green’)​

Answers

P(double green) = 3/20, P(Red | green) = 1/4, P(∪) = 7/20, P(Green’) = 4/5.

We ought to start by working out the probability of getting two green treats in progression:

P(double green) = P(first green) x P(second green given that the first was green)

The probability of getting a green sweet on the fundamental pick is 4/5, since there are 4 green treats out of 5 total. Beginning from the chief sweet was not superseded, there are by and by only 4 treats left dealt with, with 3 being green. Along these lines, the probability of picking a green sweet on the ensuing pick, taking into account that the first was green, is 3/4. Collecting this, we get:

P(double green) = (4/5) x (3/4) = 0.6

So the probability of getting two green sweets straight is 0.6, or 60%.

Then, we ought to sort out the probability of getting a red sweet on the ensuing pick, it was green to think about that the first:

P(Red | green) = P(Red and green)/P(green)

The probability of getting a red sweet and subsequently a green sweet is (1/5) x (4/4) = 1/5, since there is only a solitary red sweet left and every one of the four green pastries are as yet dealt with. The probability of getting a green sweet on the fundamental pick is 4/5, not entirely set in stone earlier. Collecting this, we get:

P(Red | green) = (1/5)/(4/5) = 0.2

So the probability of getting a red sweet on the resulting pick, taking into account that the first was green, is 0.2, or 20%.

By and by we ought to figure the probability of getting either two green treats in progression or a red sweet followed by a green sweet:

P( ∪) = P(double green) + P(Red and green)

We recently resolved P(double green) to be 0.6. The probability of getting a red sweet and subsequently a green sweet is 1/5, still up in the air earlier. Gathering this, we get:

P( ∪) = 0.6 + (1/5) = 0.8

So the probability of getting either two green treats in progression or a red sweet followed by a green sweet is 0.8, or 80%.

Finally, we ought to resolve the probability of not getting a green sweet on either pick:

P(Green') = P(Red and green') + P(first pick not green and second pick not green)

The probability of getting a red sweet on the principal pick and a non-green sweet on the resulting pick is (1/5) x (1/4) = 1/20, since there is only a solitary red sweet left and simply a solitary non-green sweet left after the essential pick. The probability of not getting a green sweet on the essential pick is 1/5, and the probability of not getting a green sweet on the ensuing pick, taking into account that the first was not green, is 3/4. Collecting this, we get:

P(Green') = (1/5) x (1/4) + (1/5) x (3/4) = 0.2

So the probability of not getting a green sweet on either pick is 0.2, or 20%.

In summation:

P(double green) = 0.6

P(Red | green) = 0.2

P( ∪) = 0.8

P(Green') = 0.2

Having a smaller than usual PC supportive while handling probability issues is recommended.

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Philip owns 100 shares of a stock that is trading at $97. 55 and pays an annual dividend of $2. 74. How much should he receive in quarterly dividends? What's the annual yield on this stock?

Answers

Philip should receive $68.50 in quarterly dividends and the annual yield on this stock is about 2.81%.

To calculate the quarterly dividend that Philip need to acquire, we need to first calculate the quarterly dividend per share:

Quarterly dividend in step with share = Annual dividend per percentage / 4

In this situation, the once a year dividend in line with proportion is $2.74, so the quarterly dividend per proportion is:

Quarterly dividend per proportion = $2.74 / 4 = $0.685

For the reason that Philip owns 100 shares, his quarterly dividend should be:

Quarterly dividend = Quarterly dividend per share * number of stocks

Quarterly dividend = $0.685 * 100 = $68.50

Therefore, Philip should receive $68.50 in quarterly dividends.

To calculate the once a year yield on this inventory, we want to divide the yearly dividend in line with proportion by the present day stock price, after which multiply by way of 100 to specific the result as a percentage:

Annual yield = (Annual dividend per share / inventory price) * 100

In this case, the annual dividend per percentage is $2.74, and the inventory charge is $97.55. Plugging those values into the components, we get:

Annual yield = ($2.74 / $97.55) * 100

Annual yield ≈ 2.81%

Therefore, the annual yield on this stock is about 2.81%.

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The volume of a box in the shape of a
rectangular prism can be represented by
the polynomial 8x² + 44x + 48, where x is
a measure in centimeters. Which of these
measures might represent the dimensions
of the box?

Answers

The possible dimensions of the rectangular prism are (2x + 3) cm, (x + 4) cm, and 4 cm, or (2x + 3) cm, 4 cm, and (x + 4) cm, where x is a measure in centimeters.

The polynomial 8x² + 44x + 48 represents the volume of a rectangular prism in cubic centimeters, where x is a measure in centimeters.

To find the possible dimensions of the box, we need to factor the polynomial into three factors that represent the length, width, and height of the rectangular prism.

First, we can factor out the greatest common factor of the polynomial, which is 4:

8x² + 44x + 48 = 4(2x² + 11x + 12)

Next, we can factor the quadratic expression inside the parentheses:

2x² + 11x + 12 = (2x + 3)(x + 4)

Therefore, the polynomial can be factored as:

8x² + 44x + 48 = 4(2x + 3)(x + 4)

This means that the dimensions of the rectangular prism could be (2x + 3), (x + 4), and 4, where x is a measure in centimeters. Alternatively, the dimensions could be (2x + 3), 4, and (x + 4).

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Ifj is inversely related to the cube of k, and j = 3 when k is 6, which of the following is another possible value for j and K?
(A) j = 18, k = 2
(B) j=6, k = 3
(C) j=81, k = 2
(D) j = 2, k = 81
(E) j = 3, k=2

Answers

Another possible value for j and K is (A) j = 18, k = 2

How to determine the values

Note that in inverse variation, one of the variables increases while the other decreases.

From the information given, we have that;

j is inversely related to the cube of k,

This is represented as;

j ∝ 1/k³

Now, find the constant of variation

K = jk³

Substitute the vales

K = 3 × 6³

find the cube value

K = 648

Then, we have that;

j = 648 / 2³ = 81

For option B:

j = 648 / 3³ = 24

For option C:

j = 648 / 2³ = 81

For option D:

j = 648 / 81³ = 0.0008

For option E:

j = 648 / 2³ = 81

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Question 11(Multiple Choice Worth 2 points) (Line of Fit MC) A scatter plot is shown on the coordinate plane. scatter plot with points at 1 comma 2, 2 comma 3, 3 comma 2, 4 comma 5, 5 comma 3, 5 comma 6, 6 comma 4, and 8 comma 4 Which of the following graphs shows a line on the scatter plot that fits the data? scatter plot with points at 1 comma 2, 2 comma 3, 3 comma 2, 4 comma 5, 5 comma 3, 5 comma 6, 6 comma 4, and 8 comma 4, with a line passing through the coordinates 1 comma 2 and 2 comma 3 scatter plot with points at 1 comma 2, 2 comma 3, 3 comma 2, 4 comma 5, 5 comma 3, 5 comma 6, 6 comma 4, and 8 comma 4, with a line passing through the coordinates 1 comma 2 and 8 comma 4 scatter plot with points at 1 comma 2, 2 comma 3, 3 comma 2, 4 comma 5, 5 comma 3, 5 comma 6, 6 comma 4, and 8 comma 4, with a line passing close through the coordinates at about 2 comma 3 and 8 comma 5 scatter plot with points at 1 comma 2, 2 comma 3, 3 comma 2, 4 comma 5, 5 comma 3, 5 comma 6, 6 comma 4, and 8 comma 4, with a line passing through the coordinates 1 comma 3 and a half and 2 comma 3 and a half

Answers

A graph that shows a line on the scatter plot that fits the data include the following: B. scatter plot with points at 1 comma 2, 2 comma 3, 3 comma 2, 4 comma 5, 5 comma 3, 5 comma 6, 6 comma 4, and 8 comma 4, with a line passing through the coordinates 1 comma 2 and 8 comma 4.

What are the characteristics of a line of best fit?

In Mathematics and Geometry, there are different characteristics that are used for determining the line of best fit on a scatter plot and these include the following:

The line should be very close to the data points as much as possible.The number of data points that are above the line should be equal to the number of data points that are below the line.

By critically observing the scatter plot using the aforementioned characteristics, we can reasonably and logically deduce that line B represents the line of best fit because the data points are in a linear pattern.

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