Jasmine asked her classmates to name all the types of trees they found while on a field trip at a local park.

1/7 reported finding a birch tree.
7/9 reported finding a pine tree.
1/4 reported finding a maple tree.
11/23 reported finding an oak tree.

Based on the results, which statements are true? (Pick all that apply)

A. Most students found a pine tree.
B. More students found a maple tree than a pine tree.
C. More students found a birch tree than an oak tree.
D. More students found a pine tree than a birch tree.
E. More students found a maple tree than an oak tree.

According to the information, we know that the term 125x^5y^4 appears in the expansion when n = 6 and the coefficient of x^6y^7 in the expansion is zero, and the x^6y^7 term does not appear in the expansion.

We know that the binomial expansion of (x-y)^n is given by the formula:

where nCk represents the binomial coefficient "n choose k".

We are given that the term 125x^5y^4 appears in the expansion, so we can set up an equation using the binomial coefficient for that term:

Simplifying this equation, we get:

We can solve for n by finding the smallest value of n for which nC5 is greater than or equal to 125. We can use the formula for binomial coefficients:

to calculate the values of nCk for different values of n and k. However, it is easier to use Pascal's triangle to find the binomial coefficients quickly. The fifth row of Pascal's triangle is:

We see that the sixth term of this row is 10C5 = 252, which is greater than 125. Therefore, we know that the term 125x^5y^4 appears in the expansion when n = 6.

To find the x^6y^7 term in the expansion, we need to find the coefficient of x^6y^7 in the expansion. We can use the same formula as before, but with k = 7 instead of k = 5:

We can simplify this expression using the fact that (-1)^7 = -1:

We want to find the value of this expression, so we need to find the value of n. We know that n = 6 because the term 125x^5y^4 appears in the expansion. Therefore, we can substitute n = 6 into the expression:

We see that 6C7 is zero because we cannot choose 7 items from a set of 6. Therefore, the coefficient of x^6y^7 in the expansion is zero, and the x^6y^7 term does not appear in the expansion.

To find the x^7y^2 term in the expansion, we can use the same formula as before, but with k = 2:

We can simplify this expression using the fact that (-1)^2 = 1:

We want to find the value of this expression, so we need to find the value of n. We know that n = 6 because the term 125x^5y^4 appears in the expansion. Therefore, we can substitute n = 6 into the expression:

We can use Pascal's triangle to find that 6C2 = 15. Therefore, the coefficient of x^7y^2 in the expansion is 15, and the x^7y^2 term appears in the expansion as:

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One per 2,500 can be used to represent the rate of 80cm to 2km.

To write 80cm to 2km as a rate, we need to convert the units to the same system. We can convert 80cm to kilometers by dividing by 100,000 (since there are 100,000 centimeters in a kilometer):

80 cm/100,000 = 0.0008 km

Now we can express the rate as:

0.0008 km per 2 km

Or we can simplify it by dividing both the numerator and denominator by 0.0008:

1 per 2,500

Therefore, 80cm to 2km can be expressed as a rate of 1 per 2,500.

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Answer:

p=42

Step-by-step explanation:

S=104 sm^2

a=8 sm

S=a*b

104 sm^2=8*b

b=104 sm^2/8 sm=13 sm

P=2*(a+b)=2*(13 sm+8 sm)=42 sm

The requried quantity of drug that remains in the body, in the long run, is 220 mg.

Let's denote the amount of drug in the body just before taking the nth tablet by [tex]D_n[/tex]. We know that [tex]D_0 = 0[/tex](since the patient hasn't taken any tablets yet) and that 5% of the drug is present in the body just before taking a tablet remains in the body. Therefore, we can write:

[tex]D_1 = 110\\D_2 = 0.95 * D_1 + 110 = 203.5\\D_3 = 0.95 * D_2 + 110 = 292.225\\D_4 = 0.95 * D_3 + 110 = 376.81375[/tex]

We can see that the formula for [tex]D_n[/tex] is:

[tex]D_n = 110 * (1 - 0.05)^n + 110 * (1 - (1 - 0.05)^n) / 0.05[/tex]

Simplifying this formula, we get:

[tex]D_n = 220 * (1 - 0.95^n)[/tex]

Now, we want to find the amount of drug that remains in the body in the long run. This means we want to find the limit of [tex]D_n[/tex]  as n goes to infinity. Using the formula above, we can see that:

[tex]lim_ {n- > oo} D_n = lim_ {n- > oo} 220 * (1 - 0.95^n) = 220[/tex]

Therefore, the quantity of drug that remains in the body, in the long run, is 220 mg.

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Answer:

  (d)  25 feet and 20 feet​

Step-by-step explanation:

You want the possible dimensions of a pool with an area of 500 square feet and a perimeter of 90 feet.

The area is the product of the length and width. The area of the pools offered in the answer choices are ...

  (a)  15·30 = 450 . . . square feet

  (b)  10·35 = 350 . . . square feet

  (c)  50·10 = 500 . . . square feet

  (d)  25·20 = 500 . . . square feet

The area requirement eliminates answer choices A and B.

The perimeter is twice the sum of length and width. The perimeters of the possible pools are ...

  (c) 2(50 +10) = 120 . . . feet

  (d) 2(25 +20) = 90 . . . feet

The perimeter requirement eliminates answer choice C.

The pool's possible length and width are 25 feet and 20 feet, choice D.

__

Additional comment

You could write a quadratic equation for the pool dimensions, but doing that will generally involve more work than checking the given answer choices.

If x is the width, then 45-x is the length, and the area is ...

  x(45 -x) = 500

  x² -45x +506.25 = -500 +506.25 . . . multiply by -1, complete the square

  x = 22.5 -√6.25 = 20 . . . . take the square root; width is the smaller dimension

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Let [tex]x[/tex] be the unknown side of the triangle. Find the length of this side from the Pythagorean Theorem;

Another root of the equation is also negative, but we've eliminated it because length can't be a negative value.

To find the area of a triangle, we multiply the height of the triangle by the base length and take half.

Answer:

1. 90

2. 468

Step-by-step explanation:

Answer:

Question 1). 45 in

Question 2). 234 m

Step-by-step explanation:

Area = base x height x 1/2

10 x 9 = 90

90 x 1/2 = 45

Question 2)

30 x 15.6 = 468

468 x 1/2 = 234 m

Answer:

5.4

Step-by-step explanation:

square of 29 = 5.385164807

5.385164807 estimated is 5.4

The area of the rhombus who has a base of 8 cm and a height of 4.2 cm is 33.6 centimeters².

The measurement of the size of a two-dimensional shape or surface is referred to as an area.

It is the area contained within the perimeter of a flat or two-dimensional object and is expressed in square units like square centimetres, square metres, square feet, etc.

For instance, to find the area of a rectangle, multiply its length by width, and to find the area of a circle, multiply pi () by the radius square.

area of rhombus can be found as-

Area = (base x height) / 2

In this case, the base is 8 cm and the height is 4.2 cm, so we can substitute these values into the formula:

Area = (8 cm x 4.2 cm) / 2

Area = 33.6 cm²

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Check the picture below.

The depreciation expense for each year is 1,000,000 shs.

Accumulated depreciation up to year 6 is 6,000,000 shs.

The depreciation using the straight line method is given by the formula:

Depreciation expense per year = (Initial cost - Salvage value) / Useful life

Initial cost = 5,000,000 + 800,000 + 1,500,000 = 7,300,000 shs.

Salvage value = 1,300,000 shs.

Depreciation expense per year = (7,300,000 - 1,300,000) / 6

                                                    = 6,000,000 / 6

                                                    = 1,000,000 shs.

Thus, the depreciation expense for each year is 1,000,000 shs.

Accumulated depreciation up to year 6 = Depreciation expense per year * Number of years

Accumulated depreciation up to year 6 = 1,000,000 * 6 = 6,000,000 shs.

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The correct option -D. 5;  Thus, the value of x for the given external secant segment and the tangent on the circle is found as:x = 5.

A line that precisely intersects a circle at two points is said to be a secant.

The size of the angle created when two tangents, two secants, or two tangents cross outside of a circle is equal to one-half a positive difference between the sizes of the intercepted arcs.

Using the Theorem:

The square of a length of tangent is equal the the product of such external secant segment and the overall length of the secant if one secant and one tangent both drawn to a circle from a single exterior point:

4(4 + x) = 6²

16 + 4x = 36

4x = 36 - 16

4x = 20

x = 20/4

x = 5

Thus, the value of x for the given external secant segment and the tangent on the circle is found as:x = 5.

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In a a case whereby factory that has 6 X 10³ workers makes 2.4 X 105 products each day, the average amount of products made per worker is 4 *10^1 products per worker

The term "average" in mathematics typically refers to a measure of central tendency, which is a way to describe the typical or common value in a set of numbers. There are several types of averages.

We can calculate the required value as

( 2.4 X 10^5 )/ (6 X 10³)

=4 *10^1 products per worker

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Answer:

1/8

Step-by-step explanation:

If "over" refers to (4 * 6) as a whole,

[tex]\frac{3}{4*6}\\\\=\frac{3}{24}\\\\=\frac{1}{8}[/tex]

If "over" refers to division,

[tex]3 \div 4 \times 6\\= 0.75 \times 6\\= 4.5[/tex]

I would suppose it's the first one, so, ignore the second one if you haven't learnt BODMAS yet.

Hope this helps and be sure to mark this as brainliest! :)

Using the total area of the rectangular pool we know that the required width of the pathway is 3.6 ft respectively.

In the Euclidean plane, a rectangle is a quadrilateral with four right angles.

A parallelogram with a right angle or an equiangular quadrilateral, where equiangular means that all of its angles are equal, are other ways to define it.

A rectangle with four equal-length sides is a square.

Squares are not always rectangles, but rectangles are always squares.

So, the pool and walkway together have a 360 square foot total space.

Assume that the walkway is w feet in width.

Since the pool has an additional w feet of width on both sides, the total area's measurements can be expressed as (8 + 2w) by (10 + 2w).

Thus, we can construct the following equation:

(8 + 2w) x (10 + 2w) = 360

By enlarging and condensing the left side, we obtain:

4w² + 36w - 80 = 0

Using the quadratic formula, we can find w:

w = (-b ± √(b² - 4ac)) / 2a

Here, an equals 4, b equals 36, and c equals -80. When these values are added to the formula, we obtain:

w = (-36 ± √(36² - 4(4)(-80))) / 8

w = (-36 ± √(1872)) / 8

w ≈ -5.6 or w ≈ 3.6

We can ignore the first option because the width cannot be negative. Consequently, the pathway should be around 3.6 feet wide.

Therefore, using the total area of the rectangular pool we know that the required width of the pathway is 3.6 ft respectively.

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The coordinates of the vertices of the image rectangle M'P'A'T' are:

M'(2,1), P'(3,1), A'(3,3), T'(2,3).

What is rectangle?

A rectangle is a geometric shape that has four sides and four right angles (90 degrees) with opposite sides being parallel and equal in length.

To find the coordinates of the vertices of the image rectangle M'P'A'T', we need to apply a transformation to each vertex of the original rectangle MPAT.

We can see that the original rectangle MPAT has sides parallel to the x and y-axes, which suggests that it is aligned with the coordinate axes. We can also see that the length of its sides are equal, which means it is a square.

To transform this square, we can use a combination of translations, rotations, and reflections. However, since we don't have any information about the type of transformation that is being applied, we can assume that the simplest transformation is a reflection across the line y=x.

To reflect a point (x,y) across the line y=x, we swap its x and y coordinates to get the reflected point (y,x). Therefore, the coordinates of the vertices of the image rectangle M'P'A'T' are:

M'(2,1)

P'(3,1)

A'(3,3)

T'(2,3)

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The area of given trapezoid whose parallel sides are 8 inches, 16 inches & its perpendicular height is 6 inches is 72 inches².

What is a trapezoid?

Quadrilaterals or four-sided polygons with one pair of parallel sides and one pair of non-parallel sides are known as trapezoids, usually spelt trapezium. It has a perimeter and covers a certain amount of space. The bases of the trapezium are the sides that are parallel to one another. Legs or lateral sides indicates to the non-parallel sides. The altitude or perpendicular height is the separation between the parallel sides. This shape's area is equal to half of the product of its parallel sides times its height.

Given dimensions of trapezoid:

let parallel sides be denoted by a , b & height be 'h'

a= 8 inches (top side)

b= 8+4+4=16 inches (bottom side)

h= 6 inches

Area = [tex]\frac{sum of parallel sides}{2}[/tex] x height

         =[tex]\frac{(a+b)h}{2}[/tex]

         =[tex]\frac{(8+16)6}{2}[/tex]

          =[tex]\frac{24(6)}{2}[/tex]

          =24 x 3

          =72 sq. inches

The area of given trapezoid is 72 inches²

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Answer:

33 thats with the 1 dollar subtracted for the entry fee

Step-by-step explanation:

first you add all the number of marbles you have then you get 41 then divide it by 12 because you have 2 gold and 10 silver and you get 3.4 and multiply that by 10 because its 6 and 4 and you get 34 subtract the entry fee

Answer: 18

Step-by-step explanation:

Answer:

Step-by-step explanation:

9e-7 = 7e-11

add 7 to both side

9e-7 =7e-11

   +7        +7

9e=7e-4

subtract 7e from both sides

9e = 7e-4

-7e  -7e

2e = -4

divide both sides by 2

e = -2

Answer:

1629.24m

Step-by-step explanation:

starting with the easy ones

1) Rectangle 1:

Surface area of rectangle=Length x width

SAR= 24x21

= 504m

2) Rectangle 2:

SAR= 19x21

=399

3) Rectangle 3

SAR= 21x8

=168

4) Rectangle 4:

SAR= 21x11

=231

*because the top and bottom are trapeziums the formular for it is

A=1/2(a+b)h

although those trapeziums don't have h(Height)

it needs to be broken down into two triangles and a rectangle. to find the height*

5) side/height of triangle A:

formula: C squared= a squared + b squared

in this case we already have C and A. meaning we have to rearrange the formula to:

x = c^2 - a^2

x = 8^2 - 2.5^2

x = sqrt 57.75

x = 7.61

6) Trapezium

SA= 1/2(a+b)h

SA= 1/2(19+24)7.61

=163.62

7) add all surface area together

which should equal 1629.24m

The statement is discussing Proposition 3.5, which provides a strategy or method for finding the subgroups of any finite group.

The strategy involves listing all the cyclic subgroups first. Then, subgroups with two generators can be found by taking the union of two cyclic subgroups and considering inverses. Subgroups with three generators can be found by taking the union of a subgroup with two generators and a cyclic subgroup, and so on.

The statement also mentions that if the group is not too large, this strategy can quickly yield all subgroups. Additionally, it suggests making use of Lagrange's theorem (Corollary 3.14) to further aid in finding the subgroups.

This process can be repeated to find all subgroups of the given finite group. The statement also suggests that using Lagrange's theorem (specifically, Corollary 3.14) can help in efficiently finding all the subgroups, especially if the group is not too large.

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What meaning of the statement this?

Proposition 3.5 provides a strategy for finding the subgroups of any given finite group. First list all cyclic subgroups. Subgroups with two generators are also generated by the union of two cyclic subgroups (which is closed under inverses). Subgroups with three generators are also generated by the union of a subgroup with two generators and a cyclic subgroup; and so forth. If the group is not too large this quickly yields all subgroups, particularly if one makes use of Lagrange's theorem (Corollary 3.14 below).

The appropriate measurement unit for force is  kg.m/s²

A force is simply referred to as either a push or pull of an object resulting from the object's interaction with another object.

From Newton's Second Law, force is expressed as;

F = m × a

Where is mass of object and a is the acceleration

One Newton is defined as the force required to accelerate a mass of one kilogram at a rate of one meter per second squared.

Since F = m × a

Plug in m = kg and a = m/s²

F = kg × m/s²

F = kg.m/s²

Therefore, the unit of measurement is kg.m/s².

Option B is the correct answer.

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If a researcher is standing in a corner (point c) of a triangle plot. the angle to point a is S76E .  the distance between point A and point B is 210 ft.

To find the distance between points A and B, we can use the Law of Cosines. Let's first label the angles of the triangle:

   Angle ACB = 180 - (76 + 32) = 72 degrees

   Angle BAC = 76 degrees

   Angle ABC = 32 degrees

Using the Law of Cosines, we have:

AB^2 = AC^2 + BC^2 - 2(AC)(BC)cos(ACB)

where;

AB is the distance between points A and B

AC is the distance between points A and C (210 ft

BC is the distance between points B and C (150 ft)

ACB is the angle between AC and BC (72 degrees)

Plugging in the values, we get:

AB^2 = 210^2 + 150^2 - 2(210)(150)cos(72)

AB^2 = 44100

AB = sqrt(44100)

AB = 210 ft

Therefore, the distance between point A and point B is 210 ft.

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a) The angular velocity = 0.4π rad/s b) The linear velocity of the hamster = 4π cm/s.

Linear velocity is the rate of change of an object's position with respect to time. It measures how fast an object is moving in a straight line, and is often expressed in units of distance per time, such as meters per second or kilometers per hour.

a) The angular velocity of the wheel can be calculated as follows:

Angular velocity = (2π * number of revolutions) / time

Here, the wheel completes one revolution in 5 seconds, so the number of revolutions is 1 and the time is 5 seconds. Therefore,

Angular velocity = (2π * 1) / 5

Angular velocity = 0.4π rad/s (or approximately 1.26 rad/s)

b) The linear velocity of the hamster can be calculated as follows:

Linear velocity = radius * angular velocity

Here, the radius of the wheel is 10 cm, and the angular velocity we found in part (a) is 0.4π rad/s. Therefore,

Linear velocity = 10 cm * 0.4π rad/s

Linear velocity = 4π cm/s (or approximately 12.57 cm/s)

So the hamster is running at a linear velocity of approximately 12.57 cm/s.

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Answer:

$60

Step-by-step explanation:

In a set of data, the median is the value that is placed in the middle. to find the median, we must order the numbers from least to greatest, like so:

20, 40, 40, 50, 60, 60, 60, 60, 70, 70

Using this representation, we find that there are two numbers in the middle: 60 and 60 (since the amount of data is an even number, there will be two numbers in the center).

When something like this occurs, find the average of the two numbers in the middle (and the values and divide by the number of values). We have:

60 + 60 = 120;

[tex]\frac{120}{2} = 60[/tex]

Therefore, the median is $60.

Answer:

Trapezoid

Step-by-step explanation:

It's a quadrilateral and it only has one pair of parallel sides.

In the given right triangle, by using the Pythagorean theorem, the value of x is 5√2 and the value of y is 5√2

From the question, we are to determine the value of x and y in the given diagram

The diagram shows a right triangle with a hypotenuse of 10.

The right is a special type of right triangle. The base angles of the triangle are equal.

Thus,

The right triangle is an isosceles right triangle.

This means the legs of the triangle are equal.

That is,

x = y

From the Pythagorean theorem, we can write that

x² + y² = 10²

Since x = y, we can write that

x² + x² = 10²

2x² = 100

x² = 50

x = √50

x = 5√2

Hence,

y = 5√2

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Answer:

D

Step-by-step explanation:

A rotation and translation preserves the length measures of the sides, so FD is equal to 7 inches

Answer: D

Step-by-step explanation: