Does someone mind helping me with this problem? Thank you!

Prism:
- Minimum number of faces: 5 (2 bases and 3 lateral faces)
- Minimum number of edges: 9 (3 edges on each base and 3 lateral edges)

Pyramid:
- Minimum number of faces: 4 (1 base and 3 lateral faces)
- Minimum number of edges: 6 (3 edges on the base and 3 lateral edges)

Polyhedron:
- Minimum number of faces: 4 (a tetrahedron)
- Minimum number of edges: 6 (a tetrahedron)

a. A prism is a polyhedron with two parallel congruent bases and rectangular faces connecting the bases. The minimum number of faces for a prism is 5: two bases and three rectangular faces. The minimum number of edges for a prism is 9: three edges connecting each vertex of one base to the corresponding vertex of the other base, and six edges connecting the vertices of the rectangular faces to the vertices of the bases.

b. A pyramid is a polyhedron with a polygonal base and triangular faces connecting the base to a common vertex. The minimum number of faces for a pyramid is 4: one polygonal base and three triangular faces. The minimum number of edges for a pyramid is 6: one edge for each side of the polygonal base, and three edges connecting each vertex of the base to the common vertex.

c. A polyhedron is a three-dimensional shape with flat faces and straight edges. The minimum number of faces and edges for a polyhedron depends on the specific shape, and there is no general formula to determine the minimum values. For example, a tetrahedron has 4 triangular faces and 6 edges, while a cube has 6 square faces and 12 edges. The minimum number of faces and edges for a polyhedron can be calculated by examining the shape and its properties, such as symmetry and number of vertices.

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The argument for the dilation is that: No, in order for one figure to be dilated of another, both coordinates of all points must be multiplied by the same constant

The complete question is added as an attachment

From the attached table of values, we can see that:

The coordinates of x are multiplied by 3, while the coordinates of y are multiplied by 6

This means that

The figure is not properly dilated, because these coordinates must be multiplied by the same constant value

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Dr. Bills Payable A/C 5,400 and Cr. Bank A/C 5,400

In the books of Brown:

Dr. Bank A/C 6,000

Cr. Bills Receivable A/C 6,000


On 3.2.2011:

Dr. Bills Receivable A/C 5,400

Cr. Bank A/C 5,400


On the due date:

Dr. Bills Receivable A/C 5,400

Cr. Black A/C 5,400


In the books of Black:

Dr. Bills Payable A/C 5,400

Cr. Bank A/C 5,400

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Step-by-step explanation:

3.

the sum of all internal angles in a quadrilateral is always 360°.

so, the internal angle at x is given by

360 = 40 + 80 + 110 + inner angle

inner angle = 360 - 40 - 80 - 110 = 130°

an inner and an outer angle combined are together always 180°.

so,

130 + x = 180

x = 50°

4.

first, again, the sum of all inner angles is 360°.

this is a parallelogram. that means the diagonally opposing angles are equal.

so, the angle opposite of the 38° angle is also 38°.

that leaves

360 - 38 - 38 = 284°

for the 2 (again equal) remaining angles :

284 = 2 × angle

each of these remaining angles is then

284/2 = 142°

the angle JML is one of them.

so,

angle JML = 142°

Check the picture below.

we have three sides, let's look at the two smaller sides first, 1.9 and 2.7.

if we move the sides closer and ever closer to each other, to the extent that one is right on top of the other, what is the length of the red side?  Well, assuming the two smaller sides are one pancaked on top of the other, the red side will be as long as 2.7 - 1.9 = 0.8.  However, the sides can't be on top of each other, because if that's so, we have a flat-line, and thus we wouldn't have a triangle.  So whatever the third side may be, it must be greater than 0.8.

Now, if we move the sides away from each other, farther and farther to the extent that one is parallel to the other, then the third side will just be as long as 1.9 + 2.7 = 4.6.  However, we can't do that, because if that were to happen, we again will have a flat-line and not a triangle.  So whatever the third side may be, it must be less than 4.6, it can't be 4.6.

So no dice.

The values of the variables in the kite are:

x = 50°

y = 58°

z = 32°

Since a kite is symmetrical. Thus, it has two opposite and equal angles

Also, the line of symmetry divides the kite angle into equal angles and similar triangles. We have:

In ΔABO:

x + 90° + 40° = 180° (angle sum in a triangle)

x + 130 = 180

x = 180 - 130

x = 50°

In ΔBCO:

y + 90° + 32° = 180° (angle sum in a triangle)

y = 180 - 122

y = 58°

In ΔCDO:

z = 32°  (congruent triangles)

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Answer:

See below.

Step-by-step explanation:

I'm sure the question is asking to solve for ∠BDC, but we'll solve for all of the angles.

We should note that we have a Given Exterior Angle.

An Exterior Angle is an angle that is formed by extended lines.

An exterior angle is equal to the combined sum of the two nonadjacent, and interior angles.

Using what we learned, ∠BCD and ∠CDB will equal ∠DBE°.

Let's turn this problem into an equation.

60° + ∠BDC = 120°
Subtract 60 from both sides.

∠BDC = 60°.

We can also identify that ∠CBD is a linear pair with ∠DBE.

A Linear Pair is 2 adjacent angles that add up to 180°. Linear Pairs are straight lines with one line intersecting in between.

Meaning that ∠CBD + ∠DBE = 180°.

∠CBD + 120° = 180°.

∠CBD = 60°.

We can identify that this triangle is an Equilateral Triangle. An Equilateral  Triangles is a triangle that has all congruent sides and angles.

Our final answers are;

∠BDC = 60°.

∠CBD = 60°.

The correct answer is (i) and (ii). Both of the sets are subspaces of R3 because they satisfy the three criteria of a subspace. The first set, {(x,y,z)| z = (x+y)2}, is a set of all triplets (x,y,z) such that z = (x+y)2. The second set, {(x,y,z)| x=10z}, is a set of all triplets (x,y,z) such that x = 10z. Neither of the other choices are correct.

Cylinder B is taller which is 3.45 inches more than cylinder A.    

A cylinder is a three-dimensional geometric shape that consists of two parallel circular bases that are connected by a curved surface.

The formula for the volume of a cylinder is given by  

Where V is the volume of the cylinder, r is the radius of the circular base of the cylinder, and h is the height of the cylinder.

Here we have

Two cylinders have the same volume of 845π cubic inches.  

The radius of Cylinder A is 13 inches

Let 'h₁' be the height of th cylinder

By using the formula, V = π r² h₁

Volume of the cylinder A = π (13)² h₁ = 169πh₁

From the data, 169πh₁ = 845π

=> 169h₁ = 845

=> h₁ = 845/169

=> h₁ =  5  

The radius of Cylinder B is 10 inches.

Let h₂ be the height

Volume of the Cylinder B = π (10)² h₂ = 100πh₂  

From the data, 100πh₂ = 845π  

=> 100h₂ = 845

=> h₂ = 8.45

The difference between the heights of the two cylinders

= 8.45 inch - 5 inch = 3.45 inch  

Therefore,

Cylinder B is taller which is 3.45 inches more than cylinder A.  

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Step-by-step explanation:

Refer to pic...............

The value of x in the given figure of parallel lines is x = 0.89.

When two parallel lines are sliced by a transversal, alternating interior angles and alternate exterior angles result in the shape "Z".

From the figure we observe that according to alternate interior angle, the angle adjacent to x + 94 is 95x.

Thus, the two angles form a straight line.

The angle of a straight line is 180 degrees.

Thus,

x + 94 + 95x = 180

96x + 94 = 180

x = 0.89

Hence, the value of x in the given figure of parallel lines is x = 0.89.

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The simplified expression is [tex](z^{(16))}(y^{(12))}/(100663296)(x^{(8))}[/tex].

To simplify the expression ((4x^(2)z^(-4))/(20y^(-3)))^(-4) using the properties of exponents, we need to follow the steps below:

1. First, we need to distribute the exponent of -4 to each term inside the parentheses. This will give us:

(4^(-4))(x^(2*-4))(z^(-4*-4))/(20^(-4))(y^(-3*-4))

2. Next, we need to simplify the exponents by multiplying them. This will give us:

[tex](4^(-4))(x^(-8))(z^(16))/(20^(-4))(y^(12))[/tex]

3. Now, we need to simplify the terms with negative exponents by moving them to the opposite side of the fraction. This will give us:

[tex](z^(16))(y^(12))/(4^(4))(x^(8))(20^(4))[/tex]

4. Finally, we need to simplify the terms with the same base by adding their exponents. This will give us:
[tex](z^(16))(y^(12))/(4^(4))(x^(8))(2^(8))(5^(8))[/tex]

5. We can further simplify the expression by simplifying the terms with the same base. This will give us:

(z^(16))(y^(12))/(16^(2))(x^(8))(2^(8))(5^(8))

6. Now, we can combine the terms with the same base to get our final answer:

(z^(16))(y^(12))/(256)(x^(8))(256)(390625)

7. Our final answer is:

(z^(16))(y^(12))/(100663296)(x^(8))

Therefore, the simplified expression is (z^(16))(y^(12))/(100663296)(x^(8)).

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The height in meters is 1.73 meters (rounded to two decimal places), the weight in other unit (kg) approximately 92.1 kg.The distance ran is approximately 546 meters

The distance you have run is 597 yards. To convert yards to meters, we can use the conversion factor 1 yard = 0.9144 meters. Therefore, the distance you have run in meters is approximately 546 meters (rounded to the nearest meter).

Your weight is currently expressed in pounds (lbs). To express your weight in other units, we can use conversion factors. For example, your weight in kilograms (kg) can be found by multiplying your weight in pounds by 0.453592. Using this conversion, your weight would be approximately 92.1 kg (rounded to one decimal place). Alternatively, your weight in stones (st) can be found by dividing your weight in pounds by 14. Using this conversion, your weight would be approximately 14.5 st (rounded to one decimal place).

Therefore, the hieght, weight and distance ran are 1.73 meters,  92.1 kg and 546 meters respectively.

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The question is :

What is the height in meters and how many meters has he run, and in what unit could you express his weight, for someone who is 5 ft 8 in tall and weighs 203 lbs and ran a distance of 597 yards ?

The 90% confidence interval for the mean test score of the students is (81.06, 83.74), which means that we can be 90% confident that the true mean test score of the population is between 81.06 and 83.74.

a) What is the sample? (5 points)

The sample is the set of A students sitting in the front row who stated their latest test scores.

b) What is the population? (5 points)

The population is the entire class of 105 students who took the test.

c) What is the variable of interest? (5 points)

The variable of interest is the mean test score of the students.

d) Do you think that the sample is representative of the population? Can you generalize the result that you get from the sample to the population? Why? Why not? Discuss (5 points).

The sample may or may not be representative of the population. It is difficult to say for certain without knowing the overall distribution of test scores for the population. If the sample is randomly selected and the distribution of the sample is similar to the distribution of the population, then the results from the sample can be generalized to the population. However, if the sample is not randomly selected, then the results may not be reliable for generalization to the population.

e) Suppose that the sample mean is 82.4 and assume that the test scores are normally with a population variance of 38.2. Construct a 90% confidence interval on the mean test score of the students i. Write the appropriate formula. (5 points)

The appropriate formula for a 90% confidence interval is:
Mean ± (1.645 * (Standard Error of the Mean))

ii. Find the necessary table value. (5 points)

The necessary table value is 1.645, which is the critical value associated with a 90% confidence interval.

iii. Substitute the quantities into your formula. (5 points)

Mean ± (1.645 * (Standard Error of the Mean))

82.4 ± (1.645 * (Standard Error of the Mean))

iv. Calculate the confidence interval. (10 points)

Standard Error of the Mean = (Population Variance/Sample Size)0.5

Standard Error of the Mean = (38.2/105)0.5

Standard Error of the Mean = 0.8244


Confidence Interval = 82.4 ± (1.645 * 0.8244)

Confidence Interval = 82.4 ± 1.34

Confidence Interval = (81.06, 83.74)

v. Interpret your interval. (5 points)

The 90% confidence interval for the mean test score of the students is (81.06, 83.74), which means that we can be 90% confident that the true mean test score of the population is between 81.06 and 83.74.

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The average percentage change in population from 2000-20009 is 1.36%.

A figure or ratio stated as a fraction of 100 is called a percentage. Frequently, it is indicated with the per cent sign, "%". If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage, therefore, refers to a component per hundred. Per 100 is what the word per cent means. As there is no unit of measurement for percentages, they are dimensionless numbers. This is because we divide numbers with the same units in percentage calculation.

a) Average percentage change

= Sum of percentage change in each year/number of years

= (1.97+1.71+1.65+1.42+1.22+1.02+1.07+1.22+0.93) / 9

= 1.36%

Therefore the average percentage change in population from 2000-20009 is 1.36%.

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The areas of section 1, 2 and 3 are  8 inches square, 80 inches square and 8 inches square respectively.

The area of the trapezium is 96 inches square.

Section 1 and 2 are right triangles.

Area of a right triangle = 1/2 x base x height

Height = 8cm

Base = (14 - 10) / 2 = 2cm

Area of a right triangle = 1/2 x 2 x 8 = 8cm²

Section 3 is a rectangle.

Area of a rectangle = length x width

8 x 10 = 80 cm²

A trapezoid is a convex quadrilateral. A trapezoid has at least on pair of parallel sides. the parallel sides are called bases while the non parallel sides are called legs

Area of a trapezoid =   1/2 x (sum of the lengths of the parallel sides) x height

= 1/2 x (10 + 14) x 8

1/2 x 24 x 8 = 96cm²

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Answer:

57,600 if talking about hundreds. If talking about hundredths, 57.61

Answer:

57600

Step-by-step explanation:

nearest hundred (100)

614 is closer to 600

from 651 it becomes near 700 therefore the answer becomes 57600

a) U is subspace of R^3.

b) The set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) 2.

a) To show that U is a subspace of R^3, we need to verify the following three conditions:

i) The zero vector (0, 0, 0) is in U.

ii) U is closed under addition.

iii) U is closed under scalar multiplication.

i) The zero vector is in U since 0 + 2(0) - 3(0) = 0.

ii) Let (x1, y1, z1) and (x2, y2, z2) be two vectors in U. Then we have:

x1 + 2y1 - 3z1 = 0 (by definition of U)

x2 + 2y2 - 3z2 = 0 (by definition of U)

Adding these two equations, we get:

(x1 + x2) + 2(y1 + y2) - 3(z1 + z2) = 0

which shows that the sum (x1 + x2, y1 + y2, z1 + z2) is also in U. Therefore, U is closed under addition.

iii) Let (x, y, z) be a vector in U, and let c be a scalar. Then we have:

x + 2y - 3z = 0 (by definition of U)

Multiplying both sides of this equation by c, we get:

cx + 2cy - 3cz = 0

which shows that the vector (cx, cy, cz) is also in U. Therefore, U is closed under scalar multiplication.

Since U satisfies all three conditions, it is a subspace of R^3.

b) To find a basis for U, we can start by setting z = t (where t is an arbitrary parameter), and then solving for x and y in terms of t. From the equation x + 2y - 3z = 0, we have:

x = 3z - 2y

y = (x - 3z)/2

Substituting z = t into these equations, we get:

x = 3t - 2y

y = (x - 3t)/2

Now, we can express any vector in U as a linear combination of two vectors of the form (3, -2, 0) and (0, 1/2, 1), since:

(x, y, z) = x(3, -2, 0) + y(0, 1/2, 1) = (3x, -2x + (1/2)y, y + z)

Therefore, the set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) Since the basis for U has two elements, the dimension of U is 2.

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The probability for the bear visits using Poisson process of rate one visits per month is given by ,

P(X=i, Y=j) j=i                            j=2i                                        j=3i

X=i              e^(-1)(1/ i!) × 1/3^i 1/3^i + 4/3^(i-1) × e^(-1)/i!     2/3^i× e^(-1)/i!

Bear visits form a Poisson process of rate 1 visit per month.

Number of visits in a month  = Poisson distribution with parameter λ = 1.

Let X be the number of visits in a month.

And Y be the total number of bears in the month.

Probability of X and Y is equal to ,

P(X = i, Y = j), for i = 0, 1, 2, 3 and j = i, 2i, or 3i.

Law of total probability for  P(X = i, Y = j) for each i and j.

P(X = i, Y = i)

= P(X = i) × P(Y = i | X = i)

= e^(-λ) × λ^i / i! × 1/3^i

= e^(-1) × 1^i / i! × 1/3^i

= e^(-1) (1/ i!) × 1/3^i

Now,

P(X = i, Y = 2i)

= P(X = i) × P(Y = 2i | X = i)

= e^(-λ) × ( λ^i / i!) ×  [(1/3)^i + 2(1/3)^(i-1)(2/3)]

= e^(-1) / i! × [1/3^i + 4/3^i-1]

For,

P(X = i, Y = 3i)

= P(X = i) × P(Y = 3i | X = i)

= e^(-λ) × λ^i / i! × (1/3)^i × 2

= 2e^(-1) / i! × 1/3^i

Therefore, the probability of the size of bears for given condition is equal to,

P(X=i, Y=j) j=i                            j=2i                                        j=3i

X=i              e^(-1)(1/ i!) × 1/3^i 1/3^i + 4/3^(i-1) × e^(-1)/i!     2/3^i× e^(-1)/i!

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The given question is incomplete, I answer the question in general according to my knowledge:

A village in Alaska is sometimes visited by polar bears. In fact, bear visits form a Poisson process of rate 1 visits per month. At each visit a group of bears shows up; the size of a group is equal to 1,2, or 3 with equal opportunity. Find the probability for each size.

After evaluating using the correct order of operations, the result will become 22/9.

The correct order of operations is to perform any calculations inside parentheses first, then exponents, then multiplication and division from left to right, and finally addition and subtraction from left to right. This order of operations is known as PEMDAS. Using this order, we can evaluate the expression as follows:

(17)/(18) + (6)/(35) ÷ (5)/(7) x (25)/(4)

Divide 6/35 by 5/7 by multiplying 6/35 by the reciprocal of 5/7.
= (17/18) + (6/35) x (7/5) x (25/4)
= (17/18) + (6/25) x (25/4)

Multiply 6/25 by 25/4.
= (17/18) + (6/4)

Finally, add 17/18 and 6/4 together.
= 22/9

Therefore, the final answer is 22/9,

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A. The amount of aspirin in the dose is 22.066 milligrams.

B. ƒ (60) = 7.483 milligrams
This means that 60 hours after ingesting a dose of 22.066 milligrams of aspirin, the amount of aspirin in the person's blood will be 7.483 milligrams.

C. The aspirin level will be less than 10 milligrams after approximately 45.06 hours.

a. The initial amount of aspirin in the dose can be found by evaluating f(0):

f(0) = 300 * (1/2)^(1/30) ≈ 22.066

Therefore, there are approximately 22.066 milligrams of aspirin in the dose.

b. We can find f(60) by substituting t = 60 into the equation:

f(60) = 300 * (1/2)^(1/30 * 60) ≈ 7.483

Therefore, there are approximately 7.483 milligrams of aspirin in the person's blood 60 hours after ingesting the dose. This is significantly less than the initial amount of 22.066 milligrams, indicating that the aspirin is being metabolized and eliminated from the body over time.

c. We want to solve for t when f(t) < 10:

300 * (1/2)^(1/30t) < 10

Dividing both sides by 300:

(1/2)^(1/30t) < 1/30

Taking the natural logarithm of both sides:

ln[(1/2)^(1/30t)] < ln(1/30)

Using the properties of logarithms:

(1/30t)ln(1/2) < ln(1/30)

Simplifying:

-0.6931t < ln(1/30)

Dividing both sides by -0.6931 (which is ln(1/2)):

t > ln(1/30) / (-0.6931)

t > 45.06

Therefore, the aspirin level will be less than 10 milligrams after approximately 45.06 hours.

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Answer:

232.5 units²

Step-by-step explanation:

Quadrilateral QRST would become a Rhombus if all the conditions discussed below are fulfilled.  

What is a Rhombus?

Rhombuses are a particular sort of quadrilateral in Euclidean geometry. It is a unique instance of a parallelogram in which the diagonals meet at a 90-degree angle and all sides are equal. This is a rhombus' fundamental characteristic. A rhombus has a diamond-shaped form. As a result, it is also known as a diamond.

Given QRST Quadrilateral.

In order to be Rhombus, these conditions must fulfill:

1. all sides are equal i.e. QT=TS=SR=RQ

2. Diagonals meet at 90-degree i.e. ∠11 = ∠10=∠9=∠12 = 90°

3. Diagonals bisect the angles of a rhombus i.e. ∠6=∠7, ∠5=∠4, ∠3=∠2 and ∠8=∠1.

4. Opposite angles are equal.

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To make a parallelogram a rhombus, make its sides equal, angles should be 90° and diagonals should be equal.

What is a parallelogram?

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.

A parallelogram becomes a rhombus if and only if all four sides are congruent, which means they have the same length.

Therefore, to make the parallelogram QRST a rhombus, we need to ensure that all four sides are of equal length.

This can be achieved by satisfying any of the following conditions -

All four sides have the same length.

The diagonals of the parallelogram are perpendicular bisectors of each other.

In other words, they meet at right angles and divide each other into equal halves.

The diagonals of the parallelogram have equal length.

Therefore, if we can make sure that any of these three conditions are true for the parallelogram QRST, then we can make it a rhombus.

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After comparing the image and the figure, we found that the direction and angle of rotation are 180° counterclockwise rotation.

A transformation known as a rotation involves turning the figure either clockwise or counterclockwise. The centre of rotation is the fixed location where the rotation occurs. The term "angle of rotation" refers to the amount of rotation. A figure can be rotated 90 degrees, or a quarter turn, in either a clockwise or counterclockwise direction.

You have rotated the figure 180 degrees when you have spun it exactly halfway. The figurine may be rotated 360° by turning it all the way around. A counterclockwise turn has a positive magnitude because a clockwise rotation indicates a negative magnitude. Rotational symmetry exists in every regular polygon. When an object is rotated around its centre, it retains its original appearance. The object is then referred regarded as having rotational symmetry.

Let's write the coordinates of the original figure,

A = (1, -5)

B = (6, -2)

C = (6, -5)

D = (1, -8)

Now, if we rotate it 90 degrees counterclockwise, the coordinates are:

A' = ( 5, 1)

B' = (2, 6)

C' = (5, 6)

D' = (8, 1)

Now if we rotate it again 90 degrees counterclockwise, the coordinates are:

A'' = ( -1, 5)

B'' = (-6, 2)

C'' = (-6, 5)

D'' = (-1, 8)

Now from the figure, let's write the coordinates.

A' = ( -1, 5)

B' =  (-6, 2)

C' = (-6, 5)

D' =  (-1, 8)

This is the same as the coordinates of the second 90 degrees counterclockwise rotation.

Since we did two 90 degrees rotations, we can say we did a total of 180° counterclockwise rotation.

Therefore after comparing the image and the figure, we found that the direction and angle of rotation are 180° counterclockwise rotation.

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The expression which represents t as the subject of the formula is; t = (p + 4s) / √(s (3s - p)).

As evident in the task content; it follows that the expression which represents t as the subject of the formula is to be determined.

Given; ( (p + 4s) / t )² = s (3s - p)

(p + 4s) / t = √(s (3s - p))

t = (p + 4s) / √(s (3s - p))

Ultimately, the correct expression is; t = (p + 4s) / √(s (3s - p)).

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It takes approximately0.082 seconds for the eraser to hit the student in the head.

The equation that models the flight of the eraser is h(t)=-16t^(2)+35t+6. We need to find the time it takes for the eraser to hit the student's head, which is 3 feet off the ground. This means that we need to solve the equation h(t)=3 for t.

First, we will set h(t) equal to 3 and rearrange the equation:

-16t^(2)+35t+6=3

Next, we will subtract 3 from both sides of the equation and simplify:
-16t^(2)+35t+3=0

Now, we will use the quadratic formula to solve for t:
t= (-35±√(35^(2)-4(-16)(3)))/(2(-16))

Simplifying further, we get:
t= (-35±√(1417))/(-32)

Using a calculator, we can find the approximate values of t:
t≈0.082 or t≈2.27

Since we are looking for the time it takes for the eraser to hit the student's head, we will choose the larger value of t, which is 0.082.

Therefore, it takes approximately0.082 seconds for the eraser to hit the student in the head.

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Formula explicitly = n² + 2 n, where n is a full number and the first 5 numbers of the sequence would be 4, 8, 12, 20, and 24.

Let 4,8,12,20,24 be the sequence's first five terms.

Let me define the terms explicit formula and recursive formula.

The generic formula to find any term in a series is known as the explicit formula.

Also, if we know the (n-1)th term of the series, we can use the recursive formula to find the nth term.

Thus, the sequence's explicit formula is,

Y equals 4 n, where n is any positive integer.

And this is the recursive formula.

Y = 4 (n-1), and we can find the nth term by using the (n-1)th term.

Initial term = 4 = 4 1

Term two = 8 = 4 2

Term three =12=43

Fourteenth term = 16 = 4 4

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(n-1) th term =4 × (n-1)

nth term =4 × n

The universal and recursive formula is obtained by applying the straightforward technique of examining the first, second, and direction of the next term.

You stated that you did not desire a simpler sequence.

Think about the sequence's first five terms: 0, 3,8, 15, and 24.

Well stated formula =n2 + 2 n

Recursive equation: (n-1)

²+2(n-1)

If you examine the sequence, neither geometry nor arithmetic applies.

First term =0=0²+0×0

Second term =3=1+2=1²+2 × 1

Third term =8=4+4=2²+2×2

Fourth term =15=9+6=3²+2×3

Fifth term =24=16 +8=4²+2×4

In the explicit formula, n is a whole number and n²+2n.

Therefore, the formula explicitly = n² + 2 n, where n is a full number and the first 5 numbers of the sequence would be 4, 8, 12, 20, and 24.

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Using point-slope form, the coordinate of D(2, X) is 2 units away from point X(1, 1).

To find the coordinates of point D, we need to know the location of point X on the line YZ. We can use the slope-intercept form of the equation of a line to find the equation of the line passing through points Y and Z:

slope m = (y2 - y1) / (x2 - x1) = (0 - 2) / (3 - 2) = -2

Using the point-slope form of the equation of a line with point Y(2, 2) and slope m = -2:

y - y1 = m(x - x1)

y - 2 = -2(x - 2)

y - 2 = -2x + 4

y = -2x + 6

Now we can substitute x = 2 into the equation of the line to find the y-coordinate of point D:

y = -2x + 6

y = -2(2) + 6

y = 2

Therefore, the coordinates of point D are (2, 2).

So, D(2, 2) is the point that lies on line YZ and is 2 units away from point X(1, 1).

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Answer: A

Step-by-step explanation:

You can prove it by Pythagorean's Theorem, a² + b² = c²

3² + 4² = 5²

9 + 16 = 25

25 = 25

It has to be a right triangle.