If a ball is thrown in the air with a velocity 44 ft/s, its height in feet t seconds lateris given by y = 44t -16t2. (a) Find the average velocity for thetime period beginning when t = 2 and lasting 0.5second. ft/s(b) Find the average velocity for the time period beginning whent = 2 and lasting 0.1 second. ft/s(c) Find the average velocity for the time period beginning whent = 2 and lasting 0.05 second. ft/s(d) Find the average velocity for the time period beginning whent = 2 and lasting 0.01 second. ft/s(e) Estimate the instantaneous velocity when t = 2.

Answer:

Her brother has 33 video games

Step-by-step explanation:

You take 15 plus 18 because hailey has 15 stuffed animals and her brother has 18 more video games then she has animals so you add 15+ 18 to get your final answer of 33 video games

The number of video games Hailey brother is having will be equal to 93.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the information given in the question,

Stuffed animals = 5 × dolls    (i)

Video games = 18 + stuffed animals      (ii)

Total number of dolls Hailey has is 15

Then, put this in equation (i)

Stuffed animals = 5 × 15

= 75

Now, put 75 in equation (ii)

Video games = 18 + 75

= 93

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Answer:

  CN = 7

Step-by-step explanation:

In the attached figure, we have drawn line CD parallel to AB with D a point on line MK. We know ΔMNT ~ ΔDCT by AA similarity, and because of the given angle congruence, both are isosceles with CD = CT. Likewise, we know ΔCDK is congruent to ΔBMK by AAS congruence, since BK = CK (given).

Then CD = BM (CPCTC). Drawing line NE creates isosceles ΔNEC ~ ΔTDC and makes CE = AB. Because ΔNEC is isosceles, CN = CE = AB = 7.

The length of segment CN is 7.

_____

If you assume CN is constant, regardless of the location of point N (which it is), then you can locate point N at B. That also collocates points T and K and makes ΔBMK both isosceles and similar to ΔBAC. Then CN=AB=7.

Answer:

  4 1/5 gallons per minute

Step-by-step explanation:

Divide gallons by minutes.

  (9 4/5 gal)/(2 1/3 min) = (49/5 gal)/(7/3 min) = (49/5)(3/7) gal/min

  = 21/5 gal/min = 4 1/5 gal/min

Answer:

length 8 feet and width 8 feet

Step-by-step explanation:

Lets x  be the length and width of the sheet

An open box is to be constructed from a square piece of sheet metal by removing a square of side 2 feet from each corner

so height is 2 feet

length of the box is x-4 feet

width of the box is also x-4 feet

Volume of the box is length times width times height

[tex]V= (x-4)(x-4)2[/tex]

[tex]32=2 (x-4)^2[/tex]

divide both sides by 2

[tex]16=(x-4)^2[/tex]

take square root on both sides

[tex]4=x-4[/tex]

Add 4 on both sides

[tex]x=8[/tex]

So dimension of the sheet is

length 8 feet and width 8 feet

Answer:

  29

Step-by-step explanation:

Let c, r, g stand for the current ages of Carolina, Raul, and Ginny. Then we have the relations ...

  c = 2r

  g = 3r +4

  c + r + g = 52

Substituting for c and g, we get ...

  2r + r + (3r +4) = 52

  6r = 48 . . . . . . . . . . . . . subtract 4

  r = 8 . . . . . . . . . . . . . . . divide by 8

  g = 3(8) +4 = 28 . . . . . .Ginny is presently 28

On Ginny's next birthday, she will be 29.

Answer: Ginny would be 29 years old on her next birthday.

Step-by-step explanation:

Let c represent Carolina's current age.

Let r represent Raul's current age.

Let g represent Ginny's current age.

Carolina is twice as old as Raul. It means that

c = 2r

Ginny is the oldest and is three times Raul's age plus four. It means that

g = 3r + 4

Their ages add up to be 52. It means that

c + r + g = 52 - - - - - - - - - - - - 1

Substituting

c = 2r and g = 3r + 4 into equation 1, it becomes

2r + r + 3r + 4 = 52

6r + 4 = 52

6r = 52 - 4 = 48

r = 48/6 = 8

c = 2r = 2 × 8

c = 16

g = 3r + 4 = 3 × 8 + 4

g = 24 + 4 = 28

On Ginny's next birthday, she would be 28 + 1 = 29 years old

Final answer:

Billy and Ken both ran 1/4 of the training course before it started raining, making the distance they ran identical; neither ran further than the other.

Explanation:

Comparison of Distances Run by Billy and Ken

To determine which cross-country star, Billy or Ken, ran the furthest, we need to calculate the fractions of the total distance each one ran. Firstly, we'll look at Billy. Billy intended to run 3/4 of the course and finished 1/3 of his planned run. Therefore, the actual distance Billy ran is (3/4) × (1/3).

Now, for Ken. Ken planned to run 1/2 of the course and completed 1/2 of his intended distance. Hence, Ken's actual distance is (1/2) × (1/2). Calculating both distances:

Billy's distance: (3/4) × (1/3) = 1/4

Ken's distance: (1/2) × (1/2) = 1/4

Both Billy and Ken ran 1/4 of the total training course, hence they ran the same distance before it started raining. Therefore, neither ran further than the other.

Answer:

Reflection over the x-axis and translation 4 units left

Step-by-step explanation:

Answer:

10.6 feet

Step-by-step explanation:

Length = 22ft

width= 14ft

Maximum area = 800 sq. ft

Let X be increase in the number of feet for the length and width.

The new length = (22 + x) ft

New width= (14 + x) ft

Area = (22+x)(14+x) ≤ 800

308 + 36x + x^2 ≤ 800

x^2 + 36x + 308 - 800 ≤ 0

x^2 + 36x - 492 ≤ 0

Solve using quadratic equation

x = (-b +/- √b^2 - 4ac) / 2a

a= 1, b = 36, c= 492

x = (-36 +/- √36^2 - 4*1*-492)/ 2*1

= (-36 +/- √1396 + 1968) / 2

= (-36 +/- √3264) / 2

= (-36 +/- 57.13) / 2

x = (-36 + 57.13)/2 or (-36 - 57.13)/2

x = 21.13/2 or -93.13/2

x = 10.6 or -31.0

x = 10.6 ft

The length and width must increase by 10.6 ft each

The number of whole feet by which the length and width of the deck can be increased would be calculated by setting up and solving an equation taking into account the original dimensions and maximum allowed area for the deck.

The question is asking to find by how many whole feet the length and width of the rectangular deck can be increased, given a maximum area limit set by the building code. Let's suppose x is the number of feet by which both the length and width are to be increased. Given that the original area of the deck is 14 feet by 22 feet (which gives an area of 308 square feet), the new dimensions would be (14 + x) feet by (22 + x) feet.

According to the building code, the maximum area allowed for the deck is 800 square feet. We can write and solve the following equation to find x: (14 + x) * (22 + x) = 800.

Solving this equation would yield the maximum integral number of feet each dimension can be increased while still not exceeding the allowed 800 square feet.

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The hockey player must score 20 goals in order to make the same money as the first contract

Solution:

Given that, hockey player is offered two options for a contract

Let "x" be the number of goals made

A base salary of 50,000 and 1000 per goal

Therefore, money earned is given as:

Money earned = 50000 + 1000(number of goals)

Money earned = 50000 + 1000x ------- eqn 1

Base salary of 40,000 and 1500 per goal

Therefore, money earned is given as:

Money earned = 40000 + 1500(number of goals)

Money earned = 40000 + 1500x --------- eqn 2

In order to make the same money as the other contract, eqn 1 must be equal to eqn 2

50000 + 1000x = 40000 + 1500x

1500x - 1000x = 50000 - 40000

500x = 10000  

x = 20

Thus he must score 20 goals in order to make the same money as the first contract

Answer: the population in 2005 is

199393207

Step-by-step explanation:

The formula for exponential growth which is expressed as

A = P(1 + r/n)^ nt

Where

A represents the population after t years.

n represents the periodic interval at which growth is recorded.

t represents the number of years.

P represents the initial population.

r represents rate of growth.

From the information given,

P = 173 million

A = 178 million

t = 1997 - 1995 = 2 years

n = 1

Therefore

178 × 10^6 = 173 × 10^6(1 + r/1)^2 × 1

178 × 10^6/173 × 10^6 = (1 + r)^2

1.0289 = (1 + r)^2

Taking square root of both sides, it becomes

√1.0289 = √(1 + r)^2

1 + r = 1.0143

r = 1.0143 - 1 = 0.0143

Therefore, in 2005,

t = 2005 - 1995 = 10

A = 173 × 10^6(1 + 0.0143)^10

A = 173 × 10^6(1.0143)^10

A = 199393207

Answer:

YES!!!

Step-by-step explanation:

Answer:

Your answer is going to be C

Step-by-step explanation:

So, when it is on the top, your X will always be first and you can see it is not in the negatives. When it is on the bottom Y is first and you can see it is in the negatives.

Answer:Kathy is correct

Step-by-step explanation: We need to solve both equations separately in order to determine with certainty which one is correct and which one is not.

Kevin thinks the new equation should be

3(6x-1) + 2y = 43

This can now be solved as follows;

18x - 3 + 2y = 43

Add 3 to both sides of the equation

18x - 3 + 3 + 2y = 43 + 3

18x + 2y = 46

2(9x + y) = 46 (factorize the left hand side of the equation by 2)

Divide both sides of the equation by 2

9x + y = 46

The variables remain unsolved

On the other hand, Kathy thinks the new equation should be

3x + 2(6x - 1) = 43

This can now be solved as follows;

3x + 12x - 2 = 43

Collect like terms (in this equation, x)

15x - 2 = 43

Add 2 to both sides of the equation

15x - 2 + 2 = 43 + 2

15x = 45

Divide both sides of the equation by 15

x = 3

In essence, Kathy's equation has a solution (x=3) while that of Kevin remains unsolved

Final answer:

Neither Kevin nor Katy's equations are correct in the context of solving a system of linear equations, as they do not logically combine the given equations correctly.

Explanation:

The question revolves around which sibling is correct in forming a new equation to solve a system of linear equations. To determine this, we need to see which sibling correctly used the properties of equality to combine or manipulate equations. Kevin's equation, 3(6x-1)+2y=43, is an attempt to modify an existing equation by distributing a 3. Katy's equation, 3x+2(6x-1)=43, seems to combine different parts of the given equations.

Upon closer inspection, neither Kevin nor Katy is entirely correct because their proposed equations do not logically follow from the given set. To solve for a system of equations, we would typically add, subtract, multiply, or divide entire equations by constants or variables to eliminate one variable, so we can solve for the other.

Answer:12cm

Step-by-step explanation:

The ratio are:

4:6:9

Perimeter=57cm

Let a be the unknown value.

The triangle has three sides: 4a, 6a, 9a

Perimeter=The sum of three sides

57=4a + 6a +9a

57=19a

Divide both side by 19

a=57/19

a=3

Therefore

4a:6a:9a

4×3:6×3:9×3

12:18:27

So the shortest side is 12cm

Final answer:

The shortest side of the triangle is found by setting up the sides as a proportion with a common multiplier and using the given perimeter to solve for it. Upon finding the multiplier, we multiply it by the smallest ratio to find the shortest side, which is 12 cm.

Explanation:

To solve for the length of the shortest side of the triangle, we should initially set up the ratio of the sides as 4x:6x:9x, where x is the common multiplier for each side of the triangle. Since the perimeter of the triangle is given as 57 cm, we can write the equation 4x + 6x + 9x = 57 to represent the sum of the sides of the triangle. This simplifies to 19x = 57, and by dividing both sides of the equation by 19, we find that x = 3. Therefore, the shortest side of the triangle, represented by 4x, will be 4 × 3 = 12 cm.

Answer:

  -5, multiplicity 3; +9, multiplicity 2; -1

Step-by-step explanation:

The roots of f(x) are those values of x that make the factors be zero. For a factor of x-a, the root is x=a, because a-a=0. If the factor appears n times, then the root has multiplicity n.

f(x) = (x+5)^3(x-9)^2(x+1) has roots ...

Answer:

a. -5 with multiplicity 3

d. 9 with multiplicity 2

f.  -1 with multiplicity 1

Step-by-step explanation:

edge

the answer is (-2,0)

Answer:

  C.  x = -4

Step-by-step explanation:

Graphing calculators make solving a problem like this very easy. The two functions both have the value -1 at x = -4.

The solution to f(x) = g(x) is x = -4.

The dimensions of lake are length 1.5 miles and width 0.3 miles

Solution:

Given that,

Artificial lake is in the shape of a rectangle

Let the length of lake be "a"

The width of the lake is 1/5 the length of the lake

[tex]width = \frac{length}{5}\\\\width = \frac{a}{5}[/tex]

The area of lake is 9/20 square miles

The area of rectangle is given by formula:

[tex]Area = length \times width[/tex]

Substituting the values we get,

[tex]\frac{9}{20} = a \times \frac{a}{5}\\\\a^2 = \frac{9}{20} \times 5\\\\a^2 = \frac{9}{4}\\\\\text{Taking square root on both sides }\\\\a = \frac{3}{2} = 1.5[/tex]

Thus, we get

[tex]length = a = 1.5 \text{ miles }\\\\width = \frac{a}{5} = \frac{1.5}{5} = 0.3 \text{ miles }[/tex]

Thus the dimensions of lake are length 1.5 miles and width 0.3 miles

Answer:

Step-by-step explanation:

If p and w represent the speeds of the plane and wind, respectively, the speed into the wind is ...

  p - w = (3000 mi)/(6 h) = 500 mi/h

And, the speed with the wind is ...

  p + w = (3000 mi)/(5 h) = 600 mi/h

Adding these two equations gives us ...

  2p = 1100 mi/h

  p = 550 mi/h . . . . . . . divide by 2

Then the wind speed is ...

  w = 600 mi/h - p = (600 -550) mi/h

  w = 50 mi/h

The rate of the plane in still air is 550 mi/h; the rate of the wind is 50 mi/h.

Answer:

Step-by-step explanation:

let speed of plane in still air =x

speed of wind=y

(x-y)6=3000

x-y=3000/6=500   ...(1)

(x+y)5=3000

x+y=3000/5=600   ...(2)

adding (1) and (2)

2x=1100

x=1100/2=550

550 +y=600

y=600-550=50

speed of plane in still air=550 m/hr

speed of wind=50 m/hr

Answer:

[tex]25t+19\leq 144[/tex]

[tex]t\leq5[/tex]

The number of minutes she can continue to descend if she does not want to reach a point more than 144 feet below the ocean surface is at most 5 minutes.

Step-by-step explanation:

Given:

Initial depth of the scuba dive = 19 ft

Rate of descent = 25 ft/min

Maximum depth to be reached = 144 ft

Now, after 't' minutes, the depth reached by the scuba dive is equal to the sum of the initial depth and the depth covered in 't' minutes moving at the given rate.

Framing in equation form, we get:

Total depth = Initial Depth + Rate of descent × Time

Total depth = [tex]19+25t[/tex]

Now, as per question, the total depth should not be more than 144 feet. So,

[tex]\textrm{Total depth}\leq 144\ ft\\\\19+25t\leq 144\\\\or\ 25t+19\leq 144[/tex]

Solving the above inequality for time 't', we get:

[tex]25t+19\leq 144\\\\25t\leq 144-19\\\\25t\leq 125\\\\t\leq \frac{125}{25}\\\\t\leq 5\ min[/tex]

Therefore, the number of minutes she can continue to descend if she does not want to reach a point more than 144 feet below the ocean surface is at most 5 minutes.

Answer:

  8

Step-by-step explanation:

We assume there are 2 bushings per bolt, and 2 bolts per spring. Whether you count springs and multiply by 2, or count bushings and divide by 2, you get 8 eyebolts.

_____

Comment on the question

There are conceivable mechanical arrangements in which the number of eyebolts might be some other number. There is not actually enough information here to properly answer the question.

To replace all the bushings in a Jeep YJ, a total of 8 leaf spring eyebolts would be required considering each spring uses two eyebolts.

To be able to replace all the bushings in your Jeep YJ's leaf springs, you need to first establish how many leaf spring eyebolts you will need. In a standard leaf spring setup, each end of the spring (both front and back) is held in place by a leaf spring eyebolt. Since you have 4 springs and each spring uses 2 leaf spring eyebolts (one for the front leaf spring eye and one for the back), you'll require a total of 8 leaf spring eyebolts for your Jeep YJ.

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Answer:

Step-by-step explanation:

Total area = Dining space + Kitchen and Storage space

Dining space = 90 multiplied by 20 = 1800 square feet

Kitchen and Storage space = 1/3 of Total area

Total area = 1800 + 1/3 of Total area

(1-1/3) Total area = 1800

2/3 Total area = 1800

Total area = 3*1800/2 = 2700

Kitchen and Storage space = 2700*1/3 = 900 square feet

Answer:

54 minutes

Step-by-step explanation:

From the question, we are given;

We are required to determine the time taken to exchange the air in the room;

First we are going to determine the volume of the room;

Volume of the room = length × width × height

                                  = 5.2 m × 4.3 m × 2.9 m

                                  = 64.844 m³

Then we should know, that 1 m³ = 1000 L

Therefore, we can convert the volume of the room into L

= 64.844 m³ × 1000 L

= 64,844 L

But, the rate is 1200 L/min

Thus, time = Volume ÷ rate

                  = 64,844 L ÷ 1200 L/min

                   = 54.0367 minutes

                   = 54 minutes

Therefore, it would take approximately 54 minutes

Answer:

P = ₁₅C₀ (0.76)¹⁵ + ₁₅C₁ (0.24)¹ (0.76)¹⁴ + ₁₅C₂ (0.24)² (0.76)¹³

Step-by-step explanation:

Binomial probability:

P = nCr pʳ qⁿ⁻ʳ

where n is the number of trials,

r is the number of successes,

p is the probability of success,

and q is the probability of failure (1−p).

Here, n = 15, p = 0.24, and q = 0.76.

We want to find the probability when r is at most 2, which means r = 0, r = 1, and r = 2.

P = ₁₅C₀ (0.24)⁰ (0.76)¹⁵⁻⁰ + ₁₅C₁ (0.24)¹ (0.76)¹⁵⁻¹ + ₁₅C₂ (0.24)² (0.76)¹⁵⁻²

P = ₁₅C₀ (0.76)¹⁵ + ₁₅C₁ (0.24)¹ (0.76)¹⁴ + ₁₅C₂ (0.24)² (0.76)¹³

The correct answer is When P = ₁₅C₀ (0.76)¹⁵ + ₁₅C₁ (0.24)¹ (0.76)¹⁴ + ₁₅C₂ (0.24)² (0.76)¹³

                     P = nCr pʳ qⁿ⁻ʳ

                    So that Here, n = 15, p = 0.24, and q = 0.76.

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Answer:

17/24

Step-by-step explanation:

11/8 becomes 33/24

2/3 becomes 16/24

(33-16)/24 = 17/24

Answer:

The answer to your question is  250 - 20 < 80 + 15x

Step-by-step explanation:

Data

Beth  has 250 books and sells 20 each week

Martin has 80 books and sells 15 each week

week = x

Process

1.- Write an equation for each situation

Beth         250 - 20x            

Martin       80 + 15 x

2.- Write the inequality

                   250 - 20 < 80 + 15x

Answer: a) 0.0001, b) 0.0081.

Step-by-step explanation:

Since we have given that

Probability that a person will make a mistake on their state income tax return = 0.1

Probability that a person will not make any mistake = [tex]1-0.1=0.9[/tex]

Since the events are independent.

So, (a) four totally unrelated persons each make a mistake;

Our probability becomes,

[tex]P(A\cap B\cap C\cap D)=P(A)\times P(B)\times P(C)\times P(D)\\\\=0.1\times 0.1\times 0.1\times 0.1\\\\=0.0001[/tex]

(b) Mr. Jones and Ms. Clark both make mistakes, and Mr. Roberts and Ms. Williams do not make a mistake.

So, our probability becomes,

[tex]P(A\cap B\cap C'\cap D')=P(A)\times P(B)\times P(C')\times P(D')\\\\=0.1\times 0.1\times 0.9\times 0.9\\\\=0.0081[/tex]

Hence, a) 0.0001, b) 0.0081.

Final answer:

The probability that four unrelated persons each make a mistake on their tax returns is 0.0001. The probability that Mr. Jones and Ms. Clark both make mistakes, while Mr. Roberts and Ms. Williams do not, is 0.0081, calculated by multiplying the individual probabilities of each event.

Explanation:

The probability of independent events occurring simultaneously is calculated by multiplying the probabilities of each individual event. For part (a), we need to find the probability that four totally unrelated persons each make a mistake on their tax returns. Since the probability of one person making a mistake is 0.1, and the events are independent, we multiply this probability four times.

Probability (four unrelated persons each make a mistake) = 0.1x0.1x0.1x0.1 = 0.0001

For part (b), we are looking for the probability that Mr. Jones and Ms. Clark both make mistakes, while Mr. Roberts and Ms. Williams do not make mistakes. The probability of making a mistake is 0.1 and not making a mistake is 0.9 (which is 1 - 0.1).

Probability (Jones and Clark make mistakes, Roberts and Williams do not) = 0.1x0.1x0.9x0.9 = 0.0081

Answer:

  about $525,900

Step-by-step explanation:

Each year, the value is multiplied by (1 +4%) = 1.04. After 20 years, it will have been multiplied by that value 20 times. That multiplier is 1.04^20 ≈ 2.19112314.

The value of the house in 20 years will be about ...

  $240,000×2.19112314 ≈ $525,900 . . . . . rounded to hundreds

Answer: it would be worth $52587 in 20 years.

Step-by-step explanation:

If the value of the house increases at a rate of 4% per year, then the rate is exponential. We would apply the formula for exponential growth which is expressed as

A = P(1 + r/n)^ nt

Where

A represents the value of the house after t years.

n represents the period of increase.

t represents the number of years.

P represents the initial value of the house.

r represents rate of increase.

From the information given,

P = $24000

r = 4% = 4/100 = 0.04

n = 1 year

t = 20 years

Therefore

A = 24000(1 + 0.04/1)^1 × 20

A = 24000(1.04)^20

A = $52587

Answer:

The rider is 15.91  seconds  50 ft above the ground after reaching the low point

Step-by-step explanation:

We can evaluate the angle  α

using trigonometry applied to the orange small triangle with height 50-30 = 20 ft and  hypotenuse equal to the radius  r = 25ft

Now

[tex]20 = \frac{25}{sin(\alpha)}[/tex]

[tex]\alpha = arcsin{\frac{20}{25}[/tex]

[tex]\alpha = 53.13^{\circ}[/tex]

So  50 ft  of height corresponds to the total angle:

[tex]90^{\circ} =53.13^{\circ} = 143.13 6^{\circ}[/tex]  = 2.498 radians

Now the angular velocity

[tex]\omega = \frac{2\pi}{T}[/tex]

[tex]\omega = \frac{2 \pi}{40}[/tex]

[tex]\omega =0.157rad/s[/tex]

To describe  2.498  rad  it will take:

[tex]t = \frac{2.498}{0.157}[/tex]

t = 15.91 s

The rider reaches 50 feet above the ground approximately 4.09 seconds after reaching the lowest point.

To solve the problem of determining how long after reaching the low point a rider on the Ferris wheel is 50 feet above the ground, we can follow these steps:

Step 1: Define the parameters

Diameter of the Ferris wheel: 50 feet.

Radius of the Ferris wheel: [tex]\( r = \frac{50}{2} = 25 \)[/tex] feet.

Center of the wheel height: 30 feet above the ground.

Rotation period: 40 seconds per revolution.

Step 2: Establish the equation for the height of a rider

The vertical position ( h(t) ) of a rider at time ( t ) seconds can be modeled using the cosine function (assuming the lowest point at ( t = 0 ):

[tex]\[ h(t) = 30 + 25 \cos\left(\frac{2\pi t}{40}\right) \][/tex]

Step 3: Set the height equation to 50 feet

Since we want the height h(t) to be 50 feet:

[tex]\[ 50 = 30 + 25 \cos\left(\frac{2\pi t}{40}\right) \][/tex]

Step 4: Solve for the cosine term

[tex]\[ 50 = 30 + 25 \cos\left(\frac{2\pi t}{40}\right) \][/tex]

[tex]\[ 20 = 25 \cos\left(\frac{2\pi t}{40}\right) \][/tex]

[tex]\[ \cos\left(\frac{2\pi t}{40}\right) = \frac{20}{25} \][/tex]

[tex]\[ \cos\left(\frac{2\pi t}{40}\right) = 0.8 \][/tex]

Step 5: Determine the angle

[tex]\[ \frac{2\pi t}{40} = \cos^{-1}(0.8) \][/tex]

[tex]\[ \frac{2\pi t}{40} = 0.6435 \][/tex]

[tex]\[ t = \frac{0.6435 \times 40}{2\pi} \][/tex]

[tex]\[ t \approx 4.09 \text{ seconds} \][/tex]

Thus, the rider reaches 50 feet above the ground approximately 4.09 seconds after reaching the lowest point.

a. The number of 7th grade students expected to move by the end of the year is 8 students.

b. if 12 students actually moved, more 7th grade students move than expected.

how many 7th grade students are expected to move by the end of the year?

a.

Number of Students: 6th 250, 7th 200, 8th 150 Moves: 6th 2%, 7th 4%, 8th 8%

Number of 7th grade students expected to move by the end of the year = Moves × number of students

= 4% × 200

= 8 students

b.

if 12 students actually moved,

This means number of of 7th grade students expected to move by the end of the year are more.

Complete question:

How many 7th grade students are expected to move by the end of the year? If 12 students actually moved, did more or fewer 7th grade students move than expected? Justify your answer.

Number of Students: 6th 250, 7th 200, 8th 150 Moves: 6th 2%, 7th 4%, 8th 8%