Select the correct answer.
Which expression is equivalent to 107-8y +3? Assume that the denominator does not equal zero.
O A. y2 (10y³ - 8y² + 3)
О в.
10³ - 8y² + 3
V
O c.
y (10y³
OD. 10²¹ - $y² +3
8y² + 3)
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The values of p and q are 1 and 3, respectively.

Given the equation x^2-4x + 1 = (x-p)- q, we can compare the coefficients of the corresponding terms on both sides of the equation.

We compared the coefficients of the x^2 terms on both sides of the equation. The coefficient of the x^2 term on the left-hand side is 1, and the coefficient of the x^2 term on the right-hand side is 1. This means that the two terms are equal, and therefore p = 1.

We compared the coefficients of the x terms on both sides of the equation. The coefficient of the x term on the left-hand side is -4, and the coefficient of the x term on the right-hand side is -1. This means that the two terms are equal, and therefore q = 3.

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The speed of the car is 108 kilometers per hour and the distance covered in 5 hours is 540 kilometers.

Speed is simply referred to as distance traveled per unit time.

It is expressed as;

Speed = Distance ÷ time.

Given that the car is traveling at a rate of 30 meters per second.

First, convert the car's speed from meters per second to kilometers per hour using the conversion factor.

1 kilometer = 1000 meters

1 hour = 3600 seconds

Hence;

Speed = 30m/s = ( 30 × 3600/1000 )kmh

Speed = 108 kmh

Next, the distance covered in 5 hours will be:

Speed = Distance / time

Distance = speed × time

Distance = 108 kmh × 5 h

Distance = 540 km

Therefore, the disatnce covered is 540 kilometers.

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Navern Corporation's manufacturing cycle efficiency (MCE) for its elevators is approximately 11.36%.

Value-added time is the time spent on activities that directly add value to the product.

Value-added time: Process time = 5 days (the process of manufacturing the elevators)

Total cycle time: Wait time + Inspection time + Process time + Move time + Queue time

= 12 days + 12 days + 5 days + 6 days + 9 days

= 44 days

MCE = (Value-added time / Total cycle time) * 100

= (5 days / 44 days) * 100

≈ 11.36%

Therefore, Navern Corporation's manufacturing cycle efficiency (MCE) for its elevators is approximately 11.36%.

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Q1- The annual depreciation for the equipment is $2,000.

Q2- The book value of the equipment at the end of Year 3 is $6,500.

Q1: What is the annual depreciation for the equipment?

To calculate the annual depreciation, we need to determine the difference between the initial value and the salvage value, and divide it by the number of years.

Initial value = $12,500

Salvage value = $2,500

Number of years = 5

Annual depreciation = (Initial value - Salvage value) / Number of years

= ($12,500 - $2,500) / 5

= $10,000 / 5

= $2,000

Therefore, the annual depreciation for the equipment is $2,000.

Q2: What is the book value of the equipment at the end of Year 3?

The book value of the equipment at the end of a specific year can be calculated by subtracting the accumulated depreciation from the initial value.

Initial value = $12,500

Annual depreciation = $2,000

Number of years = 3

Accumulated depreciation = Annual depreciation * Number of years

= $2,000 * 3

= $6,000

Book value at the end of Year 3 = Initial value - Accumulated depreciation

= $12,500 - $6,000

= $6,500

Therefore, the book value of the equipment at the end of Year 3 is $6,500.

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Answer:

If Delaware was proportional to Alabama in enrollment to the district, it would have approximately 37 districts.

The ratio of students to districts in Alabama is 630,683/137 = 4,603 students per district. If Delaware had the same ratio of students to districts, it would have 120,475/4,603 = 26.16 districts. Rounding to the nearest whole number, Delaware would have approximately 26 districts if it was proportional to Alabama in enrollment to the district.

The element of A n B is { 7, 8}

A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind.

For example, if the element of P is even numbers from 1 to 20 and element of Q is factor of 6 from 1 to 20 then we can say that set Q is a subset of set P.

The sign 'n' means intersection and this means what is common to two or more set.

If set A = { 1,2,5,7,8}

set B = { 6,7,8,9}

then we can see that 7 and 8 are common to both sides, then

A n B = { 7,8}

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Since each child buys a double scoop with 2 flavors and no two children choose the same combination, we can determine the number of children by finding the number of unique flavor combinations possible.

To calculate the number of unique flavor combinations, we can use the concept of combinations without repetition. The formula for this is given by nCr = n! / ((n-r)! * r!), where n is the total number of flavors and r is the number of flavors chosen for each double scoop.

In this case, there are 9 flavors available and each child chooses 2 flavors. Using the formula, we have:

9C2 = 9! / ((9-2)! * 2!) = 9! / (7! * 2!) = (9 * 8) / 2 = 36 / 2 = 18.

Therefore, there are 18 children in the group, as each child can choose from 18 unique flavor combinations without repetition.

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The height of the upper end of the handrail above the floor is approximately 3.467726 meters.

To calculate the height of the upper end of the handrail above the floor, we can use trigonometry and the given information about the length of the handrail and the angle of inclination.

Let's break down the problem into two right triangles:

The first right triangle is formed by the handrail, the floor, and a vertical line connecting the lower end of the handrail to the floor. The vertical line represents the height of the lower end above the floor, which is given as 0.7m.

The second right triangle is formed by the handrail, the floor, and a horizontal line parallel to the floor, connecting the upper end of the handrail to the floor. This horizontal line represents the height we need to calculate.

Now, let's apply trigonometric ratios to find the height of the upper end of the handrail above the floor.

In the first right triangle:

Opposite side = height of the lower end = 0.7m

Hypotenuse = length of the handrail = 5.4m

Using the sine function:

sin(angle) = Opposite / Hypotenuse

sin(40°) = 0.7 / 5.4

Now, let's solve for the sin(40°):

sin(40°) ≈ 0.64279

Multiplying both sides of the equation by 5.4:

0.64279 * 5.4 ≈ 3.467726

So, the length of the vertical line in the second right triangle (representing the height of the upper end of the handrail above the floor) is approximately 3.467726 meters.

Therefore, the height of the upper end of the handrail above the floor is approximately 3.467726 meters.

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The algebra class of 14 students in the Algebra 2 class of 23 students do not play basketball or baseball.

The number of students in a certain Algebra 2 class of 23 students who play basketball and baseball is 9, given that 7 of them play basketball and 2 of them play baseball.

The number of students in the class who do not play basketball or baseball is given by the number of students who do not play basketball plus the number of students who do not play baseball and the students who do not play basketball or baseball.

However, since each student is either playing basketball or baseball or neither, we can say that the total number of students who do not play basketball or baseball is given by the number of students in the class minus the total number of students who play basketball or baseball.

Thus, the number of students who do not play basketball or baseball is given by:

23 - 9 = 14

Therefore, 14 students in the Algebra 2 class of 23 students do not play basketball or baseball.

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The solution to the system of inequalities in interval notation is [-2, 1].

Based on the information provided in the image below, we have the following system of inequalities;

-12 < 3x - 6

-3 ≥ 3x - 6

By adding 6 to both sides of the equation (inequality), we have;

-12 < 3x - 6

-12 + 6 < 3x - 6 + 6

-6 < 3x

-2 < x

x > -2 (flip)

-3 ≥ 3x - 6

-3 + 6 ≥ 3x - 6 + 6

3 ≥ 3x

1 ≥ x

x ≤ 1

Therefore, the solution to the system of inequalities is given by:

-2 < x ≤ 1

In interval notation, we have [-2, 1].

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The time taken for 1414 people to paint 14 walls is 6,430.44 minutes.

To find out how many minutes it would take 1414 people to paint 14 walls, we can use the information given to find the ratio.

We know that it takes 9 people 41 minutes to paint 9 walls.

Let's find the ratio:

(9 people) : (1414 people) = (41 minutes) : (x minutes)

Use the mutual multiplication property of the resulting ratio:

9 * x = 1414 * 41

Right simplification:

9x = 57974

To solve this problem, create a ratio using the information provided:

(9 people) : (1414 people) = (41 minutes) : (x minutes)

We can multiply the ratios:

9 * x = 1414 * 41

On the right side of the equation, calculate the product of 1414 and 41, which equals 57974.

4 444 So:

444 9x = 57974 To separate

4 share both sides of the equation with 9:

4 x = 57974/9

share both sides with 9:

4 x = 6430.44

It will take 6,430.44 minutes for 1,414 people to paint 14 walls.

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To simplify the expression (2x-3)(5x^2-2x+7), we can use the distributive property.

First, multiply 2x by each term inside the second parentheses:

2x * 5x^2 = 10x^3

2x * -2x = -4x^2

2x * 7 = 14x

Next, multiply -3 by each term inside the second parentheses:

-3 * 5x^2 = -15x^2

-3 * -2x = 6x

-3 * 7 = -21

Combine all the resulting terms:

10x^3 - 4x^2 + 14x - 15x^2 + 6x - 21

Now, combine like terms:

10x^3 - 19x^2 + 20x - 21

So, the simplified expression is 10x^3 - 19x^2 + 20x - 21.

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The triangles are congruent because of S.A.A

Congruent triangles are triangles having corresponding sides and angles to be equal. This means that for two triangles to be congruent, the corresponding angles must be equal and the corresponding sides must also be equal.

In the triangles the corresponding angles are equal.

In triangle ABC, the third angle is calculated as;

180-(90+30)

= 180-120

= 60°

I'm triangle DCE, the third angle is calculated as;

180-(90+30)

= 180-120

= 60°

Therefore the two triangles are congruent because the corresponding angles are equal.

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Answer:

The common difference in the given sequence is 5.

Step-by-step explanation:

The common difference in the sequence is 5 because they all add by 5 each time for example 5 + 5= 10 and 10+5=15

The missing coordinate in the ordered pair (5, ?) that satisfies the equation 4x - 3y = 18 is y = 2/3. Hence, the complete ordered pair is (5, 2/3).

To determine the missing coordinate in the ordered pair (5, ?) that satisfies the equation 4x - 3y = 18, we can substitute the given x-coordinate, which is 5, into the equation and solve for y.

Let's substitute x = 5 into the equation:

4(5) - 3y = 18

20 - 3y = 18

Now, we can solve for y by isolating it on one side of the equation:

-3y = 18 - 20

-3y = -2

Divide both sides of the equation by -3 to solve for y:

y = -2 / -3

y = 2/3

Therefore, the missing coordinate in the ordered pair (5, ?) that satisfies the equation 4x - 3y = 18 is y = 2/3. Hence, the complete ordered pair is (5, 2/3).

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Question

Following equation. 4x-3y=18 Determine the missing coordinate in the ordered pair (5,?) so that it will satisfy the given equation.

Therefore, BC is equal to 4 cm.

To solve this problem, we can use the Angle Bisector Theorem and the Pythagorean Theorem.

Let's start by applying the Angle Bisector Theorem. According to the theorem, the ratio of the segments of the hypotenuse formed by the altitude is equal to the ratio of the corresponding sides of the triangle.

In triangle ABC, we have:

AD/DB = AC/CB

Given that AD = 8 cm, we need to find DB. Let's denote DB as x.

8/x = AC/CB

Since AC is the altitude, it can be determined by applying the Pythagorean Theorem in right triangle ACH.

AC^2 = AH^2 + HC^2

AC^2 = (AB - BH)^2 + HC^2

AC^2 = (BC - 4)^2 + HC^2

Now, let's apply the Pythagorean Theorem in right triangle BCH.

BC^2 = BH^2 + HC^2

BC^2 = 4^2 + HC^2

Since AC = BC - 4, we can substitute these expressions into the equation:

(BC -4)^2 + HC^2 = BC^2

Expanding and simplifying this equation, we get:

BC^2 - 8BC + 16 + HC^2 = BC^2

Simplifying further, we have:

-8BC + 16 + HC^2 = 0

Now, let's substitute the value of HC = AD - AH = 8 - 4 = 4 into the equation:

-8BC + 16 + 4^2 = 0

-8BC + 16 + 16 = 0

-8BC + 32 = 0

-8BC = -32

BC = -32 / -8

BC = 4

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Answer: 4 pages

Step-by-step explanation:

To solve this problem, we need to use the formula:

Rate = Output/Time

Let's use "p" to represent the number of pages Ethan can type and "t" to represent the time he has before the meeting starts.

Rate = 2 pages/(1/8 hour) = 16 pages/hour

Since the meeting starts 3/4 hour later than the scheduled time, Ethan has t = 1 - 3/4 = 1/4 hour to type pages before the meeting starts.

Output = Rate * Timep = (16 pages/hour) * (1/4 hour) = 4 pages

Therefore, Ethan can type 4 pages before the meeting starts.

Answer: 4 pages

The statement "there exists x ∈ S ∖ m" means that there exists an element x that belongs to the set S but does not belong to the set m. In other words, x is an element that is present in S but is not present in m.

The phrase "m ⊊ m ∪ {x} ∈ X" states that the set m is a proper subset of the set m ∪ {x}, and this union belongs to the set X. This implies that the set m ∪ {x} contains all the elements of m along with the additional element x.

The phrase "a contradiction" indicates that the statement or assumption being made leads to a logical inconsistency or contradiction. In this context, the contradiction arises from the fact that the assumption that x is not in m contradicts the statement that m ∪ {x} is a proper superset of m.

Overall, the given statement implies that the existence of an element x in S, which is not in m, leads to a contradiction when considering the relationship between m and m ∪ {x}.

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The total cost of membership for both Club A and Club B will be the same, amounting to $74.

To determine after how many months the total cost of each health club will be the same, we can set up an equation where the total cost of Club A is equal to the total cost of Club B.

Let's assume the number of months is represented by 'm'. The total cost of Club A after 'm' months can be calculated as:

Total Cost of Club A = $18 + $14m

Similarly, the total cost of Club B after 'm' months can be calculated as:

Total Cost of Club B = $26 + $12m

We want to find the value of 'm' where the total costs are equal, so we can set up the following equation:

$18 + $14m = $26 + $12m

Now, we can solve this equation for 'm':

$14m - $12m = $26 - $18

$2m = $8

m = $8 / $2

m = 4

Therefore, after 4 months, the total cost of each health club will be the same.

To find the total cost for each club after 4 months, we substitute 'm' into the total cost equations:

Total Cost of Club A = $18 + $14(4) = $18 + $56 = $74

Total Cost of Club B = $26 + $12(4) = $26 + $48 = $74

So, the total cost for each club after 4 months will be $74.

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(A) Triangle ABC, and triangle QPR are similar based on side-side-side (SSS) similarity.

(B) Triangle ABC and triangle DEF are similar based on side-side-side (SSS) similarity.

(C) ) Triangle STU and triangle JPM are similar based on side-angle-side (SAS) similarity.

(D) ) Triangle SMK and triangle QTR are similar based on angle-angle (AA) similarity.

Similar triangles have the same corresponding angle measures and proportional side lengths.

The triangle similarity criteria are:

(A) Triangle ABC, and triangle QPR are similar based on side-side-side similarity.

12/8 = 9/6

1.5 = 1.5

(B) Triangle ABC and triangle DEF are similar base on side-side-side similarity as shown in the side lengths.

(C) ) Triangle STU and triangle JPM are similar base on side-angle-side similarity.

14/10 = 21/15

1.4 =

(D) ) Triangle SMK and triangle QTR are similar base on angle-angle similarity.

SMK = 90⁰, 60⁰, 30⁰

QTR =  90⁰, 30⁰, 60⁰

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The true statement about the set is n.

The correct answer choice is option A.

The intersection of two sets for instance, set A and B, denoted (n) is the set containing all elements of set A that also belongs to set B.

{6, 8, 10, 12} _ {5, 6, 7, 8, 9} = {6, 8}

Let

{6, 8, 10, 12} = set A

{5, 6, 7, 8, 9} = set B

A n B = {6, 8}

Therefore, the intersection of set A and set B, that is, the elements of set A that are also contained in B are {6, 8}

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Answer:

y= -x²-4x+2

Step-by-step explanation:

write in vertex form

a(x-h)²+k

in our case h = -2 and k= 6

y=a(x+2)²+6

now we just need to solve for a. we know that when x= 1 y = -3. plug these values in and solve for a

-3= a(1+2)²+6

-9=9a

a= -1

thus the formula is -(x+2)²+6

generally, teachers want things in standard form, so expand the exponent and simplify.

-(x²+4x+4)+6

y= -x²-4x+2

Answer:

[tex]y = -x^2 - 4x + 2[/tex]

Step-by-step explanation:

The equation of a parabola in vertex form is:

[tex]y = a(x - h)^2 + k[/tex]

where (h, k) is the vertex of the parabola.

In this case, the vertex is (-2, 6), so h = -2 and k = 6.

We also know that the parabola passes through the point (1, -3).

Plugging these values into the equation, we get:

[tex]-3 = a(1 - (-2))^2 + 6[/tex]

[tex]-3 = a(3)^2 + 6[/tex]

-9 = 9a

a = -1

Substituting a = -1 into the equation for a parabola in vertex form, we get the equation of the parabola:

[tex]y = -1(x + 2)^2 + 6[/tex]

This equation can also be written as:

[tex]y = -x^2 - 4x -4+6\\y=x^2-4x+2[/tex]

Answer:

[tex]\displaystyle 64-32\sqrt{2}+\frac{32\sqrt{2}}{3}\approx3.66[/tex]

Step-by-step explanation:

[tex]\displaystyle \iint_R(3x-y)\,dA\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0(3r\cos\theta-r\sin\theta)\,r\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0(3r^2\cos\theta-r^2\sin\theta)\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\int^4_0r^2(3\cos\theta-\sin\theta)\,dr\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\frac{64}{3}(3\cos\theta-\sin\theta)\,d\theta\\\\=\int^\frac{\pi}{2}_\frac{\pi}{4}\biggr(64\cos\theta-\frac{64}{3}\sin\theta\biggr)\,d\theta[/tex]

[tex]\displaystyle =\biggr(64\sin\theta+\frac{64}{3}\cos\theta\biggr)\biggr|^\frac{\pi}{2}_\frac{\pi}{4}\\\\=\biggr(64\sin\frac{\pi}{2}+\frac{64}{3}\cos\frac{\pi}{2}\biggr)-\biggr(64\sin\frac{\pi}{4}+\frac{64}{3}\cos\frac{\pi}{4}\biggr)\\\\=64-\biggr(64\cdot{\frac{\sqrt{2}}{2}}+\frac{64}{3}\cdot{\frac{\sqrt{2}}{2}}\biggr)\\\\=64-32\sqrt{2}+\frac{32\sqrt{2}}{3}\biggr\\\\\approx3.66[/tex]

Answer: Read the solution

Step-by-step explanation:

A. For diagram A, triangles ANC and BDE are similar. Thus, we can use similarity ratios to find the length of AC. (x+1)/12 = (x+5)/15. 15x+15=12x+60. Thus 3x=45, and x=15. Since we need to find AC, AC = 15+1 = 16.

B. For diagram B, triangles SRT and VUT are similar. Again, using similarity ratios, (4x-1)/14=(x+2)/6 or 14x+28=24x-6. 10x=34, x=3.4.

Answer:

total age = 84 years

Step-by-step explanation:

mean is calculated as

mean = [tex]\frac{total}{count}[/tex]

here count = 7 and mean = 12 , then

[tex]\frac{total}{7}[/tex] = 12 ( multiply both sides by 7 )

total = 7 × 12 = 84 years

The forecasted level of output for the 15th year would be 14/15000.

To forecast the level of output for the 15th year, we need to analyze the given information about the firm's total production of cars at the end of ten years of operation and its production during the first year.

According to the information provided, the firm's total production of cars at the end of ten years of operation is 14/1500. However, the production of logo cars during the first year is not specified. We need this information to accurately forecast the level of output for the 15th year.

If we assume that the production of logo cars during the first year is constant throughout the ten-year period, we can use the given information to estimate the average annual production. Since we have 14/1500 as the total production over ten years, we can calculate the average annual production as (14/1500) / 10.

(14/1500) / 10 = 14/15000

Therefore, the estimated average annual production is 14/15000.

Now, to forecast the level of output for the 15th year, we can assume that the average annual production remains constant. Therefore, the forecasted production for the 15th year would be the same as the average annual production.

Hence, the forecasted level of output for the 15th year would be 14/15000.

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The equation of the line that passes through the points (1,0) and (3,6) is y = 3x - 3.

The formula for equation of line is expressed as:

y = mx + b

Where m is slope and b is the y-intercept.

Given that, the line passes through points  (1,0) and (3,6).

First, we determine the slope:

[tex]Slope\ m = \frac{y_2 - y_1}{x_2 - x_1} \\\\Slope\ m = \frac{6 - 0}{3 - 1} \\\\Slope\ m = \frac{6}{2} \\\\Slope\ m = 3[/tex]

Now we plug the  slope m = 3 and one point (1,0)into the point-slope form to find the equation:

( y - y₁ ) = m( x - x₁ )

( y - 0 ) = 3( x - 1 )

y = 3x - 3

Therefore, the equation of the line is y = 3x - 3.

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The axis of symmetry of the function f(x) = x² - 6x-1 is equal to 3.

In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical equation:

Axis of symmetry, Xmin = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

By substituting the parameters, we have the following:

Axis of symmetry, Xmin = -b/2a

Axis of symmetry, Xmin = -(-6)/2(1)

Axis of symmetry, Xmin = 6/2

Axis of symmetry, Xmin = 3.

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Answer:

a. 0.9375, 0.46875

b. geometric sequence

c. equation: [tex] 7.5 * (\frac{1}{2})^(n-1)[/tex]

Step-by-step explanation:

a.

The table can be finished as follows:

n t(n)

1 7.5

2 3.75

3. 1.875

4. 0.9375

5 0.46875

b.

The type of sequence is a geometric sequence.

A geometric sequence is a sequence of numbers where the ratio between any two consecutive terms is constant.

In this case, the ratio between any two consecutive terms is 3.75/7.5=½ ,

so the sequence is geometric.

c.

The equation for the sequence is t(n) = 7.5 * (1/2)^n.

This equation can be found by looking at the first term of the sequence (7.5) and the common ratio (1/2).

t(1) = 7.5

t(2) = 7.5 * (1/2) = 3.75

t(3) = 7.5 * (1/2)^2 = 1.875

The equation can also be found by looking at the general formula for a geometric sequence,

which is [tex]t(n) = a*r^{n-1}[/tex]

In this case,

t(n) =[tex] 7.5 * (\frac{1}{2})^{n-1}[/tex]

This is the required equation.

Answer:

[tex]\textsf{a.}\quad \begin{array}{|c|c|c|c|c|c|}\cline{1-6}\vphantom{\dfrac12} n&1&2&3&4&5\\\cline{1-6}\vphantom{\dfrac12}t(n)&7.5&3.75&1.875&0.9375&0.4687\\\cline{1-6}\end{array}[/tex]

[tex]\textsf{b.} \quad \textsf{Geometric sequence.}[/tex]

[tex]\textsf{c.} \quad t(n)=7.5(0.5)^{n-1}[/tex]

Step-by-step explanation:

Before we can complete the table, we need to determine if the sequence is arithmetic or geometric.

To determine if a sequence is arithmetic or geometric, examine the pattern of the terms in the sequence.

Calculate the difference between consecutive terms by subtracting one term from the next:

[tex]t(2)-t(1)=3.75-7.5=-3.75[/tex]

[tex]t(3)-t(2)=1.875-3.75 = -1,875[/tex]

As the difference is not common, the sequence is not arithmetic.

Calculate the ratio between consecutive terms by dividing one term by the previous term.

[tex]\dfrac{t(2)}{t(1)}=\dfrac{3.75}{7.5}=0.5[/tex]

[tex]\dfrac{t(3)}{t(2)}=\dfrac{1.875}{3.75}=0.5[/tex]

As the ratio is common, the sequence is geometric.

To complete the table, multiply the preceding term by the common ratio 0.5 to calculate the next term:

[tex]t(4)=t(3) \times 0.5=1.875 \times 0.5=0.9375[/tex]

[tex]t(5)=t(4) \times 0.5=0.9375 \times 0.5=0.46875[/tex]

Therefore, the completed table is:

[tex]\begin{array}{|c|c|c|c|c|c|}\cline{1-6}\vphantom{\dfrac12} n&1&2&3&4&5\\\cline{1-6}\vphantom{\dfrac12}t(n)&7.5&3.75&1.875&0.9375&0.4687\\\cline{1-6}\end{array}[/tex]

To find an equation for the sequence, use the general form of a geometric sequence:

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Geometric sequence}\\\\$a_n=ar^{n-1}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\\phantom{ww}$\bullet$ $r$ is the common ratio.\\\phantom{ww}$\bullet$ $a_n$ is the $n$th term.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]

In this case, the first term is the value of t(n) when n = 1, so a = 7.5

We have already calculated the common ratio as being 0.5, so r = 0.5.

Substitute these values into the formula to create an equation for the sequence:

[tex]t(n)=7.5(0.5)^{n-1}[/tex]