Make a forecast for week 3, find the error for week 4, and make a final prediction for week 7.
Use the moving average method with k = 2
Rounding correctly will help ensure you get credit for this question. Please round to 2 decimal places.
Week Time Series Moving average Error 1 30 _____ _____
2 19 _____ 5.5
3 30 _____ -------- 4 16 24.5000 -----------
5 21 23.0000 -2.00
6 25 18.5000 6.5
7 Prediction -> _____ _____

The evaluation of the expression -0.25 + 0.3 - ( - 3/10 ) + 1/4 is 3 / 5.

An algebraic expression is made up of variables and constants, along with algebraic operations such as addition, subtraction, division, multiplication etc.

To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.

Therefore, let's solve the expression as follows:

-0.25 + 0.3 - ( - 3/10 ) + 1/4

let's convert it to fraction

- 1 / 4 + 3 / 10 + 3 / 10 + 1 / 4

Hence,

3 / 10 + 3 / 10 +  1 / 4  - 1 / 4

3 + 3 / 10

6 / 10 = 3 / 5

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Answer:

Correct option is C)

Simple interest =

100

3000×6×2

=360

Compound interest =3000(1+

100

6

)

2

−3000=18×20.6=370.8

∴ Difference is Rs.10.8.

you can convert this value to $$

or simply the answer will be 2. $10

(hob-evzw-zjw) come

Answer:

B is your answer.
10.80$ which you just round to 10. 10 is your answer.

Step-by-step explanation:

For simple interest, the formula is:

Simple Interest = Principal × Rate × Time

For compound interest, the formula is:

Compound Interest = Principal × (1 + Rate)^Time - Principal

Let's calculate the values:

Principal = $3,000

Rate = 6% or 0.06

Time = 2 years

Simple Interest = $3,000 × 0.06 × 2 = $360

To calculate compound interest, we need to use the formula:

Compound Interest = $3,000 × (1 + 0.06)^2 - $3,000

= $3,000 × (1.06)^2 - $3,000

= $3,000 × 1.1236 - $3,000

= $3,370.80 - $3,000

= $370.80

The difference between simple and compound interest is:

$370.80 - $360 = $10.80

The derivative of f(x) = x⋅5x is f'(x) = 10x, which means that the rate of change of the function at any point x is 10 times the value of x at that point.

Using the product rule of differentiation, we can find the derivative of the function f(x) = x⋅5x as follows:

f'(x) = (x)'(5x) + x(5x)'

where (x)' and (5x)' are the derivatives of x and 5x with respect to x, respectively.

(x)' = 1 (the derivative of x with respect to x is 1)

(5x)' = 5 (the derivative of 5x with respect to x is 5)

Substituting these values, we get:

f'(x) = 1⋅5x + x⋅5

Simplifying further, we get:

f'(x) = 5x + 5x

Therefore, f'(x) = 10x.

In conclusion, the derivative of f(x) = x⋅5x is f'(x) = 10x, which means that the rate of change of the function at any point x is 10 times the value of x at that point.

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The length of BC is approximately 3.5 cm

A triangle is described as a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.

We construct triangle ABC, through the following steps:

The law of sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.

Mathematically shown as:

a/sin(A) = b/sin(B) = c/sin(C)

5/sin(95) = BC/sin(34)

BC = (5*sin(34))/sin(95)

BC ≈ 3.5cm

In conclusion, the length of BC is approximately 3.5 cm.

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(a) False; A subspace is formed by the set of vectors that do not belong to the column space.

(b) True; If the matrix contains solely the zero vector, then it is the zero matrix.

(c) True; The column space of a particular matrix is equivalent to the column space of another specified matrix.

(d) False; The column space of one matrix is identical to the column space of another matrix.

(a) False; if A = [1 0; 0 0], then the column space of A is { e1 }, where e1 is the standard unit vector in the plane. If v is not in the column space of A, but w is not in the column space of A, then v + w is not in the column space of A.

Therefore, the set of vectors that are not in the column space of A does not form a subspace.

(b) True; if every vector in Rn is in the null space of A, then in particular, every standard unit vector is in the null space of A. Thus, the ith column of A is zero for i = 1, . . . , n, so A is the zero matrix.

(c) True; the column space of A is generated by the columns of A, while the column space of AB is generated by linear combinations of the columns of AB. By definition of matrix multiplication, the columns of AB are linear combinations of the columns of A, so the column space of AB is a subspace of the column space of A. Conversely, let b be in the column space of A. Then there is an x in Rm such that Ax = b. Thus, ABx = A(Bx), so b is in the column space of AB. Therefore, the column space of A is a subspace of the column space of AB. Hence the two column spaces are equal.

(d) False; if A = [1 0; 0 0] and B = [0 0; 0 1], then the column space of A is { e1 }, while the column space of B is { e2 }. The column space of AB is { 0 }, so it is not equal to either column space.

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Answer: 2 solutions

Step-by-step explanation:

To find the angle of a regular polygon, use the formula 180(n-2)/n (where n is the amount of sides.)

Setting them equal, we get (180n-360)/n = 1680.

Multiplying by n on both sides, we get 180n-360 = 1680n.

Solving, we get 1500n = 360.

n = 0.24, which means it is not a shape, as you cannot have a shape with 0.24 sides.

The other way to look at it is to take full revolutions of 360 away from each angle, giving us 240 (the smallest remainder without it going negative). However, all the angles would be concave. If all the angles are concave, then it might connect backwards.

Subtracting 240 from 360 (to get the "exterior" angles, we get 120. Plugging it in to our equation 180(n-2)/n and solving, we get 180n-360 = 120n, and solving gives us 60n = 360, or n=6.

Since the amount of sides came together cleanly, we can classify this polygon as a normal hexagon, which has 6 sides.

Answer:

34

Step-by-step explanation:

1/2 multiplied by 68=34

34 is 1 half of 68 .

Here, we have,

given that,

what is 1 half of 68

we know that,

Half of a number can be found by dividing the number by 2.

i.e. we have to find half of 68,

for that, we need to divide 68 by 2

so, we get,

To find half of 68:

68 / 2 = 34

Therefore, half of 68 is 34.

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Answer:

the answer is 3/2

Step-by-step explanation:

Answer:

the answer si 3/2

The length of the shortest altitude of the triangles is 15 units by using Heron’s formula.

We have, The sides of a triangle have lengths of 15, 20, and 25.

To find, The length of the shortest altitude of the triangle.

Steps to solve the problem:

Area = 1/2 * base * height

Area of the triangle = 1/2 * 20 * h ⇒ 10h

A = √(s(s-a)(s-b)(s-c))

Where a, b, and c are the sides of the triangle, and s is the semi-perimeter of the triangle.

According to the given problem, the sides of the triangle are 15, 20, and 25.

s = (a + b + c)/2

= (15 + 20 + 25)/2

= 30

Therefore, the area of the triangle can be calculated as:

A = √(30(30-15)(30-20)(30-25))

= √(30*15*10*5)

= 150 sq. units

Therefore, we can write the formula for the area of the triangle as:

150 = 10 h

h = 15 units

Therefore, the length of the shortest altitude of the triangle is 15 units.

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Using the unitary method we calculate that the friend would be 20 miles closer in an hour.

If you are running towards a faraway friend at a speed of 5 miles per hour and she is biking towards you at 15 miles per hour, According to relative motion's concept, the total speed at which you are approaching each other is:

5 miles / hour - (- 15 miles / hour) = 20 miles / hour

Also, we know that

speed= distance/time according to which, after 1 hour, you and your friend would have closed the distance by,

20 miles/hour × 1 hour = 20 miles

Therefore, you would be 20 miles closer to each other after 1 hour.

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The exteriοr angle οf the pοlygοn is 15°.

A pοlygοn has as many pairs οf interiοr and exteriοr as number οf its sides. Further each pair οf exteriοr and interiοr add up tο 180°.

Sum οf all the exteriοr angles οf any pοlygοn is 360°.

As sum οf all the interiοr angles οf the pοlygοn is  3960°.

Sum οf all pairs οf exteriοr and interiοr angles is

=> 3960°+360°=4320°

As each pair is 180° , Number οf sides οf pοlygοn = 4320/180 = 24

Sum οf exteriοr angles is always 360° and if pοlygοn is regular (i.e. all sides and angles are equal), size οf each exteriοr angle is

=> 360°/24 = 15°

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The number of claims filed by the policyholders has a poisson distribution. Therefore, the variance of the number of claims filed will be about 2.5.

We need to use the Poisson Distribution for solving the question, which is as follows:

P(x) = (λˣ/x!) × [tex]e^(-lambda)[/tex]

where is the mean value of distribution and x is the number of events we want to calculate.

If a random variable follows a Poisson distribution, its variance is equal to its mean.

So, the mean will be λ.

Let the probability of filing four claims be p1.

Then, probability of filing two claims will be ⁵p₁

We know the sum of probabilities of different events of Poisson distribution will always be equal to 1.

So,

p₁ + ⁵p₁ = 1

p₁ = 1/6

The mean number of claims is λ, which is given by:

Now, the variance of the Poisson distribution is also λ.

So, the variance of the number of claims filed is 2.5.

Hence, the answer is variance of the number of claims filed is 2.5.

The mean number of claims is λ, which is given by:

λ = ⁴p₁ + 2⁵p₁ = 2.5

Now, the variance of the Poisson distribution is also λ.

So, the variance of the number of claims filed is 2.5.

Hence, the answer is variance of the number of claims filed is 2.5.

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The area of the cylinder's base is 25π square units. The volume of the cylinder is 100π cubic units.

a. The base of a cylinder is a circle. We can shade the circle at the bottom of the cylinder to represent the cylinder's base.

b. The diameter of the cylinder is 10 units, which means the radius of the base is half of that or 5 units. The area of a circle is calculated using the formula A = πr^2, where A is the area and r is the radius.

Therefore, the area of the cylinder's base is:

A = πr^2 = π(5^2) = 25π

So the area of the cylinder's base is 25π square units.

c. The volume of a cylinder is calculated using the formula V = πr^2h, where V is the volume, r is the radius of the base, and h is the height of the cylinder.

Substituting the values given, we get:

V = πr^2h = π(5^2)(4) = 100π

So the volume of the cylinder is 100π cubic units.

A cylinder is a three-dimensional object with a circular base and straight sides that rise to a circular top. The area of a cylinder is the total amount of space on the surface of the cylinder. It can be calculated by finding the sum of the areas of the two circular bases and the curved surface area in between.

The formula for finding the surface area of a cylinder is A = 2πr² + 2πrh, where "r" is the radius of the circular base, "h" is the height of the cylinder, and "π" is a constant value of approximately 3.14159. To calculate the area of a cylinder with a radius of "r" and height of "h", we first find the area of the circular base by using the formula for the area of a circle: A_base = πr².

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Complete Question: -

Here is a cylinder with height 4 units and diameter 10 units. a. Shade the cylinder’s base. b. What is the area of the cylinder’s base? Express your answer in terms of π. c. What is the volume of this cylinder? Express your answer in terms of π.

(a) The probability that the series will last exactly m games is:(1 - (pA + pB))^m(pA (1 - pB) + pB (1 - pA))where pA and pB are the probabilities of teams A and B, respectively. Therefore, the probability that the series will last less than 5 games is the probability that the series will last exactly 3 games or exactly 4 games:1 - (1 - 0.6 * 0.4)^3 - (1 - 0.6 * 0.4)^4 ≈ 0.684.

The probability that the series will last 5 games is the probability that the first four games have two wins for each team, and the last game is won by Team A:0.6^3 * 0.4^3 * 4 ≈ 0.055.The probability that the series will last 6 games is the probability that the first five games have two wins for each team, and the last game is won by Team A:0.6^3 * 0.4^3 * 5 ≈ 0.077The probability that the series will last 7 games is the probability that the first six games have two wins for each team, and the last game is won by Team A:0.6^3 * 0.4^3 * 6 ≈ 0.091.

The expected number of games played is thus approximately:0.684 * 4 + 0.055 * 5 + 0.077 * 6 + 0.091 * 7 + ∑m=8^∞ (1 - (pA + pB))^m(m + 1)(pA (1 - pB) + pB (1 - pA))The sum above can be computed by expressing it as the product of three factors:1 - (pA + pB) is a common factor for all terms, (pA (1 - pB) + pB (1 - pA)) is a sum of two terms that can be replaced by 1 - (1 - pA)(1 - pB), and m + 1 is a sum of m and 1. After replacing the sum of two terms, we obtain:0.684 * 4 + 0.055 * 5 + 0.077 * 6 + 0.091 * 7 + (1 - (0.6 + 0.4))^8(8 + 1)(1 - (1 - 0.6 * 0.4)^2) / (0.6 + 0.4 - 0.6 * 0.4) ≈ 0.684 * 4 + 0.055 * 5 + 0.077 * 6 + 0.091 * 7 + 0.02525 / 0.34 ≈ 5.43.

Therefore, the expected number of games played is approximately 5.43.(b) Given that Team B wins the first game, the series can last 7 or 8 games. The probability that the series will last 8 games is the probability that the first seven games have three wins for each team, and the last game is won by Team A:0.6^3 * 0.4^3 ≈ 0.013824.The probability that the series will last at least 8 games is therefore approximately 0.091 + 0.013824 = 0.104824, or 10.48%.Answer: (a) The expected number of games played is approximately 5.43. (b) The probability that the series will last at least 8 games is approximately 0.104824 or 10.48%.

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The 21 square root of 98 divided by 7 square root of 21 = 21√98 / 7√21 = 6.4807407

A square root of a number x is a number y such that y2 = x; in other words, a number y who's square and the result of multiplying the number by itself, or y ⋅ y, is x.

Every nonnegative real number x has a unique nonnegative square root, called the principal square root, which is denoted by √where the symbol √ is called the radical sign.

Every positive number x has two square roots: √ which is positive, and -√ which is negative. The two roots can be written more concisely using the ± although the principal square root of a positive number is only one of its two square roots, the designation "the square root" is often used to refer to the principal square root.

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On the first day of ticket sales for the school’s spring musical, 46 senior citizen tickets and 44 child tickets were sold, bringing the total number of tickets sold to 362.

Number is a mathematical object used to count, measure, and label. It is an abstract concept, though it is often used to refer to concrete objects such as numbers, figures, objects, and symbols. Numbers can be used to represent quantities, relationships, and functions. They are used to describe, measure, and compare various aspects of the world around us.

The second day saw a slightly lower number of tickets sold, with two senior citizen tickets and 25 child tickets purchased, for a total of 85. The price of a senior citizen ticket and a child ticket was likely the same on both days, and likely the same price as it is for the rest of the ticket sales.

The school likely has a set price for tickets, which would not change as the number goes up or down. It is common for schools to give discounts for senior citizens, so the price of their tickets is usually lower than the price of a child ticket. The school set the prices of the tickets in a way that would bring in the most money, while still being affordable for the community to attend.

The school likely had a plan in place for how many tickets they wanted to sell and what prices they wanted to set. They also likely had a goal of how much money they wanted to bring in from the ticket sales. After the two days of ticket sales, the school was able to see how many tickets were sold and how much money was collected. This can help the school to adjust their plan, if necessary, to reach their goal.

The money brought in from the ticket sales will likely help the school to cover the costs of putting on the musical. It may also help to pay for any other expenses associated with the production of the show. The school may also use the money to purchase new materials or supplies for the performing arts department.

Overall, the school was able to bring in a total of 447 from the two days of ticket sales. This money will help to ensure that the school’s spring musical is a success. The school was also able to offer discounted tickets to senior citizens, which allowed more people to attend the show.

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The price of a senior citizen ticket at Jack's school is 42.50, and the price of a child ticket is 3.40.

Number is a mathematical object used to count, measure, and label. It is an abstract concept, though it is often used to refer to concrete objects such as numbers, figures, objects, and symbols. Numbers can be used to represent quantities, relationships, and functions. They are used to describe, measure, and compare various aspects of the world around us.

Jack's school is selling tickets to a spring Musical. On the first day of ticket sales, the school sold a total of 362 tickets, 46 of which were senior citizen tickets and 44 of which were child tickets. On the second day of ticket sales, the school sold two senior citizen tickets and 25 child tickets, for a total of 85 tickets.

To calculate the price of each ticket, we can divide the total amount taken in by the number of tickets sold. For senior citizen tickets, the total amount taken in was 85, and two were sold, so the price of a senior citizen ticket is 85/2 = 42.50. For child tickets, the total amount taken in was 85, and 25 were sold, so the price of a child ticket is 85/25 = 3.40.

In conclusion, the price of a senior citizen ticket at Jack's school is 42.50, and the price of a child ticket is 3.40.

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Answer: Gavin drank 2.25 quarts today.

Step-by-step explanation: First you need to find out how many quarts are in 8 ounces -the answer to that is 0.25. Then you will need to times that by 9.

The exponential probability distribution is employed with a random variable that is continuous in nature.

What do you mean by exponential probability distribution ?

In the field of probability, a probability distribution refers to a mathematical function that gives the probabilities of various possible outcomes of an experiment. The exponential probability distribution is a probability distribution that models the time between events in a Poisson process, where events occur continuously and independently at a constant average rate. It is a continuous probability distribution, meaning that the random variable takes on values within a continuous range, as opposed to a discrete probability distribution, where the random variable takes on only a finite or countable set of values.

Explanation of the correct answer :
The exponential probability distribution is defined by a single parameter, [tex]\lambda[/tex] which represents the average rate of occurrence of events in the Poisson process.

The probability density function (pdf) of the exponential distribution is given by [tex]f(x) = \lambda e^{(-\lambda x)}[/tex], where x is the time between events. The cumulative distribution function (cdf) is given by [tex]F(x) = 1 - e^{-\lambda x}[/tex].

The exponential probability distribution is used in many applications, such as queuing theory, reliability theory, and finance. For example, it can be used to model the time between customer arrivals in a queue, the time between machine failures in a manufacturing process, or the time until default on a bond.

In summary, the exponential probability distribution is a continuous probability distribution that is used with a continuous random variable, specifically to model the time between events in a Poisson process.
Hence, option B is correct.

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Beth receives £103.45 when she changes €120 back into pounds.

An exchange rate is the value of one currency expressed in terms of another currency. In other words, it is the rate at which one currency can be exchanged for another currency.

Pound is a unit of currency that is used in several countries, including the United Kingdom, Egypt, Lebanon, and Sudan, among others. The pound symbol is "£".

In the given question,

If the exchange rate is £1 = €1.16, this means that for every euro, Beth will get £1/€1.16.

Therefore, the number of pounds Beth receives when she changes €120 back into pounds is:

120 euros * £1/€1.16 = £103.45 (rounded to two decimal places)

So Beth receives £103.45 when she changes €120 back into pounds.

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The tangential component of the acceleration vector at point t = 1 is aT(1) = 233/3 and The normal component of the acceleration vector at point t = 1 is aN(1) = (1/3)√10459

The acceleration vector can be found from the following formula:

[tex]a(t) = r''(t) = (-3,-10t,-8t3).[/tex]

To find the tangential component of the acceleration vector, we first need the velocity vector v(t).

[tex]v(t) = r'(t) = (-3,-10t,-8t3) .[/tex]

Next, we need to normalize the velocity vector using the following formula:

[tex]T(t) = v(t) / ||v(t)||,[/tex]

Where ||v(t)|| is the magnitude of the velocity vector.

[tex](1) = (-3,-10,-8) / \sqrt{(3^2 + 10^2 + 8^2)} = (-3/3, -10/3, -8/3) = (-1 , -10/3, -8/3) .[/tex]

Then, the tangential component of a(1) is:

[tex]aT(1) = a(1) T(1) = (-3, -10, -8) (-1, -10/3, -8/3) = 3 + 100/3 + 64/3 = 233/3.[/tex]

To find the normal component of a(1), we simply need to find the magnitude of the tangential component and subtract it from the magnitude of the acceleration vector.

[tex]aN(1) = \sqrt{ (a^2 - aT(1)^2)} = \sqrt{(3^2 + (10)^2 + (8)^2 - (233/3)^ 2)}  = \sqrt{(9 + 100 + 64 - 54289/9)} = \sqrt{(10459/9)} = (1/3)\sqrt{10459}[/tex]

Therefore, the tangential and normal components of the acceleration vector at the point t = 1 are:

[tex]aT(1) = 233/3[/tex] and [tex]aN(1) = (1/3)\sqrt{10459}[/tex]

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Answer:

y = 2x/15 + 6

Step-by-step explanation:

3y/2 = x/5 + 9

3y = (x/5 + 9) (2)    The 2 that was dividing goes on to multiply on the other side.

3y= 2x/5 + 18

y = (2x/5 + 18) / 3   The 3 that was multiplying goes on to divide on the other side.

y = 2x/15 + 6

The population of Toledo, Ohio is increasing at a rate of approximately 32,263 people per year after 10 years.

An exponential function is a mathematical function of the form f(x) = a^x, where "a" is a positive constant called the base, and "x" is a variable that can take on any real value. The base "a" is typically greater than 1, which means the function grows at an increasing rate as "x" increases.

a. The exponential function that relates the total population as a function of t is given by:

P(t) = P₀ × (1 + r)ᵗ

where P₀ is the initial population, r is the annual growth rate (as a decimal), and t is the time in years.

Using the given values, we have:

P₀ = 500,000 (given)

r = 0.05 (5% expressed as a decimal)

Thus, the exponential function is:

P(t) = 500,000 × (1 + 0.05)ᵗ

b. The rate at which the population is increasing in t years is given by the derivative of the population function with respect to time:

dP/dt = P₀ × r × (1 + r)ᵗ

Substituting the given values, we get:

dP/dt = 500,000 × 0.05 × (1 + 0.05)ᵗ

c. To determine the rate at which the population is increasing in 10 years, we simply substitute t = 10 into the expression we derived in part b:

dP/dt = 500,000 × 0.05 × (1 + 0.05)¹⁰

Using a calculator, we get:

dP/dt ≈ 32,263

Therefore, the population of Toledo, Ohio is increasing at a rate of approximately 32,263 people per year after 10 years.

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By answering the presented question, we may conclude that Sanderson amount Equipment Company owes $42,000 Galaxy Furniture Supply owes $13,360. $55,360 in total liabilities

aggregate attempting to determine the time required, total number or amount. The quantity at sight or under consideration is extremely active. the overall effect, relevance, or import. Principle, interest, or a third accounting are all included. Word forms include amounts, amounting, and amounted. pliable noun A quantity signifies how much there still is, how often you have, the amount you require, or the amount that you get. He needs that quantity of cash to get by.

The following figures would appear on Dr. Ortiz's balance sheet:

Assets:

Cash: $31,000

$11,300 for dental supplies

$57,100 for dental equipment

$20,000 for office furnishings

The total value of the assets is $119,400.

Liabilities:

Sanderson Equipment Company owes $42,000

Galaxy Furniture Supply owes $13,360.

$55,360 in total liabilities

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Answer:

5:3 = 5/3

Step-by-step explanation:

Given Sin∅ = 3/5

We know sin∅ = Perpendicular/Hypotenuse

And, By inverse relationship, we get

cosec∅ = Hypotenuse/Perpendicular = 1/sin∅

So, csc∅ = 5/3, 5:3

Answer:

82

Step-by-step explanation:

divide this shape into a triangle and rectangle and use 24 as the base of the triangle using the Pythagoras theorem you get that the perpendicular is 7 and since 13 is also parallel to that side, 13+7=20 so one side equals 20 one side equals 25 one side equals 24 and one side equals 13 now add all of these to get 82

Step-by-step explanation:

See image below ..... perimeter = 25 + 13 + 24 + 13 + x

  x is found using pythagorean theorem for right triangles

x = 7 units

total perimeter is then 82 units

The first 4 terms of the sequence represented by the expression 3n + 5

is 8, 11, 14 and 17.

Sequence:

In mathematics, an array is an enumerated collection of objects in which repetition is allowed and in case order. Like a collection, it contains members (also called elements or items). The number of elements (possibly infinite) is called the length of the array. Unlike sets, the same element can appear multiple times at different positions in the sequence, and unlike sets, order matters. Formally, a sequence can be defined in terms of the natural numbers (positions of elements in the sequence) and the elements at each position. The concept of series can be generalized as a family of indices, defined in terms of any set of indices.

According to the Question:

Given, aₙ = (3n+5).

First four terms can be obtained by putting n=1,2,3,4

a 1=(3×1+5) = 8

a 2 =(3×2+5) = 11

a 3 =(3×3+5) = 14

a 4 =(3×4+5) = 17

First 4 terms in the sequence are 8, 11, 14, 17.

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Answer:

The square root of 2,100 is approximately 45.8257569495584 when rounded to 15 decimal places.

Answer:

Zeros: x = -10 and x = -3

Vertex: [tex](-\frac{13}{2} , \frac{49}{4} )[/tex]

Step-by-step explanation:

We are given the following function:
f(x) = -(x+3)(x+10)

We want to find the zeros and the vertex of the parabola.

The zeros are the values of the function where f(x) = 0.

So, in order to find the zeros, we can set f(x) = 0.

0 = -(x+3)(x+10)

We can divide both sides by -1, to get:

0 = (x+3)(x+10)

To solve this, we will use zero product property.
Split and solve:

x+3 = 0

x = -3

x+10=0

x = -10

Now, to find the vertex, we first get the average of the zeros.

Add the values of the zeros together, then divide by two:

[tex]\frac{-3-10}{2}[/tex] = [tex]\frac{-13}{2}[/tex]

Now, we plug this in for x to get the y value (found through f(x)) of the vertex.

[tex]f(-\frac{13}{2}) = -(-\frac{13}{2} + 3) (-\frac{13}{2} + 10)[/tex] = [tex]\frac{49}{9}[/tex]

So, the vertex is [tex](-\frac{13}{2} , \frac{49}{4} )[/tex]

The ball reaches a maximum height of approximately 146 feet, to the nearest foot.

Maximum Height refers to the highest point of the structure or sign as measured from the average natural ground level at the base of the supporting structure.

The ball is thrown upward with an initial velocity of 75 feet per second, implying that v0 = 75. We are also told that the ball is thrown from a height of 4 feet, implying that h0 = 4.

The function: can be used to model the ball's vertical motion.

16t2 + v0t + h0 = h(t).

Substituting v0 and h0 values yields:

h(t) = -16t^2 + 75t + 4

To determine the maximum height of the ball, we must first locate the vertex of the parabolic function h. (t). The vertex of the parabola is given by the equation y = ax2 + bx + c:

x = -b / 2a

y = c - b^2 / 4a

a = -16, b = 75, and c = 4 in this case. Substituting these values into the above formulas yields:

t = -75 / 2(-16) = 2.34 sec

h(t) = 4 - (752) / (4(-16)) 146 ft.

As a result, the ball reaches a maximum height of about 146 feet to the nearest foot.

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