a fancy bed and breakfast inn has 5 rooms, each with a distinctive color-coded decor. one day 5 friends arrive to spend the night. there are no other guests that night. the friends can room in any combination they wish, but with no more than 2 friends per room. in how many ways can the innkeeper assign the guests to the rooms?(2014 amc 12a

These intercepts are even multiple of π, such as 0, ±π, ±2π, etc.

The θ-intercepts of a function are the values of θ for which the function equals zero.  the θ-intercepts of the graph of f(θ) = tan(Θ), we have  to solve the equation tan(θ) = 0.

we know that the tangent function has zeros at θ = kπ, where k is an integer. the tangent function is undefined at odd multiples of π/2,

Therefore, the Θ-intercepts of the graph of f(θ) = tan(θ) are the values of θ that satisfy the equation tan(θ) = 0, which are θ = kπ for any integer k. These intercepts occur at every even multiple of π, such as 0, ±π, ±2π, etc.

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Answer:

Using chain of thought reasoning, the answer and explanation to the given math problem is as follows:

Step 1: Recognize that the arc's length can be calculated using the formula L = θ_arc*r, where L stands for the arc's length, θ_arc is the measure of the angle in radians, and r is the radius of the circle.

Step 2: We can calculate θ_arc by rearranging the formula to derive θ_arc = L/r. Assuming the arc's length is the same as the sector's perimeter, L = perimeter = 2πr, meaning that θ_arc = 2πr/r.

Step 3: Since the radius of the circle is 8 feet, θ_arc = 2π(8 feet/8 feet) = 2π.

Step 4: We then can calculate the angle measure of the arc bounding the sector. Calculate the area of the sector, A = θ/2πr^2. Rearranging the formula to derive θ = 2πr^2/A and inserting the given values yields θ = 2π(8^2 feet^2/6 square feet) ≈ 6.36 radians.

Answer:

The angle measure of an arc bounding a sector with area 6 square feet is 6.36 radians.

The solutions to the quadratic equation 4x² + 3x - 1 = 0 are: x = 1/2 and x = -1. None of the answer choices match these solutions, so none of the options provided are correct.

it's a second-degree quadratic equation which is an algebraic equation in x. Ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form.

To use the quadratic formula, we need to first identify the values of a, b, and c in the quadratic equation:

ax² + bx + c = 0

In the given equation,

a = 4

b = 3

c = -1

Now, we can substitute these values into the quadratic formula:

[tex]$ \rm x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

Plugging in the values for a, b, and c gives:

x = (-3 ± sqrt(3² - 4(4)(-1))) / 2(4)

[tex]$ \rm x = \frac{ -3 \pm \sqrt{3^2 - 4(4)(-1)}}{2(4)}[/tex]

Simplifying inside the square root:

[tex]$ \rm x = \frac{-3 \pm \sqrt{9 + 16}}{8}[/tex]

[tex]$ \rm x = \frac{-3 \pm \sqrt{25}}{8}[/tex]

[tex]$ \rm x = \frac{-3 \pm 5}{8}[/tex]

Now, we have two solutions:

x = (-3 + 5) / 8 = 1/2

x = (-3 - 5) / 8 = -1

Therefore, the solutions to the quadratic equation 4x² +3x - 1 = 0 are:

x = 1/2 and x = -1

None of the answer choices match these solutions, so none of the options provided are correct.

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Answer:

[tex] \sf \: 3x + 12 [/tex]

Step-by-step explanation:

Now we have to,

→ Simplify the given expression.

The property we use,

→ Distributive property.

The expression is,

→ 3(x + 4)

Let's simplify the expression,

→ 3(x + 4)

→ 3(x) + 3(4)

→ (3 × x) + (3 × 4)

→ 3x + 12

Hence, the answer is 3x + 12.

The probability that the first spinner will land on 7 and the second spinner will land on C is 1/4. So correct option is D.

Probability is a branch of mathematics that deals with the study of random events or phenomena. It provides a framework for quantifying uncertainty and making predictions based on data and observations.

Probability is typically expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. For example, the probability of flipping a coin and getting heads is 0.5, or 50%, since there are two equally likely outcomes (heads or tails).

The probability of an event can be determined by calculating the ratio of the number of favorable outcomes to the total number of possible outcomes. For example, the probability of rolling a 6 on a standard die is 1/6, since there is only one favorable outcome (rolling a 6) out of six possible outcomes (rolling a 1, 2, 3, 4, 5, or 6).

The probability that the first spinner will land on 7 and the second spinner will land on C is 1/4.

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There is a 10.91% chance that the package will be refused.

The possibility that an event will occur is its probability, which is given as a number between 0 and 1.

Sample = 400 units

n = 400 units

If less than 10% of the units are the desired hue, the shipment will be rejected.

12% of the units are, in fact, the desired hue.

So, P = 12%

We can write it as

P = 0.12

Q = 1 - 0.12

Q = 0.88

σ = √PQ/n

Substitute the value

σ = √(0.12 × 0.88)/400

σ = √0.1056/400

σ = √0.000264

σ = 0.01625

Probability that the shipment will be rejected;

P(x < 10%) = P(x < 0.1)

P(x < 10%) = P([tex]Z_{0.1}[/tex])

[tex]Z_{0.1}[/tex] = (0.1 - 0.12)/0.01625

[tex]Z_{0.1}[/tex] = -0.02/0.01625

[tex]Z_{0.1}[/tex] = -1.231

P([tex]Z_{0.1}[/tex]) = 0.1091

P(x < 10%) = 0.1091

P(x < 10%) = 10.91%

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Answer:

how many fluid ounsous you need

Step-by-step explanation:

Answer:

------------------------------

Perimeter is the sum of side lengths:

Substitute side lengths into formula:

Answer:

24 ft

Step-by-step explanation:

The perimeter is the sum of a shape's side lengths.

We can add the given side lengths of this polygon to solve for its perimeter.

2 + 4 + 3 + 7 + 4 + 4 = 24 ft

Answer:

To solve the equation XX/2-6=-18, we need to isolate the variable on one side of the equation. First, we can add 6 to both sides of the equation to eliminate the constant term on the left side: XX/2-6+6=-18+6 Simplifying the left side, we get: XX/2=-12 Next, we can multiply both sides by 2 to eliminate the fraction: 2*(XX/2) = 2*(-12) Simplifying the left side, we get: XX = -24 Therefore, the value of XX that satisfies the equation is -24.

Answer:

The average monthly revenue last year would be 99,020.

Step-by-step explanation:

69,314 = 70%

69,314 ÷ 70 = 990.2 (this equals one percent of the revenue)

990.2 × 100 = 99,020

99,020 = 100%

The following descriptions of the function passing through (0,7) and (4,4) are true:

The slope of the function is -3/4 and the y-intercept is 7.

The function is linear and continuous.

y=-3/4x + 7 represents this function.

y = -4/3x + 9 represents this function.

In mathematics, a function is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output. A function is often represented by a mathematical expression, formula or graph. Functions can be described using different notations, such as f(x), y = f(x), or y = g(u,v), and they can take various forms, such as linear, quadratic, polynomial, exponential, logarithmic, trigonometric, and many others.

Here,

To determine which descriptions of the function are true, we need to use the information given about the two points (0,7) and (4,4) to find the slope and y-intercept of the linear function that passes through them. Using the formula for the slope of a line:

slope = (4 - 7) / (4 - 0) = -3/4

So the slope of the function is -3/4.

To find the y-intercept, we can use the point-slope form of the equation of a line, which is y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line. We can use either of the two points given:

y - 7 = (-3/4)(x - 0)

y - 7 = (-3/4)x

y = (-3/4)x + 7

So the y-intercept of the function is 7.

Using this information, we can now evaluate the given descriptions of the function:

y = 7x - 3/4: This represents the function, but the slope is incorrect (should be -3/4).

The function is decreasing: This is not true, since the slope is negative but less than -1.

y=-3/4x + 7: This represents the function, and the slope and y-intercept are both correct.

The slope of the function is -4/3 and the y-intercept is 9: This is not true, since the slope is -3/4 and the y-intercept is 7.

The function is increasing: This is not true, since the slope is negative.

The slope of the function is -3/4 and the y-intercept is 7: This is true, as shown by the calculations above.

y = -4/3x + 9: This represents a different function with a different slope and y-intercept.

The function is linear and continuous: This is true, since the function is a linear equation and is continuous over its domain.

The function is linear and discrete: This is not true, since the function is continuous over its domain.

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Two lines intersect at (2,4). The last choice listed, "a coordinate grid with one line that passes through the points 0,0 and 1,2 and another line that runs through the points 0,-2 and 1,-1," is the graph.

The given system of linear equations is y = 2x and y = x + 2. To find the solution to this system, we can set the two equations equal to each other:

2x = x + 2

Subtract x from both sides:

x = 2

Substitute x = 2 into either equation:

y = 2x = 2(2) = 4

Therefore, solution to system of linear equations is (2, 4).

To check our answer, we can graph the two lines y = 2x and y = x + 2 on a coordinate grid. The intersection point of the two lines will be the solution to the system.

The line y = 2x passes through the points (0,0) and (1,2). The line y = x + 2 passes through the points (0,2) and (1,3). We can plot these points and draw the lines to get the following graph:

Linear equation graph is attached.

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Answer:

To complete the square and rewrite the quadratic function y = x² + 7x + 3 in vertex form, we follow these steps:

Factor out the coefficient of x² from the first two terms:

y = 1(x² + 7x) + 3

Take half of the coefficient of x (which is 7 in this case) and square it. Add this value inside the parentheses, and subtract the same value multiplied by the coefficient of x² (which is 1) outside the parentheses to maintain the same value of the expression:

y = 1(x² + 7x + (7/2)² - (7/2)²) + 3

Simplify inside the parentheses by combining the first three terms using the square of the binomial formula (a + b)² = a² + 2ab + b²:

y = 1(x + 7/2)² - 1/4 + 3

Combine the constant terms to simplify:

y = 1(x + 7/2)² + 11/4

Therefore, the quadratic function y = x² + 7x + 3 can be written in vertex form as y = (x + 7/2)² + 11/4. The vertex is located at the point (-7/2, 11/4).

Hope This Helps!

Answer:

A banana costs $0.05

Step-by-step explanation:

Let a = the cost of an apple

Let b = the cost of a banana.

a + b = 1.10

a = b + 1  Substitute b + 1 for a in the bold equation.

b + 1 + b = 1.10  Combine like terms

2b + 1 = 1.10  Subtract 1 from both sides

2b = .10  Divide both sides by 2

b = .05

An apple would cost

a = .05 + 1

a = 1.05

An apple and a banana together would cost 1.10

a + b = 1.10

1.05 + .05 = 1.10

1.10 = 1.10 checks.

Helping in the name of Jesus.

Hello and regards taylahflynn2965

Answer: The cost of the banana is $0.05.

This is an exercise in elementary algebra, which is a branch of mathematics that focuses on the study of the fundamental operations and properties of numbers and algebraic expressions. In particular, in elementary algebra you learn to solve problems by manipulating algebraic expressions and applying basic algebraic rules and procedures.

One of the fundamental skills of elementary algebra is solving systems of linear equations with two variables. Such a system is a set of two or more equations involving two or more variables. In the case of a system of two linear equations with two variables, the solution of the system consists in finding the numerical values of the two variables that satisfy both equations.

The substitution technique is one of the main tools used to solve systems of linear equations with two variables in elementary algebra. This technique consists of isolating one of the variables in one of the equations and substituting that expression in the other equation. The resulting equation is then solved to find the value of the other variable. Finally, this value is substituted into one of the original equations to find the value of the other variable.

Let x be the cost of the banana.

From the statement, we know that:

Solving the equation:

2x + $1 = $1.10

2x = $1.10 - $1

2x = $0.10

x = $0.10 / 2

x = $0.05

Therefore, the cost of the banana is $0.05.

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The measures of central tendency of the dot plot is:

Range = 6

Mode: 5.5 and 6

Median is 6

A measure of central tendency is defined as a single value that explains the way by which a group of data cluster near the center value. In other words it is the center of data set.

The range is the difference between the highest and lowest values of the dataset. Thus:

Range = 11 - 5

Range = 6

Mode is defined as the term that has the most frequency of occurrence. Thus, the mode of the dot plot is:

5.5 and 6

The median is defined as the middle term when arranged in ascending or descending order:

5, 5, 5.5, 5.5, 5.5, 5.5, 6, 6, 6, 6, 6.5. 6.5, 7, 7, 7.5, 8, 8, 9, 11

Thus, the median is 6

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Answer:

d=91

Step-by-step explanation:

Answer:   d=91

Step-by-step explanation:

First thing first, you have to use the distributive property. Distribute the 8 to the d-87.

(8*d) - (8*87) = 32  =    8d - 696= 32  

Next, you have to add 696 to both sides of the equation:

8d-696 +696= 32+696  =  8d= 728

Last step is to divide both sides by 8:

8d/8 = 728/8 =  

d= 91

We can check this by plugging the number 91 to the variable d in the equation:

(8*91) - (8 *87) = 32    =  728 - 696= 32

the line of reflection is the vertical line x = 7.Thus, if we reflect polygon ABCDE across the line x = 7, we get polygon A' B' C' D' E'.

To determine the line of reflection, we need to find the axis that maps each point of polygon ABCDE to its corresponding point on polygon A' B' C' D' E'.

If we observe the coordinates of the vertices of the polygons, we can see that the x-coordinates of the corresponding points are related by x' = 14 - x, where x is the x-coordinate of the point in polygon ABCDE. Similarly, the y-coordinates of the corresponding points are related by y' = y.

Now, if we reflect polygon ABCDE across the line of reflection, each point of polygon ABCDE will map to its corresponding point on polygon A' B' C' D' E' such that the distance between the line of reflection and the point is equal to the distance between the line of reflection and its image.

If we consider a point (x, y) in polygon ABCDE and its corresponding point (x', y') in polygon A' B' C' D' E', we can see that the line of reflection is the vertical line that passes through the midpoint of the segment joining (x, y) and (x', y').

We can find the midpoint of this segment by using the midpoint formula:

((x + x')/2, (y + y')/2)

Substituting the values of x and y in terms of x' and y', we get:

((14 - x' + x')/2, y/2) = (7, y/2)

Therefore, the line of reflection is the vertical line x = 7.

Thus, if we reflect polygon ABCDE across the line x = 7, we get polygon A' B' C' D' E'.

In summary, the line of reflection is x = 7.

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Answer:

32.83= 15(x) +1.93

32.83- 1.93= 30.90

30.9= 15x

30.9/ 15 =2.06

X= 2.06

Which means each bottled juice cost 2.06 each

Step-by-step explanation:

To find the expected value of the largest of the three claims, we will first need to understand the probability density function (pdf) of the maximum of the three independent random variables.   The formula is = ∫x * 3 * F(x)^2 * f(x) dx

Let's denote the common density function as f(x), and the cumulative distribution function (CDF) as F(x), where x is the amount of a claim in thousands.
Step 1: Find the CDF of the maximum of three claims
Since the claims are independent random variables, the CDF of the maximum of three claims (denoted as M) is given by the product of the individual CDFs: F_M(x) = F(x)^3.
Step 2: Find the pdf of the maximum of three claims
To obtain the pdf of M, we need to differentiate the CDF with respect to x. Let's denote the pdf of M as f_M(x):
f_M(x) = d(F_M(x))/dx = d(F(x)^3)/dx = 3 * F(x)^2 * f(x).
Step 3: Compute the expected value of the largest claim
The expected value of the largest claim (denoted as E[M]) is given by the integral of the product of the pdf and the variable x over the support of the distribution:
E[M] = ∫x * f_M(x) dx
= ∫x * 3 * F(x)^2 * f(x) dx
To evaluate this integral, you would need the specific form of the common density function f(x) and the cumulative distribution function F(x). However, the general formula for the expected value of the largest claim is provided above.

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The percentile value to construct a 90% bootstrap confidence interval for the true mean amount of ammonium in the rainwater is equals to 5%.

If the bootstrap distribution is approximately symmetric, we can construct a confidence interval by finding the percentiles in the bootstrap distribution so that the proportion of bootstrap statistics between the percentiles matches the desired confidence level. We have a forest ranger which select a random rainwater sample from a watershed area in tennessee with

Sample size, n = 10

Ranger measures the amount of ammonium in each sample. Measurements to construct a 90% bootstrap confidence interval for true mean amount of ammonium in the rainwater. We have to determine the p-value for her ordered. Now,

The percentile bootstrap interval is just the interval between the 100×(α/2)100 and 100×(1−α/2) percentiles of the distribution of θ estimates obtained from resampling, where θ represents a parameter of interest and α is the level of significance. but we have to determine percentile value for 90% confidence interval. Here, level of significance for 90% is α = 1 - 0.90 = 0.10, α/2 = 0.05

So, percentile value = α/2 = 0.05

= 5%

The number of the bootstrap sample that must be chopped off to produce a 90% confidence interval is N = 10 ×α/2

=> N = 10× 0.05 = 0.5

Hence, required percentile value is 5%.

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It takes Marilyn approximately 6.64 seconds to travel 49.5 yards.

A logarithm is the inverse operation of exponentiation. In other words, it is a way to find the exponent that a certain base must be raised to in order to produce a given number.

To solve the problem, you can use a geometric series formula. Let's say the remaining distance to the goal is d at time t. Then, Marilyn moves 1/2d every second, so after one second, the remaining distance is 1/2d, after two seconds, it's 1/4d, after three seconds, it's 1/8d, and so on.

So, the distance remaining at time t is given by the formula:

d(t) = d(0) * [tex](1/2)^t[/tex]

where d(0) is the initial distance remaining.

To find how long it takes to travel 49.5 yards, we need to solve for t when d(t) = 0.5 yards (since Marilyn moves half the remaining distance every second).

0.5 = d(0) * [tex](1/2)^t[/tex]

d(0) = 49.5 yards, so we have:

0.5 = 49.5 * [tex](1/2)^t[/tex]

Dividing both sides by 49.5:

0.01 = [tex](1/2)^t[/tex]

Taking the logarithm of both sides (using any base):

log(0.01) = log([tex](1/2)^t[/tex])

log(0.01) = t * log(1/2)

Solving for t:

t = log(0.01) / log(1/2) = 6.64 seconds (rounded to two decimal places)

Therefore, it takes Marilyn approximately 6.64 seconds to travel 49.5 yards.

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The area of the shape as shown in the picture is 68.76 m².

Area is the region bounded by a plane shape.

To calculate the area of the picture above, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the area is 68.76 m².

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The required probability of  more than five students being born on Christmas Day as per total of 1095 students is approximately 0.0735.

Let X be the number of students in the college who were born on Christmas Day.

Birth rates are constant throughout the year,

Assume that X follows a binomial distribution with

n = 1095

and p = 1/365,

where n is the total number of students in the college

And p is the probability that a student is born on Christmas Day.

The probability of more than five students being born on Christmas Day can be written as,

P(X > 5) = 1 - P(X ≤ 5)

Use the normal approximation to the binomial distribution to estimate P(X ≤ 5)

And then subtract this value from 1 to obtain an estimate of P(X > 5).

Use the normal approximation,

First check if the conditions for using it are met.

For a binomial distribution with n trials and probability of success p, the mean and standard deviation are,

μ = np

σ = √(np(1-p))

here, we have,

μ = 1095 × (1/365)

  = 3

σ = √(1095 ×(1/365) × (1 - 1/365))

  ≈ 1.73

Expected value is greater than 5 .

And the standard deviation is not too small ( σ > 1),

Use the normal approximation to the binomial distribution.

Using the continuity correction, we can rewrite P(X ≤ 5) ,

P(X ≤ 5) ≈ P(Z ≤ (5.5 - μ) / σ)

where Z is a standard normal variable.

Substituting the values for μ and σ, we get,

P(X ≤ 5) ≈ P(Z ≤ (5.5 - 3) / 1.73)

≈ P(Z ≤ 1.45)

≈ 0.9265

Using a standard normal table

P(Z ≤ 4.39) ≈ 0.9265

Probability of fewer than or equal to 5 students being born on Christmas Day is very close to 1.

This implies,

Estimation of the probability of more than five students being born on Christmas Day as,

P(X > 5)

≈ 1 - 0.9265

≈ 0.0735

This means that the probability of more than five students being born on Christmas Day is extremely small.

Conclude that it is unlikely that more than five students were born on Christmas Day.

Therefore, the probability of  more than five students being born on Christmas Day is approximately 0.0735.

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If we multiply 21 by 4, we get 84 .the value of k is 84, as it is 4 times as many as 21.

Multiplication is a mathematical operation that combines two or more numbers to find their product. It is an operation of repeated addition or scaling up of a number. In multiplication, the numbers being multiplied are called factors, and the result is called the product. Multiplication is denoted by the "×" symbol or by placing the numbers adjacent to each other.

The value of k is 4 times as many as 21," we can break it down as follows:

"4 times" means multiplication, where we are multiplying a number by 4.

"As many as" implies equality, meaning the value on one side of the comparison is equal to the value on the other side.

"21" is a specific number mentioned in the statement.

Therefore,  if we multiply 21 by 4, we get 84 .the value of k is 84, as it is 4 times as many as 21.

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By answering the presented question, we may conclude that The resulting true inequality is: 25 ≤ 27.

In mathematics, an inequality is a non-equal connection between two of a expressions or values. As a result, imbalance leads to inequity. In mathematics, an inequality connects two values that are not equal. Inequality is not the same as equality. When two values are not equal, the not equal symbol is typically used (). Various disparities, no matter how little or huge, are utilised to contrast values. Many basic inequalities may be solved by altering the two sides until just the variables remain. Yet, a lot of factors contribute to inequality: Negative values are split or added on both sides. Exchange left and right.

inequality: -125 ≥ -135

-125 ÷ -5 ≤ -135 ÷ -5

25 ≤ 27

The resulting true inequality is: 25 ≤ 27.

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Step-by-step explanation:

We can use the kinematic equations of motion to solve this problem. Let's assume the initial velocity of the snowball is 18 feet per second and its initial height is 25 feet. Also, we know that the acceleration due to gravity is -32.2 feet per second squared (assuming downward direction as negative).

To find out when the snowball hits the ground, we can use the equation:

h = 25 + 18t - 16t^2

where h is the height of the snowball at time t. We want to find the value of t when h = 0 (since the snowball hits the ground at that point). Therefore, we can rewrite the equation as:

16t^2 - 18t - 25 = 0

Solving for t using the quadratic formula, we get:

t = (18 ± √(18^2 + 41625))/(2*16)

t = 2.25 seconds or -0.875 seconds

Since time cannot be negative, the snowball hits the ground after 2.25 seconds.

To find the maximum height the snowball reaches, we can use the fact that the maximum height occurs at the vertex of the parabolic trajectory. The x-coordinate of the vertex is given by:

t = -b/2a

where a and b are the coefficients of the quadratic equation. In this case, a = -16 and b = 18, so:

t = -18/(2*(-16)) = 0.5625 seconds

To find the corresponding height, we can substitute t = 0.5625 seconds into the equation for h:

h = 25 + 18(0.5625) - 16(0.5625)^2

h = 28.2656 feet

Therefore, the maximum height the snowball reaches is 28.2656 feet.