A tangent function has an amplitude (steepness) of 3, period of π, a transformation of π/2 to the right, and a transformation down 1. What is the equation for this trigonometric function?

The domain of the piecewise function g of x is all real numbers, except for x = 2, which is the point at which the two functions overlap. Therefore, the domain is (–∞, 2) ∪ (2, ∞).

A domain is a collection of computers and devices connected to one another through a network. It is a logical grouping of computers and devices, such as a local area network (LAN) or a wide area network (WAN). Each device within the network is assigned a unique address, allowing it to communicate with other devices within the network. Domains can also be used to control access to resources, such as files, folders, printers, and databases. Domains can be used to authenticate users and set permissions, which determine the type of access a user has to the domain’s resources. This is commonly used in businesses and organizations to ensure that only authorized personnel have access to sensitive information.

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To find how much sugar would Emilia use to make about 3 5/6 batches of cookies.

1 1/8 cups of sugar

Next, we need to convert the mixed number to an improper fraction:

1 1/8 = (8 + 1) / 8 = 9/8

So, the amount of sugar needed for one batch of cookies is:

9/8 cups of sugar

To find the total amount of sugar needed for 3 5/6 batches, we can multiply the amount of sugar per batch by the number of batches:

(9/8 cups of sugar) x (23/6 batches) = 69/48 cups of sugar

thus, Emilia would need 69/48 cups of sugar to make 3 5/6 batches of cookies.

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Let A, B, and C be 3x3 matrices such that det(A) =2, det(C) = 4, and 2A^TB^-1 = C the determinant of matrix B is 4.

To find the determinant of matrix B, we can use the property of determinants that states that det(AB) = det(A)det(B). We can rearrange the given equation 2A^TB^-1 = C to get B = 2A^T C^-1. Then, we can take the determinant of both sides to get det(B) = det(2A^T C^-1).

Using the property of determinants, we can expand the right side of the equation to get det(B) = det(2)det(A^T)det(C^-1). Since the determinant of a scalar multiple of a matrix is the scalar multiple of the determinant, det(2) = 2^3 = 8. Also, the determinant of the transpose of a matrix is the same as the determinant of the original matrix, so det(A^T) = det(A) = 2.

Finally, the determinant of the inverse of a matrix is the reciprocal of the determinant of the original matrix, so det(C^-1) = 1/det(C) = 1/4.

Substituting these values back into the equation, we get det(B) = 8*2*(1/4) = 4. Therefore, the determinant of matrix B is 4.
det(B) = 4.

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About 5,000 more fans attended the third round finals than the third round time trials.

From the question, we are to find the approximate difference between the attendance of the third round finals and the third round time trials.

From the given data, we have:

Attendance Time             Trials                      Finals

1st round                           12,645                    17,352

2nd round                         16,234                    21,896

3rd round                          18,817                     23,773

Third round finals attendance = 23,773

Third round time trials attendance = 18,817

The difference between these two numbers is:

23,773 - 18,817 = 4,956

Rounding this to the nearest thousand gives:

4,956 ≈ 5,000

Hence, The number of fans that attended the third round finals than the third round time trials is about 5,000

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The equation that illustrates the commutative property of addition is (1+2)+3=1+(2+3)

The equation that illustrates the commutative property of addition is (1+2)+3=1+(2+3).

The commutative property of addition states that the order of the numbers does not matter when adding them together.

In this equation, the numbers are rearranged but the result is still the same. This is because the commutative property of addition allows for the numbers to be added in any order and still have the same result.

Here is the step-by-step explanation:

Identify the commutative property of addition, which states that a+b=b+a.

Look at the given equations and see which one follows the commutative property of addition.

The equation (1+2)+3=1+(2+3) follows the commutative property of addition because the numbers are rearranged but the result is still the same.

Therefore, the equation that illustrates the commutative property of addition is (1+2)+3=1+(2+3).

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1) a) X approaches negative infinity, f(x) approaches positive infinity.

b) The degree of f(x) is 3.

c) The maximum number of turning points for f(x) is 2.

d) The leading coefficient of f(x) is -1.

e) The end behavior of f(x) is "as x approaches infinity, f(x) approaches negative infinity; as x approaches negative infinity, f(x) approaches positive infinity.

2) a) a) The end behavior of g(x) is determined by the leading term x⁴. As x approaches infinity, g(x) approaches positive infinity. As x approaches negative infinity, g(x) approaches positive infinity.

b) The degree of g(x) is 4.

c) The maximum number of turning points for g(x) is 3.

d)The leading coefficient of g(x) is 1.

e)The end behavior of g(x) is "as x approaches infinity, g(x) approaches positive infinity; as x approaches negative infinity, g(x) approaches positive infinity.

Given f(x)=-x³ + 6x³ - 9x
a) The end behavior of f(x) is determined by the leading term -x³. As x approaches infinity, f(x) approaches negative infinity. As x approaches negative infinity, f(x) approaches positive infinity.
b) The degree of f(x) is 3, as the highest exponent in the polynomial is 3.
c) The maximum number of turning points for f(x) is 2, as it is one less than the degree of the polynomial.
d) The leading coefficient of f(x) is -1, as it is the coefficient of the leading term -x³.


Given g(x)=x(x+2)(x-2)²
b) The degree of g(x) is 4, as the highest exponent in the polynomial is 4.
c) The maximum number of turning points for g(x) is 3, as it is one less than the degree of the polynomial.
d) The leading coefficient of g(x) is 1, as it is the coefficient of the leading term x⁴.

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The probability of needing exactly 4 rolls to get doubles is 0.12.

What is meant by probability?

An event's probability is a numerical representation of how likely it is that the event will take place. In mathematical notation, it is written as a number between 0 and 1, or as a percentage between 0% and 100%. The higher an event's probability, the more likely it is to occur. In a sample space, there is a probability of 1 for each event. The probability formula states that the ratio between the number of favourable outcomes and the total number of outcomes determines the likelihood that an event will occur. Sets are used in the terminology of probability theory. A set is a grouping of various things.

From the figure,

The number of times we get doubles in 1 roll = 5

The number of times we get doubles in 2 rolls = 4

The number of times we get doubles in 3 rolls = 4

The number of times we get doubles in 4 rolls = 3

The number of times we get doubles in 5 rolls = 3

The number of times we get doubles in 6 rolls = 2

The number of times we get doubles in 7 rolls = 3

The number of times we get doubles in 8 rolls = 0

The number of times we get doubles in 9 rolls = 1

Total number of outcomes = 5+4+4+3+3+2+3+1  = 25

Number of doubles in 4 rolls = 3

The probability of needing exactly 4 rolls to get doubles = 3/25 = 0.12

Therefore the probability of needing exactly 4 rolls to get doubles is 0.12.

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The classification of the variables in the question above is  as follows:

Discrete quantitative data refers to data that can be counted in whole numbers and is often used to describe things that can be categorized into groups. like the number of people in a room or the number of cars in a parking lot.

Quantitative continuous data refers to data that can be measured on a continuous scale, such as time, temperature, or weight, like the temperature of a room or the weight of a person.

Qualitative nominal data refers to data that can be categorized into groups but cannot be measured or ranked, like the type of car someone drives or the color of someone's eyes.

Qualitative ordinal data refers to data that can be categorized into groups and can be ranked or ordered, like the level of education someone has achieved or the ranking of a sports team.

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Answer:

[tex]\frac{\sqrt{x+3} }{x+1}[/tex]

Step-by-step explanation:

nothing further can happen.

1) a) ω = 2πf = 2π(50) = 100π radians per second

b) 96.78m/s.

2) (a) T = 1/f = 1/12 seconds,

(b) ω = 2πf = 2π(12) = 24π radians per second.

3) original length of the pendulum is 9.0m.

4)  original length of the spiral spring is 20cm.

5)  the initial velocity of the football is 17.32m/s At the highest

Angular speed is the speed of the object in rotational motion. Distance traveled is represented as θ and is measured in radians. The time taken is measured in terms of seconds. Therefore, the angular speed is articulated in radians per second or rad/s.

1. (a) The angular speed of a body vibrating at 50 cycles per second is:

ω = 2πf = 2π(50) = 100π radians per second

(b) The stone is projected horizontally, so its initial vertical velocity is zero. The time taken for the stone to fall from the top of the tower to the ground is given by:

t = √(2h/g) = √(2×75/10) = √15

The horizontal distance traveled by the stone is:

d = vxt = (25m/s)×(√15) ≈ 96.78m

Therefore, the speed with which the stone strikes the ground is approximately 96.78m/s.

2. (a) The period of the motion is:

T = 1/f = 1/12 seconds

(b) The angular speed of the motion is:

ω = 2πf = 2π(12) = 24π radians per second

(c) The velocity at the middle of oscillation is zero, since this is the point of maximum displacement and therefore maximum potential energy.

(d) The acceleration at the end of oscillation is given by:

a = -ω²x = -(24π)²(0.02) = -11.52 m/s²

where x is the amplitude of the motion.

3. The period of a simple pendulum is given by:

T = 2π√(L/g)

where L is the length of the pendulum and g is the acceleration due to gravity. Therefore, we can write:

17 = 2π√(L/g) (1)

8.5 = 2π√[(L-1.5)/g] (2)

Dividing (2) by (1), we get:

1/2 = √[(L-1.5)/L]

Squaring both sides and simplifying, we get:

L = 9.0m

Therefore, the original length of the pendulum is 9.0m.

4. (a) Let the original length of the spiral spring be x. Then, using Hooke's law, we have:

5N = k(25cm - x) (1)

10N = k(30cm - x) (2)

where k is the spring constant. Solving for k in equation (1), we get:

k = 5N/(25cm - x)

Substituting into equation (2), we get:

10N = [5N/(25cm - x)](30cm - x)

Simplifying and solving for x, we get:

x = 20cm

Therefore, the original length of the spiral spring is 20cm.

(b) The pressure of the trapped air column in the capillary tube is balanced by the pressure of the atmosphere. When the tube is held horizontally, the length of the air column is the same as its length in the vertical position. Therefore, the length of the air column is 15cm.

When the tube is held vertically with the open end underneath, the length of the air column is given by:

L = 76cm - 20cm = 56cm

Therefore, the length of the air column is 56cm.

5. The horizontal and vertical components of the initial velocity of the football are:

v₀x = v₀cos(60°) = (20m/s)cos(60°) = 10m/s

v₀y = v₀sin(60°) = (20m/s)sin(60°) = 17.32m/s

At the highest

Hence, the answer to each question:

1) a) ω = 2πf = 2π(50) = 100π radians per second

b) 96.78m/s.

2) (a) T = 1/f = 1/12 seconds,

(b) ω = 2πf = 2π(12) = 24π radians per second.

3) original length of the pendulum is 9.0m.

4)  original length of the spiral spring is 20cm.

5)  the initial velocity of the football is 17.32m/s At the highest

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According to the information we can infer that the statement that establishes a correct interpretation of the model is the model associates a score of 80 with 2 hours of studying.

To select the correct statement we must replace the value of (t) in the equation and check the relationship between the results of the students in the test and the hours spent studying.

According to the above, if we replace t by two we can infer that the result would be y = 80 as shown below:

So the correct answer would be statement C.

On the other hand, to identify the percentage to which the number of seventh grade students who have a laptop is equivalent, we must add the total number of students in this grade and then find the percentage with a rule of three:

So the correct answer would be 42% because this value is the closest and we could approximate it.

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The number of weeks it will take Isla to complete her assignments is 2.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

We are given that;

Number of assignments=27

Time needed by isla=2.5 hrs

hour limit per day=5

Now,

To find out how many hours Isla will spend on her English assignments, we can multiply the number of assignments by the time it takes her to complete each assignment:

27 assignments * 2.5 hours per assignment = 67.5 hours

So Isla will spend a total of 67.5 hours on her English assignments.

To find out how many days it will take Isla to complete her assignments, we need to divide the total number of hours by the number of hours she can work per day:

67.5 hours / 5 hours per day = 13.5 days

Since Isla cannot complete a fraction of a day, she will need to round up to 14 days. So it will take Isla 14 days to complete her assignments.

To find out how many weeks it will take Isla to complete her assignments, we need to divide the total number of days by the number of days per week. Assuming a standard 7-day week, we have:

14 days / 7 days per week = 2 weeks

Therefore, by unitary method the answer will be 2 weeks.

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Answer:

x = -3 to x = 2

Step-by-step explanation:

The function is decreasing where the slope is negative, seen when the y-values decrease as the x-values increase. Your answer is correct.

Answer:

X is - 3 to x is 2

Step-by-step explanation:

Look at the x axis, the point where the curve slopes down is the decreasing point

Where x is - 3 is a peak point, it begins to slope from there and rises when x is 3

The average percentage change in population in California from 2000-2009 is 1.35% and population in 2015 will be 39306963.

What is average?

In mathematics, the average is a value that represents the central or typical value in a set of numbers. There are several types of averages, including the mean, median, and mode.

The mean is the most commonly used type of average, and it is calculated by adding up all the numbers in a set and then dividing the sum by the total number of numbers. For example, the mean of the set {3, 5, 8, 12} can be calculated as:

mean = (3 + 5 + 8 + 12) / 4 = 7

Now,

To calculate average of percentage change from 2000-2009

we have to add percentage change for every year

and that will be = 1.97+1.71+1.65+1.42+1.22+1.02+1.07+1.22+0.93

=12.21%

then average=12.21/9=1.35%

hence,

          The average percentage change in population in California from 2000-2009 is 1.35%.

The population in 2015 will be = 37000000 + (1.35)⁶ × 37000000/100

=37000000+2306963.15

=39306963

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The correct answer is option C. A graphic image showing a pair of similar polygons with an X-axis showing the value range from 0 to 16 and a Y-axis values from 0 to 16.

Polygons are two-dimensional shapes with straight sides that are joined together. They are closed shapes, meaning all the sides are connected. Polygons can have anywhere from three sides to an infinite number of sides. The most common types of polygons are triangles, quadrilaterals, pentagons, hexagons, and octagons.

This correct image is showing two polygons that are similar, or which have the same shape. This means that the sides of the two polygons are equal in length and each angle is the same. In other words, they are exactly the same shape, but can be different sizes. The X-axis and Y-axis values shown in the image are the coordinates of the points that make up the polygons. The X-axis values indicate the horizontal distance from the origin, while the Y-axis values indicate the vertical distance from the origin. By looking at the coordinates of the points that make up the polygons, we can see that the two polygons are similar.

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The years 1960–1965 saw the greatest change in temperature variation per unit of time.

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

The graph for average temperature variation v/s time is given.

To find during which year maximum temperature variation with time:

We have to find the year with maximum magnitude of slope |m|.

Slope m = [tex]\frac{y_2-y_1}{x_2-x_1}\\[/tex]

Consider m for year 1950-1955:

m = 0 [line parallel to x-axis]

Consider m for year 1955-1960:

[tex]\frac{-0.05-0}{1955-1960}\\\\= 0.01[/tex]

Consider m for year 1960-1965:

[tex]\frac{-0.15-0}{1965-1960}\\\\= -0.03[/tex]

Consider m for year 1965-1970:

m = 0.01 {same as of 1955-1960}

Consider m for year 1970-1975:

m = 0 [line parallel to x-axis]

Consider m for year 1975-2000:

[tex]\frac{0.4-(-0.1)}{2000-1975}\\\\= 0.02\\[/tex]

|m| is maximum for year 1960-1965

Hence, the temperature variation changed the most per unit time in the year 1960-65.

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The system of equations that does not have a solution is {(x-2y=-3),(-2x+4y=6):}.

To see why, let's first look at the other two systems of equations:

{(4x+6y=12),(6x+9y=12):}

If we divide the first equation by 2, we get:

{(2x+3y=6),(6x+9y=12):}

If we then multiply the first equation by -3, we get:

{(-6x-9y=-18),(6x+9y=12):}

If we add these two equations together, we get:

{0= -6}

This is a false statement, so there is no solution for this system of equations.

Similarly, for the system of equations {(x+y=-1),(4x-3y=24):}, we can multiply the first equation by -4 and add the two equations together to get:

{-4x-4y=4, (4x-3y=24):}

{-7y=28}

This equation has a solution, so this system of equations does have a solution.

However, for the system of equations {(x-2y=-3),(-2x+4y=6):}, if we multiply the first equation by -2 and add the two equations together, we get:

{-2x+4y=6, (-2x+4y=6):}

{0=0}

This equation is always true, so there are an infinite number of solutions for this system of equations. Therefore, this system of equations does not have a unique solution.

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A population consists of five members 2,3,6,8,1). consider all possible samples of size two which can be doamn with replacement from this positioning population.  The mean is  4 and standard deviation of the population is 1.67. The mean and standard error of sample mean (x) from the sampling distribution of x is 4 and 1.18 respectively

i) The mean and standard deviation of the population:

Mean = (2+3+6+8+1)/5 = 20/5 = 4

Standard deviation = √[(2-4)²+(3-4)²+(6-4)²+(8-4)²+(1-4)²]/5 = √14/5 = 1.67


ii) The mean and standard error of sample mean (x) from the sampling distribution of x:

Mean of sample mean = Mean of population = 4

Standard error of sample mean = Standard deviation of population/√n = 1.67/√2 = 1.18


The mean of a population is calculated by adding up all the values and dividing by the number of values in the population. The standard deviation of a population is calculated by finding the difference between each value and the mean, squaring those differences, adding them up, and then dividing by the number of values in the population.

The mean of the sample mean is the same as the mean of the population, and the standard error of the sample mean is the standard deviation of the population divided by the square root of the sample size.

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Answer:

Step-by-step explanation:

It is given that ,

tanA=3/4 , [tex]\pi < A < \frac{3\pi }{2}[/tex]

so , angle are in 3rd Quadrant .

cosB = -15/17 ,[tex]\frac{\pi}{2} < B < \pi[/tex]

So, angle B are in 2nd Quadrant

We use Compound formula of tan(A+B)

[tex]tan(A+B) = \frac{tanA + tanB}{1- tanAtanB}[/tex]         ..........(1)

To use this formula , we need to find the value of tanA and tanB.

tanA = 3/4   ........ given

cos B =-15/17

Using Identity ,

[tex]sin^{2}B + cos^{2}B=1[/tex]

put the value of cosB

[tex]sin^{2}B + (-\frac{15}{17})=1\\ sin^{2}B = 1 - \frac{225}{289} \\sin^{2}B = \frac{64}{289} \\sinB = \frac{8}{17}[/tex]

we know that ,

tanB = sinB/cosB

put the value of sinB and CosB

[tex]tanB = \frac{\frac{8}{17} }{-\frac{15}{17}} \\tanB = - \frac{8}{15}[/tex]

[tex]tanB = -(-\frac{8}{15}) \\tanB = \frac{8}{15}[/tex]the value of tan in 2nd quadrant are negative .

We find the value of tanB and next we put the value of tanA and tanB in

equation(1)

[tex]tan(A+B) = \frac{tanA + tanB}{1- tanAtanB}\\tan(A+B) = \frac{\frac{3}{4}+\frac{8}{15}}{1 - \frac{3}{4}\frac{8}{15} } \\tan(A+B) = \frac{\frac{77}{60} }{1 - \frac{24}{60} } \\tan(A+B) = \frac{\frac{77}{60} }{\frac{36}{60} } }\\tan(A+B) = \frac{77}{36}[/tex]

Hopeful,this answer will help you!

If any wrong in this answer please let me know

The forecasted sales volume is 34.116 thousand Euro if the investment volume is planned to be 30 thousand Euro.

Let's solve this problem step by step:

Calculate the correlation coefficient (r) using the formula:
r = (ΣXY - (ΣX)(ΣY)/n) / sqrt([(ΣX^2 - (ΣX)^2/n)(ΣY^2 - (ΣY)^2/n)])

Plug in the given values into the formula:
r = (126.54 - (22)(66)/12) / sqrt([(45.8 - (22)^2/12)(369.94 - (66)^2/12)])

Simplify the formula and solve for r:
r = (126.54 - 121) / sqrt([(45.8 - 40.333)(369.94 - 363)])
r = 5.54 / sqrt[(5.467)(6.94)]
r = 5.54 / 4.967
r = 1.115

Make conclusions about the closeness of the linear relationship based on the value of r:
Since the value of r is close to 1, this indicates a strong positive linear relationship between the investments (X variable) and the main product's sales (Y variable).

Find the linear regression from variable Y to the X using the formula:
Y = a + bX

Calculate the slope (b) using the formula:
b = (ΣXY - (ΣX)(ΣY)/n) / (ΣX^2 - (ΣX)^2/n)

Plug in the given values into the formula and solve for b:
b = (126.54 - (22)(66)/12) / (45.8 - (22)^2/12)
b = 5.54 / 5.467
b = 1.013

Calculate the intercept (a) using the formula:
a = (ΣY - b(ΣX))/n

Plug in the given values into the formula and solve for a:
a = (66 - 1.013(22))/12
a = 44.714/12
a = 3.726

Plug in the values of a and b into the linear regression formula:
Y = 3.726 + 1.013X

Forecast the sales volume if the investment volume is planned to be 30 thousand Euro by plugging in the value of X into the linear regression formula:
Y = 3.726 + 1.013(30)
Y = 3.726 + 30.39
Y = 34.116

Therefore, the forecasted sales volume is 34.116 thousand Euro if the investment volume is planned to be 30 thousand Euro.

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Answer:

60

Step-by-step explanation:

24 + 36 = 60

You can use the Gold Digger for the distributive property! * Factor as if you want to find the Greatest Common Factor.

The value of x to the nearest degree is 30°.

What is Triangle ?

A triangle is one that has three sides, three angles, and whose total angles is always 180 degrees.

Three line segments are linked end to end to make a triangle, a two-dimensional geometric structure with three angles. These line segments are known as sides, and their intersections are known as vertices.

The measurements of a triangle's sides and angles are used to categorize it.

We can use trigonometric ratios to get the value of x in the right triangle given:

sin(x) = opposite/hypotenuse

[tex]sin(x) = 8/17x = sin^{-1(8/17)}x = 29.74^{o} $ (approx.) $[/tex]

Therefore, the value of x to the nearest degree is 30°.

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The smallest number among the given options is 0.125.

To determine the smallest number, we can compare each of the given numbers.

0.625 > 0.25 > 0.375 > 0.5 > 0.125

As we can see, the smallest number is 0.125, which is option E.

Comparison symbols are those that tell us whether one number is greater than, less than, or equal to another. The symbols are:

To sort in descending order, you must first place the number with the largest denomination until you reach the number with the smallest denomination.

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Answer:

Step-by-step explanation:

If x represents one day of sales and x=12, then we can substitute that value into the equation to find the total number of pencils sold:

y = 160x

y = 160(12)

y = 1920

So the supply store sold a total of 1920 pencils on the day when x=12.

The number of cubic centimeters of space that 3 ping pongs would have is 339. 29 cm ³

A ping pong ball takes the shape of a sphere and the volume of a sphere is ;

= 4 / 3 x π x radius ³

Given the radius of 3 cm, the volume of one ping pong ball is :

= 4 / 3 x π x 3 ³

= 113. 09734 cm ³

If there are three ping pong balls, the volume would then be :

= 113. 09734  x 3 ping pongs

= 339. 29 cm ³

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The expression √9−9x2 can be written as a trigonometric expression 3sin(θ) using the substitution x = cos(θ).

To write the expression as a trigonometric expression using the suggested substitution, we can substitute x = cos(θ) into the expression and simplify:

√9−9x2 = √9−9(cos(θ))^2

= √9−9(cos^2(θ))

= √9(1−cos^2(θ))

= √9(sin^2(θ))

= 3sin(θ)

Therefore, the expression √9−9x2 can be written as a trigonometric expression 3sin(θ) using the substitution x = cos(θ).

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Answer:

6

Step-by-step explanation:

[tex]1\frac{1}{2}[/tex] ÷ [tex]\frac{1}{4}[/tex] = [tex]\frac{3}{2}[/tex] ÷ [tex]\frac{1}{4}[/tex] = [tex]\frac{3}{2}[/tex] × [tex]\frac{4}{1}[/tex] = [tex]\frac{12}{2}[/tex] = 6  

Therefore, the rate per period (i) is 0.00708333 and the number of periods (n) is 84. The future value of the annuity is $34563.89.

To find i (the rate per period) and n (the number of periods) for the given annuity, we need to use the formula for the future value of an annuity:

FV = PMT × [(1 + i)^n - 1] / i

Where FV is the future value, PMT is the periodic payment, i is the rate per period, and n is the number of periods.

Given:
PMT = $305
i = 8.5% / 12 = 0.00708333 (since the interest is compounded monthly)
n = 7 × 12 = 84 (since there are 12 months in a year and the deposits are made for 7 years)

Plugging these values into the formula, we get:

FV = $305 × [(1 + 0.00708333)^84 - 1] / 0.00708333

FV = $305 × [1.80722 - 1] / 0.00708333

FV = $305 × 0.80722 / 0.00708333

FV = $34563.89

Therefore, the rate per period (i) is 0.00708333 and the number of periods (n) is 84. The future value of the annuity is $34563.89.

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