a
b
c
d
Number of Laps
Which answer is the best estimate of the residual value
when x = 5?
0.25
-3
3
-0.25

The p-value is greater than the significance level of 0.05 do not have enough evidence to reject the null hypothesis.

We cannot conclude that the proportion of adults own a cat is greater than 30% based on the given data.

To determine the p-value in this scenario, we need to conduct a hypothesis test.

Let's define our hypotheses:

Null hypothesis (H0):

The proportion of adults who own a cat is equal to or less than 30%.

Alternative hypothesis (Ha):

The proportion of adults who own a cat is greater than 30%.

Next, we can calculate the test statistic using the sample data.

The test statistic for this situation is the z-score measures how many standard deviations the sample proportion is away from the hypothesized proportion under the null hypothesis.

Let's calculate the sample proportion of adults who own a cat:

[tex]\^p[/tex] = 22/68

≈ 0.3235

Now, we need to calculate the standard error measures the variability of the sample proportion:

SE = [tex]\sqrt{[(\^p(1-\^p))/n][/tex]

= √[(0.3235(1-0.3235))/68]

≈ 0.0584

To find the z-score, we use the formula:

z = [tex](\^p - P_0)/SE[/tex]

= (0.3235 - 0.30)/0.0584

≈ 0.4046

Using a standard normal distribution table or a statistical calculator, we can find the p-value associated with the calculated z-score.

The p-value is the probability of obtaining a test statistic as extreme or more extreme than the one observed, assuming the null hypothesis is true.

For a one-tailed test with the alternative hypothesis stating that the proportion is greater than 30% want to find the area to the right of the z-score.

Consulting the standard normal distribution table find that the area to the right of 0.4046 is approximately 0.3431.

For similar questions on p-value

https://brainly.com/question/13786078

#SPJ11

The relation and equation that is modelled by the graph is y = x - 1.

To determine the relation and equation that is modelled by the graph, we must analyze the characteristics of the graph.The graph is a straight line that passes through the points (0, -1) and (4, 3).

The slope of the line can be determined by using the slope formula:slope = (y2 - y1) / (x2 - x1) = (3 - (-1)) / (4 - 0) = 4/4 = 1

Therefore, the slope of the line is 1. We can use the point-slope form of the equation of a line to determine the equation of the line.y - y1 = m(x - x1)

where y1 = -1, x1 = 0, and m = 1Substituting these values, we get:y - (-1) = 1(x - 0)y + 1 = x Simplifying this equation, we get the relation y = x - 1.

To learn more about : graph

https://brainly.com/question/19040584

#SPJ8

The exponential function that models this relationship is given as follows:

[tex]y = 8(0.5)^x[/tex]

An exponential function has the definition presented according to the equation as follows:

[tex]y = ab^x[/tex]

In which the parameters are given as follows:

The graph of the function in this problem crosses the y-axis at y = 8, hence the parameter a is given as follows:

a = 8.

When x increases by one, y is halved, hence the parameter b is given as follows:

b = 0.5.

Hence the function is given as follows:

[tex]y = 8(0.5)^x[/tex]

More can be learned about exponential functions at brainly.com/question/2456547

#SPJ1

Answer: 544,000 or 500,000

Step-by-step explanation: if you try to round the equation you will only have  544,000  cause 6 can round to 10 so meaning  it will be 544,000

Answer:

m∪n = {0, 1, 2, 4, 6, 8, 9, 10, 12, 14, 16, 18, 20, 22, 24, 25, 26, 28, 36, 49, 64}.

Step-by-step explanation:

To find the intersection (m∩n) of the set of square numbers less than 80 and the set of non-negative even numbers under 30, we need to find the numbers that are in both sets.

The set of square numbers less than 80 is: {0, 1, 4, 9, 16, 25, 36, 49, 64}

The set of non-negative even numbers under 30 is: {0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28}

The numbers that are in both sets are: {0, 4, 16}

Therefore, m∩n = {0, 4, 16}.

To find the union (m∪n) of the set of square numbers less than 80 and the set of non-negative even numbers under 30, we need to find all the unique numbers that are in either set.

The set of square numbers less than 80 is: {0, 1, 4, 9, 16, 25, 36, 49, 64}

The set of non-negative even numbers under 30 is: {0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28}

Combining both sets and removing duplicates, we get:

{0, 1, 2, 4, 6, 8, 9, 10, 12, 14, 16, 18, 20, 22, 24, 25, 26, 28, 36, 49, 64}

Therefore, m∪n = {0, 1, 2, 4, 6, 8, 9, 10, 12, 14, 16, 18, 20, 22, 24, 25, 26, 28, 36, 49, 64}.

Answer:

To find the rules for (fg)(x) and (gf)(x), we need to evaluate the composite functions.

(fg)(x) = f(g(x)) = f(sqrt(x - 5)) = (sqrt(x - 5))^2 + 5 = x - 5 + 5 = x

(gf)(x) = g(f(x)) = g(x^2 + 5) = sqrt(x^2 + 5 - 5) = sqrt(x^2) = |x|

Therefore, the rules for (fg)(x) and (gf)(x) are:

(fg)(x) = x

(gf)(x) = |x|

Step-by-step explanation:

The mass of one art book is 0.8 kg, and the mass of one biology book is 0.6 kg

Let's denote the mass of one art book by "a" and the mass of one biology book by "b".

From the given information, we have two equations:

6a + 4b = 7.2 (equation 1)

2a + 3b = 3.4 (equation 2)

We can solve for "a" and "b" by using any method of solving linear equations, such as substitution or elimination.

Here, we'll use elimination method. Multiplying equation 2 by 3 and subtracting it from equation 1 multiplied by 2, we get:

12a + 8b - (6a + 9b) = 14.4 - 10.2

6a - b = 4.2 (equation 3)

Multiplying equation 2 by 2, we get:

4a + 6b = 6.8 (equation 4)

Multiplying equation 3 by 6, we get:

36a - 6b = 25.2 (equation 5)

Adding equations 4 and 5, we get:

40a = 32

a = 0.8 kg

Substituting this value of "a" in equation 2, we get:

2(0.8) + 3b = 3.4

1.6 + 3b = 3.4

3b = 1.8

b = 0.6 kg

Therefore, the mass of one art book is 0.8 kg, and the mass of one biology book is 0.6 kg.

For more such questions on mass , Visit:

https://brainly.com/question/28916233

#SPJ11

The length of FG is approximately 15.3 cm.

To calculate the length of FG using Pythagoras' theorem, we need to find the length of the hypotenuse (FG) of a right triangle. Let's denote the length of FG as x.

According to Pythagoras' theorem, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, we have:

[tex]FG^2 = GH^2 + FH^2[/tex]

Given that GH = 8 cm and FH = 13 cm, we can substitute these values into the equation:

[tex]x^2 = 8^2 + 13^2[/tex]

[tex]x^2 = 64 + 169[/tex]

[tex]x^2[/tex] = 233

To find x, we take the square root of both sides:

x = √233 ≈ 15.26 cm (rounded to 1 decimal place)

Therefore, the length of FG is approximately 15.3 cm.

For such more questions on  length of FG

https://brainly.com/question/31613415

#SPJ11

Lucia spending $8 on a spin class occurs in the product market. Kenji earning $350 per week occurs in the factor market. Kenji spending $150 on software occurs in the product market.

To determine whether each event occurs in the factor market or the product market, we need to consider whether it involves the exchange of factors of production (such as labor or capital) or the exchange of final goods and services.

1. Lucia spends $8 to take a spin class: This event occurs in the product market. Lucia is using her income to purchase a service (spin class) provided by Silver's Gym.

2. Kenji earns $350 per week working for Silver's Gym: This event occurs in the factor market. Kenji is providing his labor as a trainer, and Silver's Gym is paying him for his services. This involves the exchange of labor (a factor of production) for wages.

3. Kenji spends $150 to purchase software from Casement: This event occurs in the product market. Kenji is using his income to purchase a product (software) from Casement. This involves the exchange of final goods and services.

In summary:

- Lucia spending $8 on a spin class occurs in the product market.

- Kenji earning $350 per week working for Silver's Gym occurs in the factor market.

- Kenji spending $150 to purchase software from Casement occurs in the product market.

For more such questions on product, click on:

https://brainly.com/question/1712056

#SPJ8

Answer:

To obtain a function g whose graph is a reflection in the x-axis of the graph of f(x) = |4x - 1| - 6, we can simply take the negative of f(x). Thus, the function g(x) is given by:

g(x) = -|4x - 1| + 6

Step-by-step explanation:

Answer: [tex]g(x) = -4x + 9[/tex]

Step-by-step explanation:

So we know that:

[tex]f(x)=4x+9[/tex]

To reflect across the y-axis, instead of x, use -x. Therefore: [tex]g(x)=f(-x)=4(-x)+9[/tex]

Simplified as:

[tex]g(x)=-4x+9[/tex]

Which is the answer.

Hope it helped :D

Please mark me brainliest

This is how you simplify.

1. Revised Net Operating Income = $66,760

2. Revised Net Operating Income  =$64,640

3. Revised Net Operating Income  =$52,

1. If the sales volume increases by 40 units:

So, New Sales = 8,700 units + 40 units = 8,740 units

and, New Contribution Margin =

= $14.00 x 8,740 units

= 122, 360

New Fixed Expenses remain the same at $55,600

Then, Revised Net Operating Income

= New Contribution Margin - New Fixed Expenses

= 122360 - 55600

= 66,760.

2. If the sales volume decreases by 40 units:

New Sales = 8,700 units - 40 units = 8,660 units

New Contribution Margin

= 14 x 8660

= 121,240

New Fixed Expenses remain the same at $55,600

Then, Revised Net Operating Income

= New Contribution Margin - New Fixed Expenses

= 65,640

3. If the sales volume is 7,700 units:

New Sales = 7,700 units

New Contribution Margin

= 14 x 7700

= 107,800

New Fixed Expenses remain the same at $55,600

Then, Revised Net Operating Income

= New Contribution Margin - New Fixed Expenses

= 52, 200

Learn more about Income Format here:

https://brainly.com/question/15312142

#SPJ1

If we assume that the three measurements represent the sides of a cube, the surface area would be 8214 square feet.

To calculate the surface area of an object, we need more information about its shape.

Simply stating "37 ft" three times does not provide enough details to determine the surface area.

Surface area is typically calculated for three-dimensional objects such as cubes, spheres, cylinders, or prisms.

Each shape has a specific formula to calculate its surface area.

If we assume that all three measurements, 37 ft, represent the sides of a cube, we can calculate the surface area of the cube.

In a cube, all sides are equal in length.

The surface area of a cube is given by the formula: 6 [tex]\times[/tex] side [tex]\times[/tex] side, where "side" represents the length of one side of the cube.

In this case, if all sides of the cube measure 37 ft, we can substitute this value into the formula:

Surface Area = 6 [tex]\times[/tex] side [tex]\times[/tex] side

[tex]= 6 \times 37 ft \times37 ft[/tex]

[tex]= 6 \times 1369 ft^2[/tex]

[tex]= 8214 ft^2[/tex]

Therefore, if we assume that the three measurements represent the sides of a cube, the surface area would be 8214 square feet.

However, without specifying the shape or providing additional information, it is not possible to determine the surface area accurately.

For similar question on surface area.

https://brainly.com/question/951562

#SPJ8

Answer:

A probability distribution for a discrete random variable X assigns probabilities to each possible value of X such that the sum of all probabilities is equal to 1. In this case, the possible values of X are 0, 1, 4, 5, and 6. You have provided the probabilities for X = 0, X = 1, and X = 5 as 0.30, 0.19, and 0.27 respectively.

The sum of these probabilities is 0.30 + 0.19 + 0.27 = 0.76. Since the sum of all probabilities must be equal to 1, the sum of the probabilities for X = 4 and X = 6 must be equal to 1 - 0.76 = 0.24.

Therefore, you can assign any non-negative values to P(X = 4) and P(X = 6) such that their sum is equal to 0.24 to give a legitimate probability distribution for the discrete random variable X.

For example, one possible probability distribution could be:

P(X = x) 0: 0.30 1: 0.19 4: 0.12 5: 0.27 6: 0.12

The probability that more than 340 out of 400 commercial airline flights will arrive on time, using the normal approximation, is approximately 0.2946 or 29.46%.

To find the probability that more than 340 out of 400 commercial airline flights will arrive on time, we can use the normal approximation to the binomial distribution.

First, let's calculate the mean (μ) and standard deviation (σ) of the binomial distribution using the given information:

Mean (μ) = n × p

= 400 × 0.84

= 336

Standard Deviation (σ) = √(n × p × (1 - p))

= √(400 × 0.84 × 0.16)

= √(53.76)

≈ 7.34

Next, we can use the normal approximation by converting the binomial distribution into a normal distribution with the calculated mean and standard deviation.

Let X be the number of flights that arrive on time out of the 400 flights. We want to find the probability P(X > 340), which is equivalent to finding the probability of Z being greater than (340 - μ) / σ.

Z = (340 - μ) / σ

= (340 - 336) / 7.34

≈ 0.546

To find the probability P(Z > 0.546), we can consult the standard normal distribution table or use a calculator that provides the cumulative distribution function (CDF) of the standard normal distribution.

Using a standard normal distribution table, we find that the probability P(Z > 0.546) is approximately 0.2946.

Therefore, the probability that more than 340 out of 400 commercial airline flights will arrive on time, using the normal approximation, is approximately 0.2946 or 29.46%.

for such more question on probability

https://brainly.com/question/13604758

#SPJ11

The radius of the given circle is: 4.4

The three main trigonometric ratios are expressed as:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

Thus, we can find the radius CD using trigonometric ratios.

AC = 16 and it divides angle C into two equal parts.

Since Point D is a tangent and also a right angle, then we can say that:

CD/16 = cos (148/2)

CD = 16 * 0.2756

CD = 4.4

Read more about Trigonometric Ratios at: https://brainly.com/question/13276558

#SPJ1

To solve this problem, I need to compare the time it will take for Abiana to reach the opposite corner of the rectangular park using a scooter and walking, respectively.

First, I need to find out the distance Abiana will need to cover if she goes around the park. To do this, I can use the Pythagorean Theorem, which states that the square of the length of the hypotenuse (in this case, the distance Abiana needs to travel) is equal to the sum of the squares of the lengths of the other two sides.

So, the square of the distance Abiana needs to travel is equal to (3/4)^2 + 1^2 = 25/16, which means the distance itself is the square root of 25/16 miles, or 5/4 miles.

If Abiana takes a scooter, it will take her 8 minutes to travel 1 mile, so it will take her 8 * 5/4 = 10 minutes to travel the distance around the park.

On the other hand, if Abiana walks directly across the grass, it will take her 20 minutes to travel 1 mile, so it will take her 20 * 5/4 = 25 minutes to travel the diagonal distance of the rectangular park.

Therefore, taking the scooter is the faster mode of transportation, as it will take Abiana 10 minutes to travel the distance around the park, whereas she will need 25 minutes to walk directly across.

Answer:

10

Step-by-step explanation:

9x4=36

36-5-9-12=10

Therefore, your answer is 10

To double check, redo math opposite:

5+9+10+12=36

36 divided by 4 = 9

Answer: 10

Step-by-step explanation:

You can create an equation for this and then solve.   Let's call that 4th number x

Add all the numbers and divide by how many.  That is your average

(5+9+12+x)/4 =9                    >Multiply both sides by 4

5+9+12+x =36                       >Simplify numbers on left

26 + x = 36                            > subtract 26 from both sides

x = 10

Experimental probability refers to the likelihood of an event occurring based on actual experimental results. If a group of students in a communications course is required to start a blog on a topic of their choice, and many have already begun blogging, and the three categories are: pop culture, literature, and business.

The following details and explanation help to find the probability of the blog being about pop culture, which is a topic of the group's choice.There are three categories, including pop culture, literature, and business.

The next blog will be about pop culture. That is, there is one successful result, which is the number of blogs that have been written about pop culture so far.

There is a total of five blogs written on pop culture, literature, and business. Hence, the experimental probability of the next blog being about pop culture can be obtained as follows:The experimental probability formula is:P(event) = number of successful outcomes ÷ total number of possible outcomesTherefore, P(event) = 5 ÷ 10= 1/2= 0.5 (as a decimal)

Therefore, the experimental probability that the next blog started will be about pop culture is 0.5, which is the chance that the blog will be about pop culture based on actual experimental results. This means that there is a 50% chance that the next blog started will be about pop culture.

For more such questions on pop culture

https://brainly.com/question/30653877

#SPJ8

Based on the given exchange rate, one would receive approximately TT 23.65 for $5.50.

We are given the exchange rate that $1.00 is equivalent to TT 4.30. This means that for every US dollar, you would receive 4.30 Trinidad and Tobago dollars.

To calculate the approximate amount in TT for $5.50, we need to multiply $5.50 by the exchange rate:

$5.50 * TT 4.30 / $1.00

By multiplying the dollar amount ($5.50) by the exchange rate (TT 4.30 / $1.00), we are effectively converting the currency from US dollars to Trinidad and Tobago dollars.

Calculating the multiplication:

$5.50 * TT 4.30 / $1.00 = TT (5.50 * 4.30)

Using a calculator, we find that the result of the multiplication, TT (5.50 * 4.30), is approximately TT 23.65.

For more question on exchange rate click on

https://brainly.com/question/4711402

#SPJ11

Answer:

Step-by-step explanation:

17/x + 75/x = 1, we can combine the two fractions by finding a common denominator. The common denominator is x. So we have:

(-17 + 75)/x = 1

58/x = 1

x = 58

There are 3276 different ways to award the prizes to the winners.

To calculate the number of different ways the prizes can be awarded, we can use the concept of combinations.

We have 28 people purchasing raffle tickets, and we need to select 3 winners. The order of selection does not matter since each prize is $1000.

The number of ways to select 3 winners out of 28 people can be calculated using the combination formula:

C(n, r) = n! / (r!(n-r)!)

Where:

C is the number of combinations,

n is the total number of items to choose from (28 people),

r is the number of items to be chosen (3 winners),

! represents the factorial of a number.

Plugging in the values, we have:

C(28, 3) = 28! / (3!(28-3)!)

= 28! / (3! × 25!)

= (28 × 27 × 26) / (3 × 2 × 1)

= 3276

Therefore, there are 3276 different ways to award the prizes to the winners.

for such more question on total number

https://brainly.com/question/19079438

#SPJ11

Step-by-step explanation:

Let's solve the given questions step by step:

1. Determine the equation of f:

From the given information, we know that the turning point of f is (1, 4). The general form of a quadratic function is f(x) = ax^2 + bx + c. We are given that f(x) = a(x + p)^2 + q, so let's substitute the values:

f(x) = a(x + p)^2 + q

Since the turning point is (1, 4), we can substitute x = 1 and f(x) = 4 into the equation:

4 = a(1 + p)^2 + q

This gives us one equation involving a, p, and q.

2. Determine the equation of g:

The equation of g is given as g(x) = 0.3x + p1.

3. Determine the coordinates of the x-intercept of g:

The x-intercept is the point where the graph of g intersects the x-axis. At this point, the y-coordinate is 0.

Setting g(x) = 0, we can solve for x:

0 = 0.3x + p1

-0.3x = p1

x = -p1/0.3

Therefore, the x-intercept of g is (-p1/0.3, 0).

4. For which values of x will f(x) ≥ g(x)?

To determine the values of x where f(x) is greater than or equal to g(x), we need to compare their expressions.

f(x) = a(x + p)^2 + q

g(x) = 0.3x + p1

We need to find the values of x for which f(x) ≥ g(x):

a(x + p)^2 + q ≥ 0.3x + p1

Simplifying the equation will involve expanding the square and rearranging terms, but since the equation involves variables a, p, and q, we cannot determine the exact values without further information or constraints.

To summarize:

We have determined the equation of f in terms of a, p, and q, and the equation of g in terms of p1. We have also found the coordinates of the x-intercept of g. However, without additional information or constraints, we cannot determine the exact values of a, p, q, or p1, or the values of x for which f(x) ≥ g(x).

Answer:

104

Step-by-step explanation:

supplementary angles always equal 180. 180-76=104.

104+76=180

the measurement of the other angle is 104 degrees.

hope this helps :) <3

The solution of the given quadratic equation -5 = -36 / m + m is,

 m = - 9 or  m = 4

The given equation is

-5 = -36 / m + m

After re arranging it we get,

m² + 5m - 36 = 0

This is nothing but quadratic equation,

Since we know that,

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the following generic form:

ax² + bx + c = 0

So now we can write,

⇒ m² + 9m - 4m - 36 = 0

⇒ m(m + 9) - 4(m + 9) = 0

⇒ (m + 9)(m - 4) = 0

Therefore,

⇒ (m + 9) = 0 or (m - 4) = 0

⇒ m = - 9 or  m = 4

Thus,

The solution of the given expression is

m = - 9 or  m = 4

To learn more about quadratic equation visit:

https://brainly.com/question/30098550

#SPJ1

To wrap 8 container 794.42 in² of plastic wrap required.

we have,

Diameter = 5.5 inch

radius=  5.5/2 inch

and, height = 3 inch

Surface area of Cylinder

= 2πrh + 2πr²

= 2 x 3.14 x 5.5/2 x 3 + 2 x 3.14 x 5.5/2 x 5.5/2

= 51.81 + 47.4925

= 99.3325 in²

Now, to wrap 8 container the amount of plastic wrap required

= 8 x 99.3325

= 794.42 in²

Learn more about Surface area here:

https://brainly.com/question/29298005

#SPJ1

The number of labor hours Melanie needed to complete the job was 19.5 hours, using the equation x = (1,370 - 200) ÷ 60.

An equation is a mathematical statement showing the equality or equivalence of two or more mathematical expressions.

An expression may be a combination of variables, numbers, and mathematical operands, like subtraction and division without the equal symbol (=).

The total bill = $1,370

The cost of parts = $200

Hourly rate for labor = $60

Let the number of hours Melanie needed to complete the job = x

x = (1,370 - 200) ÷ 60

x = 1,170 ÷ 60

x = 19.5 hours

Thus, Melanie needed 19.5 hours, based on the equation above.

Learn more about equations at https://brainly.com/question/2972832.

#SPJ1

Answer:

Step-by-step explanation:

The area of the bullseye is the difference between the areas of the two circles:

Area of inner circle = π(4 cm)² = 16π cm²

Area of outer circle = π(8 cm)² = 64π cm²

Area of bullseye = Area of outer circle - Area of inner circle = 64π cm² - 16π cm² = 48π cm²

The total area of the target is the area of the outer circle:

Total area of target = π(8 cm)² = 64π cm²

So the probability of randomly selecting a point in the bullseye is:

Probability = (Area of bullseye) / (Total area of target)

Probability = (48π cm²) / (64π cm²)

Probability = 3/4

Therefore, the probability that the randomly selected point is in the bullseye is 3/4.

The margin of error for this survey, expressed as a proportion to the nearest thousandth, is 0.021.

To calculate the margin of error for a survey, we need to use the formula:

Margin of Error = Critical Value * Standard Error

1. The critical value is determined based on the desired level of confidence. Since we want a 95% confidence level, we need to find the critical value associated with a 95% confidence interval.

2. For a 95% confidence interval, the critical value is approximately 1.96. This value corresponds to a standard normal distribution.

3. The standard error represents the standard deviation of the sample proportion. It can be calculated using the formula:

Standard Error = sqrt[(p * (1 - p)) / n]

where p is the sample proportion (proportion of respondents who preferred Candidate A) and n is the sample size.

4. In this case, the sample proportion is 350/1750 = 0.2 (or 20% in percentage terms). The sample size is given as 1750.

5. Plugging the values into the formula, we get:

Standard Error = sqrt[(0.2 * (1 - 0.2)) / 1750] = sqrt(0.00022857) ≈ 0.015.

6. Finally, we can calculate the margin of error:

Margin of Error = 1.96 * 0.015 ≈ 0.029.

Rounding the margin of error to the nearest thousandth, we get 0.029, which is equivalent to 0.021 when expressed as a proportion without the ± symbol.

For more such questions on margin, click on:

https://brainly.com/question/29328438

#SPJ8

Answer:

The time is 2 years

Step-by-step explanation:

we know that

The simple interest formula is equal to

A=P(1+rt)

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

t= ? years

P= $600

A= $600 + $84 = $684

r = 0.07

substitute in the formula above

$684 = $600(1+(0.07)t)

solve for t

t = [(684/600) - 1]/0.07 = 2 years