Jonah deposited $80 in a savings account earning 5% interest, compounded annually. To the nearest cent, how much interest will he earn in 3 years?​

Answer:1 tile 2 box 2 tile 1 box 3 tile 5 box 4 tile 6 box 6 tile 4 box

Step-by-step explanation: math

The ascending order of increasing functions are,

y = (3/4)x - 10 < y = (1/2)x - 2 < y = (4/3)x - 7/3 < y = (3/2)x - 11/2

< y = (5/2)x + 10.

The equation of a line in slope-intercept form is y = mx + b.

Where slope = m and b = y-intercept.

The y-intercept, or (0,b), is the point where the line crosses the y-axis at x = 0. The slope represents the rate of change of the y-axis relative to the x-axis.

When the equation of the form y = mx + b, the slopes of the function can be used to sort them in ascending order.

The equations in ascending order are,

y = (3/4)x - 10 < y = (1/2)x - 2 < y = (4/3)x - 7/3 < y = (3/2)x - 11/2

< y = (5/2)x + 10.

learn more about lines and slopes here :

https://brainly.com/question/3605446

SPJ2

80 marbles for $4.99 is a better buy as compared with 90 marbles for $5.99

Comparing numbers in math is defined as a process or method in which one can determine whether a number is smaller, greater, or equal to another number according to their values.

Given are 80 marbles for $4.99 and 90 marbles for $5.99.

Using Unitary method -

80 marbles cost → $4.99

1 marble will cost → (4.99/80) = $0.062

90 marbles cost  → $5.99

1 marble will cost → (5.99/90) = $0.066

Clearly $0.062 < $0.066

So, 80 marbles for $4.99 is a better buy.

Therefore, 80 marbles for $4.99 is a better buy as compared with 90 marbles for $5.99

To solve more questions on Rate comparison, visit the link below-

https://brainly.com/question/2187261

#SPJ2

The simplified trigonometric expression is sin²t.

Option D is the correct answer.

We have,

Given,

Trigonometric expression:

cost (sect - cost)

[ sec t = 1/ cos t ]

= cost (1/cos t - cos t)

Applying the distributive properties.

= cos t/cos t - cos²t

= 1 - cos²t

= sin²t

(using the trigonometric identity sin²t + cos²t = 1)

Therefore,

The simplified trigonometric expression is sin²t.

Learn more about trigonometric identities here:

https://brainly.com/question/14746686

#SPJ1

Answer:

Happened in 1986

Maybe 37 years ago?

Answer:

hello! :) have a good day!

Exact Form:

x= 87/35

Decimal Form:

x= 2.48571428

Mixed Number Form:

x= 2 17/35

Answer:

Mean = 125.136

Median = 110

Mode = 180

Step-by-step explanation:

Given the data:

75 95 180 136 89 75 110 180 100 136 180 95 180 136 75 100 110 180 180 136 75 90

Frequency distribution:

Value(X) ___freq (F) ____cumm frequency

85 _________ 4 _______ 4

89 _________ 1 _______5

90 __________1 _______6

95 __________2 ______ 8

100 _________ 2 ______10

110 __________2______ 12

136 __________4 _____ 16

180 __________6______22

2) Using the frequency distribution :

Mean = Σfx / Σf

[(85*4) + (89*1) + (90*1) + (95*2) + (100*2) + (110*2) + (136*4) + (180*6)]/ 10

= 2753 / 22

= $125.136

Median of grouped data :

Frequency + 1 / 2 = 23/2 = 11.5 th term

The median value = $110

Mode of the data:

Most frequently occurring = 180 (frequency of 6)

The mean of the frequency distribution is $125.136, the median of the frequency distribution is $110, and the mode of the frequency distribution is $180.

Given :

a) The frequency distribution is given below:

Prices              Frequency       Cumulative Frequency

85                           4                                 4

89                            1                                 5

90                            1                                  6

95                            2                                  8

100                           2                                 10

110                            2                                  12

136                            4                                 16

180                            6                                 22

b) The mean is calculated as:

\(\rm Mean = \dfrac{85\times4 + 89\times1 +90\times1 +95\times 2+100\times2 +110\times2 +136\times4 +180\times6 }{10}\)

Simplify the above expression.

Mean = $125.136

c) The median of the frequency distribution is calculated as:

\(\rm Term= Frequency + \dfrac{1}{2}=11.5\)

So, the median is $110.

The mode of the frequency distribution is $180.

For more information, refer to the link given below:

https://brainly.com/question/4393505

The expected standard deviation of stock A's returns, based on the information presented in the table, is approximately 23.57%.

To calculate the expected standard deviation of stock A's returns, we first need to calculate the variance. The variance is the average of the squared deviations from the expected return, weighted by the probabilities of each outcome.

Given the information provided:

Outcome Probability Stock A Return

Good 16% 65.00%

Medium 51% 17.00%

Let's calculate the expected return first:

Expected Return = (Probability of Good × Stock A Return in Good) + (Probability of Medium × Stock A Return in Medium)

= (0.16 × 65.00%) + (0.51 × 17.00%)

= 10.40% + 8.67%

= 19.07%

Next, we calculate the squared deviations from the expected return for each outcome:

Deviation from Expected Return in Good = Stock A Return in Good - Expected Return

= 65.00% - 19.07%

= 45.93%

Deviation from Expected Return in Medium = Stock A Return in Medium - Expected Return

= 17.00% - 19.07%

= -2.07%

Now, we calculate the variance:

Variance = (Probability of Good × Squared Deviation in Good) + (Probability of Medium × Squared Deviation in Medium)

= (0.16 × (45.93%^2)) + (0.51 × (-2.07%^2))

= (0.16 × 0.2110) + (0.51 × 0.0428)

= 0.0338 + 0.0218

= 0.0556

Finally, we calculate the standard deviation, which is the square root of the variance:

Standard Deviation = √Variance

= √0.0556

= 0.2357 or approximately 23.57%

Therefore, the expected standard deviation of stock A's returns, based on the information presented in the table, is approximately 23.57%.

To learn more about standard deviation,

https://brainly.com/question/24298037

#SPJ4

Answer:

120 cubed inches

Step-by-step explanation:

5 x (3 x 8)

5 x 24

120

Answer:

Step-by-step explanation:

Volume of rectangular prism = lwh

                                                 = 8 * 3 * 5

                                                 = 120 cubic inches

Answer:

Step-by-step explanation:

y = 15x

y = 10x + 100

15x = 10x + 100

5x = 100

x = 20 movies

The test statistic for this sample is approximately -3.780. The final conclusion is there is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 55.7 (option a).

To test the claim H₀: μ = 55.7 against the alternative hypothesis Hₐ: μ ≠ 55.7 at a significance level α = 0.02, we can use a two-tailed t-test since the population standard deviation is unknown.

Given:

Sample size n = 111

Sample mean M = 50.4

Sample standard deviation SD = 14.8

First, we calculate the test statistic:

t = (M - μ₀) / (SD / √n)

= (50.4 - 55.7) / (14.8 / √111)

= -5.3 / (14.8 / 10.54)

≈ -3.780

The test statistic for this sample is approximately -3.780.

Next, we need to calculate the p-value associated with this test statistic. Since it is a two-tailed test, we need to find the probability of observing a test statistic as extreme as -3.780 or more extreme in either tail.

Using a t-distribution table or statistical software, we find that the p-value is less than 0.0001 (accurate to four decimal places).

Since the p-value is less than the significance level α = 0.02, we reject the null hypothesis.

Therefore, the final conclusion is:

A) There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 55.7.

To know more about test statistic:

https://brainly.com/question/32118948

#SPJ4

The statement given "regression equations are usually used to predict values of unavailable data. if the data do not closely model a particular type of function, then that type of function is not appropriate to use in statistical regression. the more closely data fit a model, the more predicted values will be." is true because regression equations are indeed employed for predicting values of unavailable data.

Regression equations are commonly utilized to make predictions for unavailable data. When the data does not closely conform to a specific type of function, that function is deemed inappropriate for statistical regression. The accuracy of predicted values is contingent on the degree of resemblance between the data and the chosen model. Hence, a strong fit between the data and the model enhances the reliability of predicted values, ensuring that regression analysis is effectively applied for making accurate predictions.

You can learn more about regression equation at

https://brainly.com/question/30401933

#SPJ11

Answer:

{11, 16, 25}

Step-by-step explanation:

This is because whenever you add two sides of a triangle, it must be greater than the third side.

Answer: (6,0)

Step-by-step explanation:

Answer:

\(\dfrac{c}{3(c+2)}\)

Step-by-step explanation:

\(\dfrac{c^2+4c}{c^2-4} \div \dfrac{3c+12}{c-2}=\dfrac{c^2+4c}{c^2-4} \times \dfrac{c-2}{3c+12}=\dfrac{(c^2+4c)(c-2)}{(c^2-4)(3c+12)}\)

Factor \(c^2-4\):    \(c^2-4=(c-2)(c+2)\)

\(\implies\dfrac{(c^2+4c)(c-2)}{(c+2)(c-2)(3c+12)}\)

Cancel the common factor  \((c-2)\):

\(\implies\dfrac{(c^2+4c)}{(c+2)(3c+12)}\)

Factor  \(c^2+4c\):  \(c^2+4c=c(c+4)\)

Factor  \(3c+12\):  \(3c+12=3(c+4)\)

\(\implies\dfrac{c(c+4)}{3(c+2)(c+4)}\)

Cancel the common factor  \((c+4)\):

\(\implies\dfrac{c}{3(c+2)}\)

The normal distribution that best approximates X is N(42, 21).

In an accounting college class, 50% of students receive a B or above on the final exam. 84 students are randomly selected from an accounting class at a local college. Let X be the number of students who received a B or above on the final exam. The normal distribution that best approximates X is a normal distribution with mean µ = np and variance σ^2 = np(1 - p).

In this case, n = 84 and p = 0.5 since 50% of the students receive a B or above on the final exam, and we want to find the distribution of the number of students who receive a B or above on the final exam.X ~ N(µ, σ^2) = N(np, np(1 - p)) = N(84(0.5), 84(0.5)(0.5)) = N(42, 21)

Learn more about Normal distribution

brainly.com/question/29509087

#SPJ11

The number of hours Jackson worked washing cars is 8 hours and the number of hours he worked landscaping is 6 hours

The payment of car washing per hour = $10

The payment for landscaping = $12

Total number of hours worked = 14  hours

Number of hours worked in car washing = x

Number of hours worked in landscaping = y

Then the first equation will be

x + y = 14

x = 14 - y

Total amount he earned = $152

Next equation will be

10x + 12y = 152
Here we have to use substitution method

10(14-y) + 12y = 152

140 - 10y +12y = 152

140 + 2y = 152

2y = 152 - 140

2y = 12

y = 12/2

y = 6 hours

Then

x = 14 - y

x = 14 -6

x = 8  hours

Hence, the number of hours Jackson worked washing cars is 8 hours and the number of hours he worked landscaping is 6 hours

Learn more about substitution method here

brainly.com/question/14619835

#SPJ1

Answer:

B

Step-by-step explanation:

Because you subtract 14 from the right and left of the = sign

and now we add one on tbe right and left of the = sign. so the quadratic problem would be 3x^2 + 9x -13

The simplified form of polynomials are:

1.  (a² - 3a)² = 3a²

2. (1/2x³ + 6x)² = -12x²

Given,

We have to expand the given polynomials and simplify them.

1. The polynomial: (a² - 3a)²

Here,

The polynomial is in the form of (a - b)²

So,

(a - b)² = a² - 2ab + b²

Then,

(a² - 3a)² = (a²)² - (2 × a² × 3a) + (3a)²

(a² - 3a)² = a⁴ - 6a³ + 9a²

(a² - 3a)² = a²(a² - 6a + 9)

Here,

(a² - 6a + 9) is in quadratic form. Solve using quadratic formula.

a = 1, b = -6 and c = 9

\(\frac{-b(+-)\sqrt{b^{2} -4ac} }{2a}\) = \(\frac{6(+-)\sqrt{(-6)^{2}-4(1)(9) } }{2(1)}\) = \(\frac{6(+-)\sqrt{36 - 36} }{2}\) = \(\frac{6(+-)\sqrt{0} }{2}\) = (6±0) / 2

= 6/2 = 3

Then,

(a² - 3a)² = a²(a² - 6a + 9)

Here,

(a² - 6a + 9) = 3

So,

(a² - 3a)² = 3a²

2. The polynomial: (1/2x³ + 6x)²

Here, the polynomial is in the form (a + b)²

(a + b)² = a² + 2ab + b²

Here,

(1/2x³ + 6x)² = (1/2x³)² + (2 × 1/2x³ × 6x) + (6x)²

(1/2x³ + 6x)² = 1/4x⁶ + 6x⁴ + 36x²

(1/2x³ + 6x)² = x²(1/4x⁴ + 6x² + 36)

a = 1/4, b = 6 and c = 36

Quadratic formula: \(\frac{-b(+-)\sqrt{b^{2} -4ac} }{2a}\)

= \(\frac{-6(+-)\sqrt{(-6)^{2} -4(1/4)(36)} }{2(1/4)}\) = \(\frac{-6(+-)\sqrt{36-36} }{1/2}\) = (-6±0) / (1/2) = -6 × 2 = -12

Therefore,

(1/2x³ + 6x)² = x²(1/4x⁴ + 6x² + 36)

Here,

(1/4x⁴ + 6x² + 36) = -12

Then,

(1/2x³ + 6x)² = -12x²

That is,

The simplified form of polynomials are:

1.  (a² - 3a)² = 3a²

2. (1/2x³ + 6x)² = -12x²

Learn more about simplification of polynomials here:

https://brainly.com/question/355399

#SPJ1

Answer:

1/2x -1/2

Step-by-step explanation:

f(x) = 2x+1

y = 2x+1

Switch x and y

x = 2y+1

Solve for y

Subtract 1

x-1 = 2y+1-1

x-1 =2y

Divide by 2

(x-1)/2 = 2y/2

1/2x -1/2 = y

The inverse is 1/2x -1/2

Answer:

\(\huge\boxed{h(x) = \frac{1}{2} x - \frac{1}{2}}\)

Step-by-step explanation:

\(f(x) = 2x+1\)

Put f(x) = y

\(y = 2x + 1\)

Interchange x and y

\(x = 2y+1\)

Solve for y

\(x = 2y+1\)

Subtracting 1 to both sides

\(x-1 = 2y\)

Dividing both sides by 2

\(\frac{x-1}{2} = y \\\\ OR\\\\ y = \frac{x-1}{2}\)

Put y = h(x)

\(\bold{h(x) = \frac{1}{2} x - \frac{1}{2}}\)

Part A: The real part of (A + B) is 9.7

Part B: The imaginary part of (A + B) is approximately 5.68

Part C: The real part of (A - B) is -3.5

Part D: The imaginary part of (A - B) is approximately -0.14.

Given that,

A = 3.1∠63.2°  

B = 6.6∠26.2°

Part A: To find the real part of (A + B), we add the real parts of A and B.

In this case,

The real part of A is 3.1 and the real part of B is 6.6.

Adding them together, we get:

Real part of (A + B) = 3.1 + 6.6 = 9.7

So, the real part of (A + B) is 9.7.

Part B: To find the imaginary part of (A + B),

Add the imaginary parts of A and B.

In this case,

The imaginary part of A can be calculated using the formula

A x sin(angle),

Which gives us:

Imaginary part of A = 3.1 x sin(63.2°)

                                ≈ 2.77

Similarly, for B:

Imaginary part of B = 6.6 x sin(26.2°) ≈ 2.91

Adding these together, we get:

Imaginary part of (A + B) ≈ 2.77 + 2.91

                                        ≈ 5.68

So, the imaginary part of (A + B) is approximately 5.68.

Part C: To find the real part of (A - B),

Subtract the real part of B from the real part of A.

In this case,

The real part of A is 3.1 and the real part of B is 6.6.

Subtracting them, we get:

Real part of (A - B) = 3.1 - 6.6

                               = -3.5

So, the real part of (A - B) is -3.5.

Part D: To find the imaginary part of (A - B),

Subtract the imaginary part of B from the imaginary part of A.

Using the previously calculated values, we have:

Imaginary part of (A - B) ≈ 2.77 - 2.91

                                        ≈ -0.14

So, the imaginary part of (A - B) is approximately -0.14.

To learn more about complex numbers visit:

https://brainly.com/question/27940074

#SPJ4

Rounding this to two decimal places, the equivalent nominal interest rate compounded monthly is approximately 2.53%.

To determine the equivalent nominal interest rate compounded monthly for a given nominal interest rate compounded quarterly, we can use the formula for nominal interest rate conversion.

The formula is:

r = (1 + i/n)^n - 1

Where:

r is the nominal interest rate compounded annually (we're looking for this),

i is the nominal interest rate compounded quarterly (2.50% in this case),

n is the number of compounding periods per year (4 for quarterly compounding).

Plugging in the values, we have:

r = (1 + 0.025/4)^4 - 1

Calculating this expression, we find:

r ≈ 0.025335

Rounding this to two decimal places, the equivalent nominal interest rate compounded monthly is approximately 2.53%.

Learn more about conversion:https://brainly.com/question/97386

#SPJ11

An NFL team plays 16 games in a season, while an MLB plays 162 games in a season. Thus the Non-Scully "benchmark standard deviation" for the NFL team is 10 and for an MLB team is the answer is  100.

The Non-Scully "benchmark standard deviation" is a statistical concept introduced by Bill James, a prominent baseball analyst. It is used to compare the variability of performance between different sports or different eras within the same sport.

The formula for the Non-Scully "benchmark standard deviation" is:

SD = Sqrt[(Σ(P - E)^2)/N]

Where SD is the standard deviation, P is the observed value (wins or losses), E is the expected value (based on the team's winning percentage), and N is the number of games played.

Using this formula, we can calculate the benchmark standard deviation for an NFL team and an MLB team:

For an NFL team, N = 16 games. Assuming a .500 winning percentage, E = 8 wins. The maximum deviation from the expected value would be 8 wins (if the team won all 16 games) or -8 wins (if the team lost all 16 games). Therefore, the range of possible deviations squared would be (8-0)^2 + (-8-0)^2 = 128. The benchmark standard deviation would be the square root of this value divided by N:

SD = Sqrt[(128)/16] = Sqrt[8] ≈ 2.83

For an MLB team, N = 162 games. Assuming a .500 winning percentage, E = 81 wins. The maximum deviation from the expected value would be 81 wins (if the team won all 162 games) or -81 wins (if the team lost all 162 games). Therefore, the range of possible deviations squared would be (81-0)^2 + (-81-0)^2 = 13122. The benchmark standard deviation would be the square root of this value divided by N:

SD = Sqrt[(13122)/162] ≈ 10.37

Therefore, the answer is A. 10; 100.

Learn more about deviation from

https://brainly.com/question/475676

#SPJ11

Let's focus on writing the menu content:  Write the menu using words that appeal to the customer base and fit with the business service style. Use the correct names for the styles of cuisine and employ descriptive writing to promote the sale of menu items. For evaluating the menu items: Use the feedback obtained to evaluate and improve menu performance.

To adequately prepare for this task of identifying customer preferences for a food business, you need to follow these steps:
1. Identify and document the current customer profile for the food business, considering different customer groups with varying characteristics. This step helps you understand who your customers are and what their preferences might be.
2. Analyze and evaluate the food preferences of the customer base. This involves gathering information about the types of food they like, their dietary restrictions, and any specific preferences they may have.
Now, let's move on to planning menus based on the information you have gathered:
3. Generate a range of ideas for dishes suitable for menus. Brainstorm different options that align with your customers' preferences and consider factors such as taste, presentation, and variety.
4. Assess the merits of the ideas generated. Evaluate each dish idea based on its potential appeal to your customers and how well it fits with the overall concept of your food business.
5. Discuss the ideas with relevant personnel in the workplace. Seek input from chefs, managers, or other team members who can provide valuable insights and suggestions.
6. Choose menu items that meet the identified customer preferences. Select dishes that align with the information you have gathered about your customers' preferences and are suitable for your food business.
7. Identify the organizational service style and cuisine, and develop suitable menus that include a balanced variety of dishes and ingredients. Consider different types of menus, such as a la carte, buffet, cyclical, degustation, ethnic, set, table d'hôte, and seasonal, based on your service style and cuisine.

Now, let's move on to costing the developed menus:
8. Itemize the proposed components of each dish. Break down the ingredients and quantities required for each menu item.
9. Calculate the portion yields to determine the costs from raw ingredients. Determine how much of each ingredient is needed to prepare a single portion of a dish and calculate the cost based on ingredient prices.
10. Assess the cost-effectiveness of the dishes and select menu items that provide high yield. Consider the cost of ingredients, preparation time, and overall profitability of each dish.
11. Price the menu items to ensure maximum profitability. Use appropriate methods to set prices that will achieve the desired profit margins, mark-up procedures, and rates.

Now, let's move on to evaluating the menu items:
13. Obtain at least two types of feedback, such as customer satisfaction discussions, customer surveys, and suggestions from customers, managers, peers, staff, supervisors, and suppliers. Regular staff meetings involving menu discussions and seeking staff suggestions for menu items are also helpful.
14. Use the feedback obtained to evaluate and improve menu performance. Address any concerns or suggestions raised by customers or staff and make necessary adjustments.
15. Assess the success of the menu against customer satisfaction and sales data. Analyze the impact of the menu on customer satisfaction and the overall sales performance of your food business.
16. Adjust the menus as required based on feedback and profitability. Continuously review and update the menus to ensure they meet customer preferences and contribute to the profitability of your food business.

Remember, this process is iterative, and it's essential to regularly gather feedback and make improvements to keep your menu offerings relevant and appealing to your customers.

Read more about evaluation here:

https://brainly.com/question/30316169

#SPJ11

The discriminant of the quadratic equation is -20 and there are two non real solutions.

The discriminant of a quadratic equation uses the equation:

\(b^{2} -4ac\)

Where the value of this calculation can tell you what solutions there are, plug known values in:

\(x^{2} +6x+14\)

a=1

b=6

c=14

\(b^{2} -4ac\)

which is equal to -20 on putting the values of a,b and c in the equation

As -20 < 0, this means that there is not a real solution, resulting in the first option being correct.

For more information about discriminant, visit https://brainly.com/question/2507588

#SPJ1

Three angles are 36° , 36° , 180°.

Let us denote first, second, third angle by a, b, c respectively.

It is given that second angle is the same as first angle which implies that,

⇒ b = a

And third angle is three times the first which implies that,

⇒ c = 3a

We know that sum of the angle of triangle is 180°.

Therefore a + b + c = 180°

⇒ a + a + 3a = 180°

              5a = 180°

                 a = 36°

That means b = 26 °

and c = 3a = 3(36°) = 108°

Hence three angles are 36°, 36°, 108°.

To know more about triangle here

https://brainly.com/question/15066104

#SPJ4

The equation of the line into slope-intercept form is y = x/3 - 6

Linear equations are equations that have constant average rates of change.

Note that the constant average rates of change can also be regarded as the slope or the gradient

From the question, we have the following equation that can be used in our computation:

9y−3x= −54

Rewrite properly

This gives

9y - 3x = -54

Divide through the equation by 3

So, we have the following representation

9y/3 - 3x/3 = -54/3

Evaluate

3y - x = -18

To rewrite as slope-intercept form is to make y the subject

So, we have

3y = x - 18

Divide through the equation by 3

So, we have the following representation

y = x/3 - 6

Hence, the equation is y = x/3 - 6

Read more about linear equations at

https://brainly.com/question/4074386

#SPJ1

Answer:

Option A. \((f_of^{-1})(-2)=-2\)

Step-by-step explanation:

Point to remember while solving the question of function,

\((f_of^{-1})(x)=x\)

Here, 'f' is the parent function and \(f^{-1}\) is the inverse of the function 'f'.

So for the given function,

f(x) = 2x - 2

\((f_of^{-1})(x)=x\)

For x = -2

\((f_of^{-1})(-2)=(-2)\)

Therefore, Option A will be the correct answer.

An estimate for the total number of dragonflies around the lake is 930 by proportional equation.

Let x be the total number of dragonflies around the lake.

We know that on Saturday, Greta caught 120 dragonflies and tagged them.

Therefore, the proportion of tagged dragonflies in the lake is 120/x.

On Sunday, Greta caught 124 dragonflies, and 16 of them were tagged. This means that the proportion of tagged dragonflies in the lake is 16/124.

Since the same proportion of dragonflies were tagged on both days, we can set up an equation:

120/x = 16/124

Solving for x, we get:

x = (120 × 124) / 16 = 930

Therefore, an estimate for the total number of dragonflies around the lake is 930.

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ1

Answer:

\(\displaystyle s(t)=\frac{3}{4}t^3+10t^3+5t+3\)

Step-by-step explanation:

Integrate v(t) with respect to time

\(\displaystyle \int(3t^3+30t^2+5)\,dt\\\\=\frac{3}{4}t^4+10t^3+5t+C\)

Plug-in initial condition to get C

\(\displaystyle s(0)=\frac{3}{4}(0)^3+10(0)^3+5(0)+C\\\\3=C\)

Thus, the position function is \(\displaystyle s(t)=\frac{3}{4}t^3+10t^3+5t+3\) given the velocity function and initial condition.

Answer:

15 hours.

Step-by-step explanation:

20 can be divided into quarters, 3 quarters is 15/20 hours.