Suppose you deposit $5,000 in a savings account that earns 3% annual interest. If you make no other withdrawals or deposits, how many years will it take the account balance to reach at least $6,000? A. 10 years. B. 6 years. C. 7 years. D. 4 years

In a statistical test, the null hypothesis to be made is that the sample proportions do not have any significant differences, which means an equal distribution. This is only rejected when the estimate is equal or less than 0.95. But since in this case it is >0.95, so therefore the null hypothesis is not rejected. Therefore:

False

Answer:

A

Step-by-step explanation:

The interquartile range of the data set is 60

The interquartile range of the data set is the difference between the lower quartile (Q1) and the upper quartile (Q3)

From the given information:

We need to first identify the middle number(median) = 45

Thus:

IQR = 72.2 - 12.2

IQR = 60

Learn more about the interquartile range here:

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The cost per cracker from a box of 6 individual bags costing $5.40, with each bag containing 18 crackers, is $0.05.

In the process of calculating the cost per cracker, the initial step involves determining the cost per bag. This is accomplished by dividing the total cost of the box, which amounts to $5.40, by the number of bags contained within, totaling 6 bags. Consequently, the cost per bag is determined to be $0.90. Subsequently, to ascertain the cost per individual cracker, the cost per bag is further divided by the number of crackers present in each bag, which is 18. Following this calculation, it is established that each cracker costs $0.05. In essence, the cost analysis method involves dividing the total box cost by the number of bags to derive the cost per bag, and then dividing this value by the number of crackers per bag to determine the precise cost per cracker, amounting to 5 cents per cracker.

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Using compound interest, the better investment is of 8.3% compounded annually.

The amount of money earned, in compound interest, after t years of the investment, is given by the following formula:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which the parameters are given as follows:

For the first option, of 8.3% compounded annually, the multiplier after each year is given as follows:

[tex](1 + \frac{0.083}{1}\right)^{1} = 1.083[/tex]

As the parameters are r = 0.083, n = 1.

For the second option, the parameters are given as follows:

r = 0.08, n = 4.

Hence the multiplier after each year of the investment is given by:

[tex](1 + \frac{0.08}{12}\right)^{12} = 1.0829[/tex]

Due to the higher multiplier, the first option is better, that is, 8.3% compounded annually.

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The 8% compounded quarterly has a higher effective annual rate than 8.3% compounded annually, thereby making it the better investment choice.

To determine which investment is better, we need to compare the effective annual rates (EAR) of the two options: 8.3% compounded annually vs. 8% compounded quarterly. The formula for EAR is (1 + i/n)n - 1, where i represents the interest rate and n is the number of compounding periods per year.

For the 8.3% compounded annually, the EAR is straightforward: (1 + 0.083/1)1 - 1 = 0.083 or 8.3%.

For the 8% compounded quarterly, we calculate the EAR as follows: (1 + 0.08/4)4 - 1 = (1 + 0.02)4 - 1 = (1.02)4 - 1 = 1.082432 - 1 = 0.082432 or 8.2432%.

Comparing the two EARs, the 8% compounded quarterly has a higher effective annual rate than the 8.3% compounded annually, making it the better investment.

Answer:

D: $8.95

Step-by-step explanation:

step 1

Calculate what 15% of the normal price is.

15% as a decimal is 0.15. Multiply this by $9.99.

0.15⋅$9.99 = $1.4985

step 2

Subtract $9.99 by $1.4985 and round the difference to the nearest cent.

$9.99 − $1.4985 = $8.4915 ≈ $8.49

step 3

Match your solution to the correct answer choice.

Answer choice D is the only answer choice that matches your solution. Select answer choice D and move on to the next question.

Answer:

  $300

Step-by-step explanation:

Write an equation for the the sale price in terms of the original price. Then solve for the original price.

  sale price = (original price) - (percent off) × (original price)

Factoring out the (original price), we have ...

  sale price = (original price) × (1 - percent off)

We can find the original price by dividing this equation by (1 - percent off).

  (sale price)/(1 -percent off) = original price

Putting in the numbers, we get ...

  $225/(1 -25%) = original price

  $225/(1 - 25/100) = $225/(1 -0.25) = $225/0.75 = original price = $300

Final answer:

The code provided guides the user through entering five weights using a Scanner object, stores them in a double array, and then prints them all on one line separated by spaces.

Explanation:

To address the question of prompting the user to enter five people's weights and storing them in an array of doubles in Java, we need to provide a short piece of code executing this task.

The code will look something like this:

import java.util.Scanner;
class Main {
 public static void main(String[] args) {
   Scanner scanner = new Scanner(System.in);
   double[] weights = new double[5];

   for(int i = 0; i < weights.length; i++) {
     System.out.println("Enter weight " + (i+1) + ": ");
     weights[i] = scanner.nextDouble();
   }

   System.out.println("The entered weights are:");
   for(double weight : weights) {
     System.out.print(weight + " ");
   }
 }
}

This code initializes a Scanner to take user input, creates an array of doubles to store the weights, and uses a for loop to iterate over the array, prompting the user to enter a weight for each element. It then prints out each weight followed by a space.

The slope of the line that passes through (8, 10) and (1, 1) is 9/7.

To find the slope of a line that passes through two given points, (x1, y1) and (x2, y2), we use the formula:

m = (y2 - y1) / (x2 - x1)

Using the given points (8, 10) and (1, 1), we substitute the coordinates into the formula:

m = (1 - 10) / (1 - 8) = -9 / -7 = 9/7

Therefore, the slope of the line that passes through (8, 10) and (1, 1) is 9/7.

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The slope of the line that passes through the points (8, 10) and (1, 1) is calculated using the slope formula and it comes out to be 9/7, which is an improper fraction.

To find the slope of a line passing through two points, you use the slope formula:

Slope (m) = (change in y) / (change in x) = (y2 - y1) / (x2 - x1)

For the points (8, 10) and (1, 1), we calculate the slope as follows:

m = (1 - 10) / (1 - 8)

m = (-9) / (-7)

m = 9/7

Therefore, the slope of the line that passes through (8, 10) and (1, 1) is 9/7, which is an improper fraction.

This math problem can be solved by setting up a system of linear equations. Designate the number of $27 tickets as x and the number of $40 tickets as y. You then form two equations, one for the total number of tickets (x + y = 5000) and one for the total revenue (27x + 40y = 158400). Solve these equations to determine how many of each ticket should be sold.

The subject of this question is a problem in algebra, specifically a system of linear equations. Let's denote the number of $27 tickets as x and the number of $40 tickets as y. The total number of tickets sold will be 5000. So, we have our first equation: x + y = 5000. The total revenue is $158,400. The revenue from $27 tickets will be $27x and the revenue from $40 tickets will be $40y. So, we have our second equation: 27x + 40y = 158400. Now, we have a system of linear equations which can be solved to find the number of each ticket type that should be sold. Solve these equations to get the desired quantity of ticket type for generating the required total revenue.

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Answer: All students passed except Gino

Step-by-step explanation:

Answer:

Step-by-step explanation:

You are given a point and a slope, so you can write the linear equation relating x and y using the point-slope form of the equation for a line. That form for slope m and point (h, k) is ...

  y = m(x -h) +k

For your given values, m = 8.5, and (h, k) = (11, 5), the equation relating x and y can be written ...

  y = 8.5(x -11) +5

___

Evaluating this for several different x-values can be done with a spreadsheet or calculator. I like to write the function into a graphing calculator and let it do the tedious arithmetic. (See the attachment.)

However, to show you what is involved in doing this by hand, we can ...

  let x = 19, then ...

  y = 8.5(19 -11) +5 = 8.5·8 +5 = 73

__

  let x = -1, then ...

  y = 8.5(-1-11) +5 = 8.5·(-12) +5 = -97

____

To find the value of x for y=7, we can realize that to make y go up by 2 (from the given point of 5), we need to have x go up by 2/8.5 (from the given point of 11). That is ...

  for y = 7 ...

  x = 11 + 2/8.5 = 11 + 4/17 = 11 4/17

To determine values for y based on x in a linear function, use the equation derived. For x = 19, y equals 73; for x = -1, y equals -97. Solving for x when y is 7 gives approximately 11.24.

To solve the given problem, we use the concept of a linear function which states that the change in y with respect to x is constant. Here, the constant rate of change (slope) is given as 8.5.

We can express the linear relationship in the form of the equation:

y = 8.5x + b

We are also given a point on the line: (11, 5). Plugging these values into the equation to find b:

5 = 8.5(11) + b

5 = 93.5 + b

Subtract 93.5 from both sides:

b = 5 - 93.5 = -88.5

So, the equation becomes:

y = 8.5x - 88.5

Now, let's find the values of y for the given x values:

To find the value of x when y = 7, we can rearrange the equation:

7 = 8.5x - 88.5

Add 88.5 to both sides:

95.5 = 8.5x

Divide by 8.5:

x = 95.5 / 8.5 = 11.2353 (approximately)

Answer:

3

Step-by-step explanation:

Heart will beat 140 times in 2 minutes.
Heart beats at a rate of 70 beats per minute.

(How it's done down below)

In 0 minutes heart beats 700 times

hence in 1 minute it will beat 700/10=70 times

and heart will beat 140 times in 140/70=2 minutes

Heartbeats at a rate of 70 beats per minute.

hence in 1 minute it will beat 700 ÷ 10=70 times

divide total miles by time:

220 / 3.5 = 62.857

 rounded to nearest tenth = 62.9 miles per hour