Dominic invested $8,600 in an account paying an interest rate of 2.2% compounded daily. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $9,600?​

a). Jack has a higher 2-score than Jill. Hence, we can say that Jack performed better than Jill.

b). 2.28% of students in Prof. Lee's class can get an A.

c). 16% of students will get an F in Prof. Lee's class.

a) We must compute Jack or Jill's 2-scores in order to establish if they performed better than the rest of the class.

For Jack:

2-score = (84 - 76) / 6 = 1.33

For Jill:

2-score = (84 - 74) / 8 = 1.25

Both Jack and Jill did much better than the class average, but Jack had a higher 2-score than Jill, showing that he beat Jill relative to the rest of the class.

b) In Prof. Lee's class, a +2 z-score equates to a +2 2-score. We must determine the proportion of students whose 2-score is more than or equal to +2 in order to determine the proportion of students who can receive an A in Prof. Lee's class.

By using a calculator or a conventional normal distribution table, we determine that about 2.28% of students have a z-score of +2 or higher. So, in Prof. Lee's class, only 2.28% of students may receive an A.

c) Since a z-score of -1 in Prof. Alex's class equals one standard deviation below the mean, we can use the empirical rule to predict the proportion of students who will receive an F.

According to the empirical rule, in a normal distribution, around 68% of the data falls within one standard deviation of the mean. As a result, over 16% of students have a z-score that is less than -1. Hence, about 16% of students in Prof. Alex's class will receive an F based on his claim that those with a z-score of -1 or lower will receive failing grades.

For similar question on z-score

https://brainly.com/question/28000192

#SPJ4

According to the information, we can infer that she is going to pay $108 as total for the photos; but every photo has a different price from $12 to $0.75

To calculate the price of each photo we have to take into account how many photos fits in a sheet of pictures. Then we have to divide the total price of each sheet in the number of photos she is going to get from each sheet.

Then she is going to use 9 sheets, so she is going to pay $108 in total.

Learn more about photos in: https://brainly.com/question/26478440

#SPJ1

The system of linear equations can be solved by performing row operations to reduce the augmented matrix to reduced row-echelon form. The resulting matrix reveals that the system is consistent and has a unique solution, with x = 2 and y = -2.

To solve the given system of linear equations using row operations, we will construct the augmented matrix and perform row operations to reach reduced row-echelon form.

(a) Augmented matrix:

The augmented matrix is formed by arranging the coefficients of the variables and the constant terms of the equations in matrix form. The given system of equations is:

2x - 6y = 16 (Equation 1)

3x - 13y = 12 (Equation 2)

The augmented matrix is:

[2 -6 | 16]

[3 -13 | 12]

(b) Row operations:

Step 1: R2 = R2 - (3/2)R1

In this step, we will subtract (3/2) times the first row from the second row.

Coefficient for row operation: -3/2

Resulting matrix:

[2 -6 | 16]

[0 2 | -6]

Step 2: R1 = (1/2)R1

In this step, we will multiply the first row by 1/2.

Coefficient for row operation: 1/2

Resulting matrix:

[1 -3 | 8]

[0 2 | -6]

Step 3: R2 = R2 - R1

In this step, we will subtract the first row from the second row.

Coefficient for row operation: 1

Resulting matrix:

[1 -3 | 8]

[0 5 | -14]

Step 4: R1 = R1 + (3/5)R2

In this step, we will add (3/5) times the second row to the first row.

Coefficient for row operation: 3/5

Resulting matrix:

[1 0 | 2]

[0 5 | -14]

Step 5: R2 = (1/5)R2

In this step, we will multiply the second row by 1/5.

Coefficient for row operation: 1/5

Resulting matrix:

[1 0 | 2]

[0 1 | -2]

(c) Solution:

The reduced row-echelon form of the augmented matrix is:

[1 0 | 2]

[0 1 | -2]

From this form, we can directly read off the solution:

x = 2

y = -2

Therefore, the solution to the given system of equations is x = 2 and y = -2.

Learn more about  augmented matrix here:

https://brainly.com/question/30403694

#SPJ11

Answer:

  $9,039.81

Step-by-step explanation:

Given the exponentially decaying price history of a vehicle as $21,000; $18,900; $17,010; $15,309; $13,778.10; $12,400.29; you want to know the value after 8 years of depreciation at the same rate.

The multiplier of value each year is 18900/21000 = 0.9. This means the value of the vehicle can be represented by the price function ...

   price = (initial price) · 0.9^t

where t is the number of years the vehicle has depreciated.

After 8 years, the value will be ...

  price = $21000·0.9^8 ≈ $9,039.81

After 8 years, the value of the car will be $9,039.81.

Answer:

\(y-3=5(x+1)\)

Step-by-step explanation:

Point-Slope form is: \(y-y_1=m(x-x_1)\)

'm' - Slope

(x1, y1) - Point Coordinate

We are given the point of (-1,3) and the slope of 5.

Replace 'm' with 5, 'x1' with -1, and 'y1' with 3:

\(y-y_1=m(x-x_1)\rightarrow\boxed{y-3=5(x+1)}\)

Answer; 1

Step-by-step explanation:

18/20-3/5

15/15

Answer:

6/20 or 3/10

Step-by-step explanation:

You just convert the second fraction's denominator to equal the first's (and modify the numerator accordingly), then subtract the numerators, in this instance, you muliply the 5 by 4 and what you do the bottom, you must do to the top, so you multiply 3 by 4 and get 12. 18 - 12 = 6, giving you 6/20, which converted is 3/10.

The probability that two red balls are chosen from the vase would be = 1/9

Probability is defined as the concept that proves that an event may occur or not.

The number of red balls = 7

The number of black balls = 2

The number of green balls = 9

The total number of balls in the vase = 18

The probability of getting 2 red balls = 2/18 = 1/9

Learn more about probability here:

https://brainly.com/question/24756209

#SPJ1

Answer:

Its Constant of 40

Step-by-step explanation:

The digit "1" appears 99,920 times when writing down all whole numbers from 1 to 99,999. To determine this, we can consider each place value separately.

1. Units place (1-9): The digit "1" appears once in each number from 1 to 9.

2. Tens place (10-99): In this range, the digit "1" appears in all numbers from 10 to 19 (10 times) and in the tens place of numbers 21, 31, ..., 91 (9 times). So the digit "1" appears 10 + 9 = 19 times in the tens place.

3. Hundreds place (100-999): The digit "1" appears in all numbers from 100 to 199 (100 times) in the hundreds place. Similarly, it appears in the hundreds place of numbers 201, 202, ..., 299 (100 times), and so on up to 901, 902, ..., 999 (100 times). So in the hundreds place, the digit "1" appears 100 * 9 = 900 times.

4. Thousands place (1000-9999): Similar to the previous cases, the digit "1" appears in the thousands place 1000 times in the range from 1000 to 1999. Also, it appears 1000 times in the thousands place of numbers 2000 to 2999, and so on up to 9000 to 9999. So in the thousands place, the digit "1" appears 1000 * 9 = 9000 times.

5. Ten thousands place (10,000-99,999): The digit "1" appears in the ten thousands place 90000 times since it occurs in all numbers from 10000 to 99999.

Adding up the counts from each place value:

1 + 19 + 900 + 9000 + 90000 = 99920

Therefore, the digit "1" appears 99,920 times when writing down all whole numbers from 1 to 99,999.

Learn more about digit here: https://brainly.com/question/14961670

#SPJ11

By using permutations and combinations, We can arrange 12 people into 3 teams of 4 in 5775 different ways.

Here, we will use the concept of permutations and combinations to solve the question.

We have to arrange 12 people into 3 teams of 4.

We know that ⁿCr = n! / [(n - r)! × r!]

No. of ways to select the first 4 people in the first group = ¹²C₄

                                                                                         = 12! / [(12 - 4)! × 4!]

                                                                                             = 12! / [(8! × 4!)]

                                                                                             = 495

No. of ways to select 4 people from the remaining 8 for the second group = ⁸C₄   = 8! / [(8 - 4)! × 4!] = 8! / [(4! × 4!)] = 70

No. of ways to select 4 people from 4 for third group = ⁴C₄  = 4! / [(4 - 4)!] × 4!] = 4! / [(0! ×4!)] = 1

Total no. of ways to select people for group = (495 x 70 x 1) / 3! = 34650 /6 = 5775

Hence, we can split 12 people into 3 teams of 4 in 5775 different ways.

To learn more about permutations and combinations here:

brainly.com/question/13387529

#SPJ4

For the first problem, using the monthly payment formula monthly deposit needed is $118.69. For the second problem, using the same formula the monthly payment is $1029.73.

We have the following variables

P = Monthly payment

r = Annual interest rate = 3.7% = 0.037/12 per month

n = Number of payments = 15 months

A = Amount to be saved = $1800

Using the monthly payment formula

P = (r * A) / (1 - (1 + r)⁻ⁿ)

Substituting the given values

P = (0.003083 * 1800) / (1 - (1 + 0.003083)⁻¹⁵)

P ≈ $118.69

Therefore, you should deposit approximately $118.69 each month to save $1800 in 15 months, assuming an APR of 3.7%, compounded monthly.

We have the following variables

P = Monthly payment

r = Annual interest rate = 9.1% = 0.091/12 per month

n = Number of payments = 30 years * 12 months = 360 months

A = Mortgage amount = $127,000

Using the monthly payment formula

P = (r * A) / (1 - (1 + r)⁻ⁿ)

Substituting the given values

P = (0.007583 * 127000) / (1 - (1 + 0.007583)⁻³⁶⁰)

P ≈ $1029.73

Therefore, the monthly payment for a shack mortgage of $127,000 with a fixed APR of 9.1% for 30 years would be approximately $1029.73.

To know more about monthly payment:

https://brainly.com/question/30664343

#SPJ4

To approximate the binomial probability of no less than 75 out of 427 DVDs malfunctioning, we can use the normal distribution. Specifically, we would use the area under the normal curve to approximate the probability of getting at least 75 successes out of 427 trials.

The normal distribution is often used to approximate the binomial distribution, which is the distribution of the number of successes in a fixed number of independent trials with a constant probability of success. In this case, we are interested in the probability of getting at least 75 successes out of 427 trials, where the probability of success is unknown.

To use the normal distribution to approximate the binomial distribution, we first calculate the mean and standard deviation of the binomial distribution. For a binomial distribution with n trials and probability of success p, the mean is np and the standard deviation is sqrt(np(1-p)). In this case, n=427 and p is unknown, but we can estimate it using the sample proportion of successful trials.

Once we have the mean and standard deviation of the binomial distribution, we can standardize the distribution using the z-score formula: (X - mean) / standard deviation, where X is the number of successes we are interested in. In this case, X=75 and we would use the estimated value of p to calculate the mean and standard deviation.

Finally, we would use a standard normal distribution table or calculator to find the area under the normal curve to the right of the standardized value. This area represents the probability of getting at least 75 successes out of 427 trials, given the estimated value of p.

Learn more about Binomial:

brainly.com/question/30339327

#SPJ11

Answer: \(\$100\)

Step-by-step explanation:

Given

T-shirt cost 5 times as much as a singlet

Suppose the price of a singlet \(x\)

Price of a T-shirt is \(5x\)

According to the question, for $800, trader can buy 32 more singlet than T-shirt

\(\Rightarrow \dfrac{800}{x}=\dfrac{800}{5x}+32\\\\\Rightarrow \dfrac{800}{x}-\dfrac{160}{x}=32\\\\\Rightarrow 800-160=32x\\\\\Rightarrow x=20\)

Thus, the price of a T-shirt is \(5x=\$100\)

It will represent the change in temperature between midnight and 6, the correct option is C.

H(t) is the rate at which the temperature changes. So, if we integrate H(t), we will get the change of temperature.

In this case, we have:

\(\int\limits^6_0 {H(t)} \, dt\)

This will give the change in temperature between 6:00 AM (represented by the 6) and midnight (represented with the 0).

So the correct option is C.

If you want to learn more about integration, you can read:

https://brainly.com/question/18760518

Answer:

9) (68 + 160)/2 = 114°

10) 80/2 = 40°

11) 105 x 2 = 210°

12) 80 x 2 = 160°

13) (360 - 180 - 108)/2 = 36°

14) (360 - 69 - 95)/2 = 98°

Answer:

x = 17

Step-by-step explanation:

\(45 + 68 + (3x+16) = 180 \\ \\ 113 + 3x + 16 = 180 \\ \\ 129 + 3x = 180 \\ \\ 3x = 180 - 129 \\ \\ 3x = 51 \\ \\ x = \frac{51}{3} \\ \\ x = 17\)

Answer:

4.32%

Step-by-step explanation:

you divide 7.35 ÷ 100 = 0.0735, then multiply 0.0735 × 58.80 = 4.32%

Answer:

w=0

Step-by-step explanation:

We know a point (3,1) and the slope (-8/3), so we can use point-slope form, which is y-y1=m(x-x1)

For reference, y1 is the y in the point, m is the slope, and x1 is the x in the point

So we subsitute it

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

do distributive prop.

y-1=-8/3x+8

add 1 to both sides

y=-8/3x+9

This is the equation of the line.

Now to find w, which is the x value.

The point will pass through line, so we can susbtitute the point into the equation.

9=-8/3x+9

subtract 9 from both sides

0=-8/3x

multiply by -3/8 on both sides (the reciprocal of -8/3), we need to isolate x

0=x

x=w

therefore, w=0

Hope this helps!

Answer: 26.6 repeating number or 26 2/3

Step-by-step explanation:

Answer:

32 Fahrenheit

Step-by-step explanation:

Since it is -8, subtract -8.

Now, you have 0 Fahrenheit.

Then, you add 24, since the high was -24 Fahrenheit.

The total number you added and subtracted is 32 Fahrenheit.

Hope this helps!

The anonymous function to compute the euclidean distance given two points (x1, y1) and (x2, y2) is ``python
euclidean_distance = lambda x1, y1, x2, y2: ((x2 - x1)**2 + (y2 - y1)**2)**0.5.

To compute the Euclidean distance given two points (x1, y1) and (x2, y2). Here's the step-by-step explanation using the Euclidean distance equation:

1. Recall the Euclidean distance equation: distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
2. Use an anonymous function, which is a function without a name, typically represented using the "lambda" keyword in programming languages like Python.
3. Define the function parameters as the coordinates of the two points: (x1, y1) and (x2, y2).
4. Implement the Euclidean distance equation inside the anonymous function.

Here's an example using Python:

```python
euclidean_distance = lambda x1, y1, x2, y2: ((x2 - x1)**2 + (y2 - y1)**2)**0.5
```

Now you can use this anonymous function to compute the Euclidean distance between any two points (x1, y1) and (x2, y2) by calling it with the appropriate arguments:

```python
distance = euclidean_distance(1, 2, 4, 6)
print(distance)  # Output: 5.0
```

This example demonstrates how to write an anonymous function to compute the Euclidean distance given two points (x1, y1) and (x2, y2).

Know more about euclidean distance here:

https://brainly.com/question/28370661

#SPJ11

The correct ordering, assuming x is positive, is III: 2x < x² < 2 < 1/x²< 1.

Let's evaluate each option one by one:

I. x² < 2x < 1/x² < 2 < 1

If x is positive, x² will always be greater than 1/x². Therefore, this ordering is not possible.

II. x² < 1/x² < 2x < 1 < 2

Similarly, x² will always be greater than 1/x². Therefore, this ordering is also not possible.

III. 2x < x² < 2 < 1/x² < 1

For this ordering to be true, we need to confirm that 2x is indeed less than x². Since x is positive, we can divide both sides of the inequality by x to preserve the inequality direction. This gives us 2 < x. As long as x is greater than 2, this ordering holds true. Therefore, the correct ordering, assuming x is positive, is III: 2x < x² < 2 < 1/x²< 1.

Learn more about inequality here:

https://brainly.com/question/20383699

#SPJ11

Answer:

y=1/3x+7

Step-by-step explanation:

1. The given equation is y=1/3x-6 and it has to be parallel passing through (-12,3), so you just plug in the x and y values into the equation y=mx+b with 1/3 as the slope since its parallel (meaning the slope is the same for both eqts)

2. 3=1/3(-12)+b

3. 3=-4+b

4. 7=b

5. So, the equation is y=1/3x+7

Answer:

A. 136 stars

B. 340 stars

Answer:

At 10 pm he counted 136 stars and at 12 pm he counted 340

Step-by-step explanation:

for 10 pm:

68 x 2

for 12 pm:

68 x 5

The average slope of the function f(x) on the interval [-5, 0] is 0.

What is Derivative?

In calculus, the derivative is a fundamental concept that measures the rate at which a function changes with respect to its independent variable. It represents the instantaneous rate of change of a function at a specific point.

To find the average slope of the function f(x) = x√(x+5) on the interval [-5, 0], we can use the formula for average rate of change.

The average rate of change, or average slope, is given by the formula:

m = (f(b) - f(a)) / (b - a),

where a and b are the endpoints of the interval.

In this case, a = -5 and b = 0. Let's calculate the average slope:

m = (f(0) - f(-5)) / (0 - (-5))

= (0√(0+5) - (-5)√((-5)+5)) / (0 - (-5))

= (0 - (-5)√0) / (0 + 5)

= (0 + 0) / 5

= 0 / 5

= 0.

Therefore, the average slope of the function f(x) on the interval [-5, 0] is 0.

Now, to verify the Mean Value Theorem, we need to find a number c in the interval (-5, 0) such that the instantaneous rate of change at c, denoted by f'(c), is equal to the average slope we calculated, which is 0.

To find such a number, we can find the derivative of f(x) and solve for c when f'(c) = 0.

Let's find the derivative of f(x):

f(x) = x√(x+5)

f'(x) = (1/2)√(x+5) + (x/2√(x+5))

Now, let's solve f'(x) = 0:

(1/2)√(x+5) + (x/2√(x+5)) = 0

√(x+5) + x = 0

x + 5 = -x²

x² + x + 5 = 0.

Unfortunately, the quadratic equation x² + x + 5 = 0 does not have real solutions. Therefore, there is no number c in the interval (-5, 0) for which f'(c) = 0, and we cannot verify the Mean Value Theorem in this case.

Please note that the inability to find a suitable c in this specific example does not imply that the Mean Value Theorem is invalid in general. The Mean Value Theorem guarantees the existence of such a value c for differentiable functions under certain conditions, but it may not always be possible to find the specific value in every case.

To know more about Derivative visit:

https://brainly.com/question/28376218

#SPJ4

Answer:

1. 33%

2. 16%

3. 50%

Step-by-step explanation:

Answer:

x = 48°

Step-by-step explanation:

The sum of the interior angles of a quadrilateral = 360°

Subtract the sum of the 3 given angles from 360 for fourth angle

fourth = 360° - ( 30 + 108 + 90)° = 360° - 228° = 132°

The fourth angle and x are adjacent angles and are supplementary, thus

x = 180° - 132° = 48°

Answer:

1 15 degrees

Step-by-step explanation:

Exterior angle is equal to sum of opposite interior angles