What is the error made by the student?

Answer: C) You choose account #2

===================================================

Explanation:

Let's compute the final balance for account 1.

We'll use the compound interest formula

A = P*(1+r/n)^(n*t)

where,

where in this case

So with all that in mind, we get

A = P*(1+r/n)^(n*t)

A = 10,000*(1+0.035/4)^(4*10)

A = 14,169.0883793113

A = 14,169.09

Account #1 gets us $14,169.09 which is over our goal of $14,000

--------------------------

Let's repeat this idea for account 3. I'll get back to account 2 in the next section.

For account 3, we have these inputs

leading to...

A = P*(1+r/n)^(n*t)

A = 10,000*(1+0.032/1)^(1*10)

A = 13,702.4104633564

A = 13,702.41

This isn't larger than 14,000. So we cannot use account 3. The interest rate is too small and needs to be bumped up.

--------------------------

Now let's compute account 2. We'll use the continuously compounded interest formula which is

A = P*e^(rt)

The P, r and t are the same as before. The 'e' is a constant and it's roughly e = 2.718... similar to how pi = 3.14... approximately.

I recommend using the calculator's stored value of 'e' to get as much accuracy as possible.

So,

A = P*e^(rt)

A = 10,000*e^(0.036*10)

A = 14,333.2941456052

A = 14,333.29

This exceeds 14,000 so we can use this account.

Comparing this to account 1's value (14,169.09), we can see that account 2 gets us the most money over the 10 year time period. Not only does account 2 have the higher interest rate, but it also has an infinitely higher compounding frequency as well. These two factors help contribute as to why account 2 beats out account 1.

This is why we should go for account 2.

The probability for yellow is given by 11/15.

Here, we have given that,

P(not yellow) = 4/15

Mathematically, the addition of the probability of an event and its complement adds up to be 1

The complement we have here is P(yellow)

Thus, mathematically we have;

P(not yellow) + P(yellow) = 1

P(yellow) = 1 - P(not yellow)

From the question P(not yellow) = 4/15

Plugging this value, we have;

P(yellow) = 1 - 4/15 = 11/15

Therefore the probability for yellow is given by 11/15.

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Answer:

B. Made smoother

Step-by-step explanation:

The problem with the knives people had was that they were too pointy and could be used to cause harm. In order to prevent the knives from causing harm the king ground them down meaning that he had the points of the knives smoothed so that they were not as dangerous.

A dog is on a leash that is tied to a tree. The leash is 6 feet long. If the center of the tree could be considered the origin (0,0), the equation of the circle will be \((x)^2 + (y)^2 = 6^2\)

If a circle O has a radius of r units length and it has got its center positioned at (h, k) point of the coordinate plane, then, its equation is given as:

\((x-h)^2 + (y-k)^2 = r^2\)

A dog is on a leash that is tied to a tree. The leash is 6 feet long. If the center of the tree could be considered the origin (0,0),

we have r = 6

the equation of the circle will be

\((x-h)^2 + (y-k)^2 = r^2\)

\((x-0)^2 + (y-0)^2 = r^2\\\\(x)^2 + (y)^2 = 6^2\)



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The root of the equation sin(x) = 2 - 3 is x = 0, determined using the false position method.

To find the root of the equation sin(x) = 2 - 3 using the false position method, we need to perform iterations by updating the bounds of the interval based on the function values.

Let's define the function f(x) = sin(x) - (2 - 3).

First, we need to find an interval [a, b] such that f(a) and f(b) have opposite signs. Since sin(x) has a range of [-1, 1], we can choose an initial interval such as [0, π].

Let's perform the iterations:

Iteration 1:

Calculate the value of f(a) and f(b) using the initial interval [0, π]:

f(a) = sin(0) - (2 - 3) = -1 - (-1) = 0

f(b) = sin(π) - (2 - 3) = 0 - (-1) = 1

Calculate the new estimate, x_new, using the false position formula:

x_new = b - (f(b) * (b - a)) / (f(b) - f(a))

= π - (1 * (π - 0)) / (1 - 0)

= π - π = 0

Calculate the value of f(x_new):

f(x_new) = sin(0) - (2 - 3) = -1 - (-1) = 0

Since f(x_new) is zero, we have found the root of the equation.

The root of the equation sin(x) = 2 - 3 is x = 0.

The root of the equation sin(x) = 2 - 3 is x = 0, determined using the false position method.

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Answer:

Step-by-step explanation:

we see that y = -3x-3

substitute that into the other equation to get

-3x-3 = 2x+7

-5x = 10

x = -2

so, y = -3(-2)-3 = 3

check to make sure (-2,3) solves both equations.

\(\left(3^3 - 6 \cdot 8 \right) \div 7\\\\\\= \dfrac{27-48}{7}\\\\\\=-\dfrac{21}7\\\\\\=-3\\\)

Answer:

-3

Step-by-step explanation:

Using PEMDAS :

Exponent (in Parentheses)

Multiplication (in Parentheses)

Subtraction (In Parentheses)

Division

The 87% confidence interval for the size of the candles is (3.503 ounces, 3.937 ounces).

To calculate the 87% confidence interval, follow these steps:

1. Identify the sample size (n=15), sample mean (3.72 ounces), and standard deviation (0.963 ounces).

2. Determine the critical value (z) for an 87% confidence interval using a standard normal distribution table or calculator. For an 87% CI, the critical value is approximately 1.534.

3. Calculate the standard error (SE) using the formula SE = standard deviation / sqrt(n). In this case, SE = 0.963 / sqrt(15) ≈ 0.248.

4. Multiply the critical value (z) by the standard error (SE) to find the margin of error (MOE): MOE = 1.534 * 0.248 ≈ 0.380.

5. Find the lower limit of the confidence interval by subtracting the MOE from the sample mean: 3.72 - 0.380 = 3.503 ounces.

6. Find the upper limit of the confidence interval by adding the MOE to the sample mean: 3.72 + 0.380 = 3.937 ounces.

So, the 87% confidence interval for the size of the candles is (3.503 ounces, 3.937 ounces).

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Yes, the statement "if x is rational and y is irrational, then x + y is irrational" is true.

To understand why, let's break it down step by step:

1. First, let's define what it means for a number to be rational or irrational:
  - A rational number is a number that can be expressed as the ratio of two integers, where the denominator is not zero.
  - An irrational number is a number that cannot be expressed as the ratio of two integers.

2. Given that x is rational and y is irrational, we can express x and y as follows:
  - x = a/b, where a and b are integers and b is not zero.
  - y = c, where c is an irrational number.

3. Now, let's consider the sum x + y:
  - x + y = (a/b) + c

4. To prove that x + y is irrational, we'll assume the contrary, that is, x + y is rational. This means we can express x + y as the ratio of two integers:
  - x + y = p/q, where p and q are integers and q is not zero.

5. We can rewrite this equation as follows:
  - (a/b) + c = p/q

6. Rearranging the equation, we get:
  - (a/b) = (p/q) - c

7. Since (p/q) is a rational number and c is an irrational number, the right side of the equation (p/q) - c would be the difference between a rational and an irrational number.

8. However, the difference between a rational number and an irrational number is always irrational. Therefore, the right side of the equation is irrational.

9. This contradicts our assumption that (a/b) is rational, leading us to conclude that x + y must be irrational.

In conclusion, if x is rational and y is irrational, then x + y is always irrational.

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Answer:

7 1/5 m

Step-by-step explanation:

Find the length of a rectangular prism having a volume of 60 cubic meters, width of 2 1/2 meters, and height of 3 1/3

Volume of a rectangular prism = Length × Width × Height

Length = Volume/ Width × Height

Length = 60 m³/2 1/2 m × 3 1/3 m

Length = 60 m³/8 1/3 m²

Length = 60 m³÷ 8 1/3 m²

= 60 m³ ÷ 25/3 m²

=( 60 × 3/25 )m

= 180/25 m

Length = 7 1/5 m

She cannot draw an array of 17 counters with three rows.

The given parameters are:

Counter = 17

Rows = 3

An array is represented as:

Array = Rows * Columns

Where Rows and Columns are integers greater than 0

So, we have

3 * Column = 17

Divide by 3

Column = 5.667

Recall that Rows and Columns are integers greater than 0

This means that she cannot draw an array of 17 counters with three rows.

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Applying the power of power rule, the completed equation is given as follows:

\(x^{10} = (x^5)^2\)

The power of a power rule is used when a single base is elevated to multiple exponents, and states that simplified expression is obtained keeping the base, while the exponents are multiplied.

Hence the missing exponent for this problem is obtained as follows:

2x = 10

x = 10/2

x = 5.

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answer:

perimeter- 12

area- 4.5

step-by-step explanation:

perimeter-

p=4a

=4*3

=12

area-

a=pg/2

=3*3/2

=4.5

good luck :)

i hope this helps

brainliest would be highly appreciated

have a nice day!

Answer:

y=-1.2x-8.2

Step-by-step explanation:

the equation for the slope is mx+b=y so 6x+5y=11 is the same as 5y=11-6x and that is the same as y=11/5-6/5x. we know the slope is -6/5 and so the y intercept of the line is -7+(-6/5)=-8.2. then the answer is y=-1.2x-8.2

Answer:

y = -6/5x - 41/5

BRAINLIEST, PLEASE!

Step-by-step explanation:

y = 11/5 - 6/5x

slope = -6/5

y = -6/5x + b

(-1, -7)

-7 = 6/5 + b

b = -35/5 - 6/5

b = - 41/5

True. Poor retention of new recruits often contributes significantly to high turnover rates within organizations. When new employees leave shortly after being hired, it can be costly for the company in terms of recruitment, training, and lost productivity.

This phenomenon is particularly relevant when the turnover rate is disproportionately higher among new hires compared to existing employees.

There are several reasons why poor retention of new recruits can lead to a disproportionate amount of turnover. First, inadequate onboarding and training programs can leave new hires feeling unprepared or unsupported in their roles, leading to dissatisfaction and a higher likelihood of leaving. Second, mismatches between job expectations and the actual work environment can result in disillusionment and early departures. Finally, a lack of mentorship or opportunities for growth and advancement can make new recruits feel undervalued and prompt them to seek opportunities elsewhere.

Addressing poor retention of new recruits is crucial for organizations to reduce turnover, enhance employee engagement and satisfaction, and optimize their recruitment efforts. Implementing comprehensive onboarding programs, providing ongoing support and mentorship, and creating a positive work environment can help improve retention rates and mitigate the disproportionate impact of new hire turnover.

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Answer:

Change the equation to slope intercept form.

(y= 1.2x + 2.2) or (b= 1.2a + 2.2)

Then shade above the line.

Step-by-step explanation:

Let's say A is "x", and B is "y."

Change the equation to slope intercept form.

120x + 100y = 220.

(Move 120x to the other side of the equation by subtracting 120x from both sides)

100y= -120x +220

(Divide 100y by 100 to remove it from Y, divide the entire right side of the equation by 100)

y= -120x/100 + 220/100

y <= 1.2x + 2.2 -> (b= 1.2a + 2.2)

The new equation is much easier to graph.

THEN, Plot the new equation, since the sign is <= (greater than or equal to)

Make a solid line.

Then shade above the line whatever color necessary, since the sign is also "greater than"

Answer:

See below

Step-by-step explanation:

Given inequality

This is a linear inequality, to graph first find intercepts:

a- intercept, when b = 0

b- intercept, when a = 0

We got two points:

Now graph this with following steps

The graph is attached

Answer:

c:8

Step-by-step explanation:

10/25 = r/20

25r = 200

25       25

r = 8

Answer:2 11/24

Step-by-step explanation:

Answer:

2.4583

Step-by-step explanation:

I helped you.

First

5÷6 and 7÷8 and again similarly 3÷4 and sum the all outcome come from these eqations

Answer:

Yes , the quotient of two rational number always a rational number . Explanation : - If X and Y are integers means they are Rational number and when quotient is generated by division of previous two then the quotient must be rational as well .

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Answer:

(-39/148, -33/37)

Step-by-step explanation:

Let's choose the second equation, 12x + 3 = y, for our substitution.  Substitute (12x + 3) for y in the first equation, obtaining:

8x - 13y = 0  =>  8x - 13(12x + 3) = 0

Next, multiply out -13(12x + 3):  From the above equation we get

                          8x - 156x - 39 = 0

and this simplifies to -148x = 39  or  x = -39/148.

Substitute -39/148 for x in 8x - 13y = 0.  We get:

                              8(-39/148) + 3 = y, so that y = -33/37.

The solution of this system of linear equations is (-39/148, -33/37).

Answer:

  (d)  428,820,000 pounds of garbage

Step-by-step explanation:

Your calculator or spreadsheet can give you the product of two numbers expressed in scientific notation.

  (1.643×10^3 lb/resident) × (2.61×10^5 residents) = 4.28823×10^(3+5) lb

  ≈ 428.82×10^6 lb

  = 428,820,000 lb . . . of garbage

Answer:

bạn cực ngu

Step-by-step explanation:

bạn cực kì ngu

The easiest way to solve this problem is to substract 2π from the angle until we get an angle that is less than 2π.

13/3π is not less than 2π, so we have to substract 2π once more:

7/3π is still not less than 2π, substract 2π once more:

1/3π is less than 2π. It means that the positive angle less than 2π that is coterminal with 19/3π is 1/3π.

The length of the diagonal is 8√2 ft.

If the side of the square is 8 ft, then the diagonal will form a right triangle with legs of length 8 ft. We can use the Pythagorean theorem to find the length of the diagonal (hypotenuse).

Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

In this case, we have:

a = 8 ft (one leg)

b = 8 ft (the other leg)

c = ? (the hypotenuse)

Using the Pythagorean theorem, we have:

c² = a² + b²

c² = 8² + 8²

c² =  64 + 64

c² = 128

c = √128

c = 8√2 ft

Therefore, the length of the diagonal is 8√2 ft.

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The ordered rational numbers representing the gauge readings from least to greatest are 19/10, 63/10, 78/10, 78/10, 13/1, 25/1, 2/1.

To represent the gauge readings as rational numbers, we can express them as fractions with a common denominator.

Given readings:

25 psi pressure

13 psi vacuum

6.3 psi vacuum

7.8 psi vacuum

1.9 psi vacuum

2 psi pressure

7.8 psi pressure

Expressed as rational numbers with a common denominator:

25 psi = 25/1

13 psi = 13/1

6.3 psi = 63/10

7.8 psi = 78/10

1.9 psi = 19/10

2 psi = 2/1

7.8 psi = 78/10

Now, let's order these rational numbers from least to greatest:

1.9 psi = 19/10

6.3 psi = 63/10

7.8 psi = 78/10

7.8 psi = 78/10

13 psi = 13/1

25 psi = 25/1

2 psi = 2/1

Ordered from least to greatest:

19/10, 63/10, 78/10, 78/10, 13/1, 25/1, 2/1

Therefore, the ordered rational numbers representing the gauge readings from least to greatest are 19/10, 63/10, 78/10, 78/10, 13/1, 25/1, 2/1.

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By applying the angle bisector theorem to this triangle, the value of x is 68 units.

What is an angle bisector?

A ray that divides an angle into two equal pieces is known as an angle bisector or the bisector of an angle. For instance, each measure will be similar to 30 degrees if ray KM divides an angle of 60 degrees into two equal parts.

Here, we have

By applying the angle bisector theorem to this triangle, we have:

62/(x+2) = 99.2/112

6944 = 99.2x + 198.4

6944 - 198.4 = 99.2x

6745.6 = 99.2x

x = 68

Hence, the value of x is 68.

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The unit price of the 80-ounce bottle of ketchup is $0.85 per 8 ounces.

To calculate the unit price of a product, we divide the total price by the quantity. In this case, the total price is $8.50 for an 80-ounce bottle of ketchup.

Unit price = Total price / Quantity

Unit price = $8.50 / 80 ounces

Unit price = $0.85 / 8 ounces

Therefore, the unit price of the 80-ounce bottle of ketchup is $0.85 per 8 ounces.

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