Your friend in college decides to purchase textbooks using his credit card, which has an APR
(Annual Percentage Rate) of 12.5% compounded continuously. He charges $500 for the
textbooks. Without making any payments, after how many years will his credit card balance be
$1360? Round your answer to the nearest year.

Answer:

(1/2)(7 + 12) = 19/2 = 9.5 inches

The requried measure of the middle strip of the trapezoidal prism is 9.5 inches.

Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression. The goal is to obtain an expression that is easier to work with, manipulate, or solve.

Here,
The purse shown is a trapezoidal prism. the front face of the purse has a stripe.

The measure of the mid stripe is given by,
= 1 / 2[ sum of lower and upper strip]
= (1/2)(7 + 12)
= 19/2
= 9.5 inches

Thus, the requried measure of the middle strip of the trapezoidal prism is 9.5 inches.

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Answer:

  D.  the length of the quarter

Step-by-step explanation:

Given Patrick started playing 4 minutes into the 2nd quarter, and played until the end of the 3rd quarter, you want to know how long Patrick played.

If q is the length of a quarter, Patrick's playing time is ...

  2q -4 . . . . minutes

In order to give this a numerical value, we need to know the value of q.

The most important variable to the problem is ...

  D.  the length of a quarter.

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The line of reflection must be the line halfway between the x-coordinates of the corresponding vertices of each polygon. This line is x=4.

So, the line of reflection is x=4.

A line of reflection is a line used in mathematics that functions like a mirror, reflecting all points on one side of the line onto the other side so that each point is equally distant from the line as its reflected point on the other side. It is also known as the mirror line or the axis of reflection.

To determine the line of reflection that maps polygon ABCDE to polygon A' B' C' D' E', we need to look for a line that is equidistant from each corresponding pair of points.

Reflection across the x-axis or y-axis will not work because the corresponding vertices of the two polygons have different y-coordinates or x-coordinates, respectively.

Reflection across x=5 or y=6 will also not work because the line is not equidistant from each corresponding pair of points.

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The measure of angle ABD (which is the same as angle CBD) is 45 degrees.

The quadrilateral's opposing sides are equal. Triangles ABC and ABCD have equal angles on either side of their equal sides. In the quadrilateral ACBD, the opposing angles are also equal. A parallelogram is formed by ACBD.

We can use the fact that the total of the angles of a triangle is always 180 degrees to determine the measure of angle CBD. As a result, we have:

Angle ABD + Angle CBD + Angle BCD = 180 degrees

Substituting the given angle measures, we get:

Angle ABD + Angle CBD + 90 degrees = 180 degrees

Simplifying, we get:

Angle ABD + Angle CBD = 90 degrees

But we know that Angle ABD = Angle CBD, so we can substitute:

2 x Angle ABD = 90 degrees

Dividing both sides by 2, we get:

Angle ABD = 45 degrees

So, the measure of angle ABD (which is the same as angle CBD) is 45 degrees.

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Answer: If every hour the candle decreases in height by 2 inches, turn it into a chart! If you learned this already, figure out which variable is the constant and the decrease in height for each hour. Or you could just multiply the amount of hours by 2, there for 2x2=4 so that a 4 inch decrease. 12-4=8 and the candle will be 8 inches tall. Hope this helps :D

Step-by-step explanation:

The value of x and y is 2 , -2

The equation are as follows:

x+2y=-2....(i)

-3x+2y=-10.....(ii)

Now, Solving each system of equations by adding and subtracting:

And, find the value of x and y

Multiply by 3 in equation (i) we get:

3x + 6y = - 6 ---(iii)

And add the equations (ii) and (iii)

3x + 6y + (-3x) + 2y = -6 - 10

6y + 2y = -16

8y = -16

y = -2

Now, For solving the value of x :

Subtract the equation (i) and (ii), we get:

x + 2y - (-3x) - 2y = -2 + 10

x + 3x =  8

4x = 8

x = 2

Now, The value of x and y is 2 , -2

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The mean and range of the same population can differ if there is a significant difference between the sampled respondents.

Between Jayden and Carter, Carter's calculation will provide a better understanding of the population.

The reason is that he sampled more people with a wider time range.

The mean is the average number of minutes it took for the respondents to dress up. The goal of any survey work is to capture a significant size of the population whose opinions can give a true picture of the situation being examined.

In the case of Carter, we see that he took a more sizable amount of the population having randomly selected 7 samples of 10 students. A greater number of respondents will give a truer picture of the factor being surveyed.

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The domain of the function plotted is

In mathematics, the domain of a function is the set of all possible values of the input (independent variable) for which the function is defined.

So we can say that, it is the set of all possible values that we can substitute into the function and get a valid output (dependent variable).

In the graph, watching the x axis which is the input variables we can see that the domain is all real numbers from -4 to 4

In general, the domain of a function depends on the specific form of the function and any restrictions or conditions that may apply to the input values.

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A sample size of approximately 9604 citizens is needed to achieve at least 95% confidence that the estimate is within 1% of the true percentage.

To determine the sample size needed for a study to estimate the percentage of citizens in a town who favor water fluoridation with 95% confidence and a margin of error within 1%, you can use the following formula:

Sample Size (n) = ([tex]z^{2}[/tex] * P * (1-P)) / [tex]E^{2}[/tex]

where:
Z = 1.96 (the Z-score corresponding to a 95% confidence level)
P = estimated proportion of the population (use 0.5 if no prior knowledge)
E = margin of error (0.01 for 1%)

Plugging the values into the formula:

n = ([tex]1.96^{2}[/tex] * 0.5 * (1-0.5)) / [tex]0.01^{2}[/tex]
n = (3.8416 * 0.5 * 0.5) / 0.0001
n = 0.9604 / 0.0001
n ≈ 9604

Therefore, a sample size of approximately 9604 citizens is needed to achieve at least 95% confidence that the estimate is within 1% of the true percentage.

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The simple interest earned after 3 years on $500 at an interest rate of 6% is $90.

Simple interest is a type of interest that is calculated based only on the initial amount borrowed or invested, called the principal amount, and does not take into account any additional interest earned on the interest over time.

To find the simple interest earned on $500 at an interest rate of 6% after 3 years, we can use the formula:

Simple Interest = Principal x Rate x Time

Where

Principal = $500

Rate = 6% = 0.06 (in decimal form)

Time = 3 years

Plugging these values into the formula, we get

Simple Interest = $500 x 0.06 x 3

= $90

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I have solved the question in general, as the given question is incomplete.

The complete question is:

Find the simple interest earned after 3 years on $500 at an interest rate of 6%.

The population size of the fish species after 5 years is approximately 99.

The population size of the fish species after t years is given by the exponential function P(t)=510(0.72)^t. To find the population size, we simply need to substitute the given value of t in the equation.

For example, if we want to find the population size after 5 years, we substitute t=5 in the equation:

P(5) = 510(0.72)^5

P(5) = 510*0.1934917632

P(5) = 98.680799232

P(5) ≈ 99.

Therefore, the population size of the fish species after 5 years is approximately 99.

We can determine whether the population is growing or decaying by examining the value of the base of the exponential function, which is 0.72 in this case. Since the base is less than 1, we know that the exponential function represents exponential decay. This means that the population of the fish species in the lake is decreasing over time, and the rate of decrease is determined by the value of the base. In this case, the population is decreasing by a factor of 0.72 each year.

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BigDecimal gives you control over how values are rounded. By default option(d) all calculations are exact and rounding occurs.

BigDecimal is a Java class that provides a way to perform exact calculations on decimal numbers with a high degree of precision and control over rounding. Unlike primitive data types, such as double and float, which are prone to rounding errors due to their binary representation, BigDecimal stores numbers using a base-10 representation, allowing for more precise calculations.

Additionally, it allows the programmer to specify rounding rules, such as rounding up or down to a certain number of decimal places, ensuring that the results of calculations are accurate and consistent. This makes BigDecimal a useful tool for applications that require precise numerical calculations, such as financial and scientific applications.

Therefore, the correct option is (d) all calculations are exact and rounding occurs

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The value of 3×(2×-5) is 30

What is meant by the term value?

Value refers to the worth or usefulness of something, typically determined by its usefulness, desirability, or importance in relation to other things. It can also refer to the ethical or moral principles and beliefs that guide a person's actions and behaviours.

According to the given information

To solve the expression -3×(2×-5), we first need to evaluate the expression inside the parentheses:

2×-5 = -10

Then, we can substitute this value into the original expression and simplify further:

-3×(-10) = 30

Therefore, -3×(2×-5) = 30.

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Answer:

b + 17

Step-by-step explanation:

Now we have to,

→ Simplify the given expression.

The property we use,

→ Distributive property.

The expression is,

→ 3(6 + b) - (2b + 1)

Let's simplify the expression,

→ 3(6 + b) - (2b + 1)

Applying Distributive property:

→ 3(6) + 3(b) - (2b) - (1)

→ 18 + 3b - 2b - 1

Combining the like terms:

→ (3b - 2b) + (18 - 1)

→ (1b) + (17)

→ b + 17

Hence, the answer is b + 17.

The probability that Amber does not arrive at work by 9 am is calculated by summing the probabilities of two scenarios: the bus being on time and Amber not arriving by 9 am and the bus being late and Amber not arriving by 9 am. The calculated probability for her late arrival at work is 17/60.

The subject of this problem is probability. There are two scenarios in which Amber may not arrive at work by 9 am: either the bus is on time but she does not arrive by 9 am or the bus is late and she does not arrive by 9 am.

First, let's consider the probability that Amber's bus arrives on time, which is said to be 5/6. If her bus is on time, the probability that she arrives at work by 9 am is 4/5, which means that the probability she does not arrive by 9 am is 1-4/5 = 1/5. Therefore, the probability that the bus is on time and she does not arrive by 9 am is 5/6 * 1/5 = 1/6.

Alternatively, consider the scenario where the bus is late. We can find the probability of this by subtracting the probability that the bus is on time (5/6) from 1, so the probability that the bus is late is 1/6. If her bus is late, the probability she arrives at work by 9 am is 3/10, implying that the probability she does not arrive by 9 am is 1-3/10 = 7/10. Hence, the probability that the bus is late and she does not arrive at work by 9 am equals 1/6 *7/10 = 7/60.

Thus, the total probability that Amber does not arrive at work by 9 am is 1/6 + 7/60 = 10/60 + 7/60 = 17/60.

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The probability for the possibility on a failing the exam is  1/3 , shown on the scale.

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Any collection of results constitutes an event. Events are represented by capital letters, such as A and B. For instance, if the experiment involves flipping a single fair coin, event A might only receive one head. P(A) represents the probability of an event A.

Given that-

probability = number of favourable outcome / total outcome

number of favourable outcome = 1

number of total outcome = 3

probability = 1/3

Thus, the probability for the possibility on a  failing exam is 1/3 , shown on the scale.

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Answer:

195.5 sq. ft.

Step-by-step explanation:

If you ever wondered how to find the area of your kitchen floor using a scale drawing, you're in luck! I'm going to show you how to do it in a few easy steps. First, you need to know the scale factor, which is the ratio of the scale drawing to the actual floor. In this case, the scale factor is 1 in = 2 ft, which means that one inch on the paper is equal to two feet on the ground. Pretty neat, huh?

Next, you need to multiply the scale drawing dimensions by the scale factor to get the actual floor dimensions. For example, if the scale drawing is 5 3/4 inches long and 8 1/2 inches wide, you multiply those numbers by 2 to get 11 1/2 feet long and 17 feet wide. That's how big your kitchen floor really is!

Finally, you need to multiply the actual floor dimensions to get the area of the floor. This is where it gets tricky, because you have to deal with fractions and decimals. But don't worry, I'll walk you through it. You can use the distributive property to multiply two numbers with fractions. For example, (11 1/2) x (17) = (11 x 17) + (1/2 x 17) = 187 + 8.5 = 195.5. That's the answer! Your kitchen floor has an area of 195.5 square feet. Congratulations, you just learned how to use a scale drawing to find the area of your kitchen floor!

I hope you enjoyed this lesson and found it funny. If not, maybe you should try a different scale factor or a different kitchen. Just kidding!

High clouds are those that form at altitudes of at least 20,000 ft (6000 m).

At high altitudes, ice crystals form due to which cloud formation occurs.   Cirrus, cirrostratus, and cirrocumulus clouds are a few types of clouds. Cirrostratus clouds frequently form a thin, white layer that resembles a veil and covers the entire sky. Small, spherical, white clouds called cirrocumulus develop in long rows. Because they can provide information about changes in atmospheric pressure, temperature, and moisture levels in the upper atmosphere, these high clouds are crucial for meteorologists to investigate.

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Answer:

Step-by-step explanation:

To find x and the degree measure of each angle, we can use the fact that the sum of the angles in a triangle is always 180 degrees.

(a) Writing an equation to find x, we have:

mZH + m<1 + m<J = 180

(2x - 3) + (5x + 7) + x = 180 (substituting given angle measures)

8x + 4 = 180 (combining like terms)

8x = 176

x = 22

Therefore, x = 22 is the solution to the equation.

(b) To find the degree measure of each angle, we can substitute x = 22 into the given expressions:

mZH = 2x - 3 = 2(22) - 3 = 41 degrees

m<1 = 5x + 7 = 5(22) + 7 = 117 degrees

m<J = x = 22 degrees

Therefore, the degree measures of the angles are mZH = 41 degrees, m<1 = 117 degrees, and m<J = 22 degrees.

A) The correct features is,

⇒ a = 9000

⇒ r = 15%

B) The equation correctly models the context of the problem is,

⇒ y = 9000 (0.85)ˣ

We have to given that;

Tiffany’s mother bought a car for $9000 five years ago.

And, She wants to sell it to Tiffany based on a 15% annual rate of depreciation.

Now, We have;

the exponential growth formula is,

⇒ y = a(1 − r)ˣ

Here, We have;

⇒ a = 9000

⇒ r = 15%

Thus, We get;

The equation correctly models the context of the problem is,

⇒ y = a(1 − r)ˣ

⇒ y = 9000 (1 - 0.15)ˣ

⇒ y = 9000 (0.85)ˣ

Therefore, We get;

A) The correct features is,

⇒ a = 9000

⇒ r = 15%

B) The equation correctly models the context of the problem is,

⇒ y = 9000 (0.85)ˣ

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The sales tax owed on a $124.54 purchase at Walmart with an 8.5% sales tax rate is $10.59.

Suppose you spent $124.54 at Walmart and the sales tax rate is 8.5%. To calculate how much sales tax you owe, we first need to convert the sales tax rate from a percentage to a decimal. We do this by dividing the percentage by 100. So, the sales tax rate in decimal form is:

8.5% ÷ 100 = 0.085

Next, we multiply the purchase price by the sales tax rate in decimal form to calculate the amount of sales tax owed:

$124.54 × 0.085 = $10.59

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If in the mail, she received 14 envelopes, and each envelope included $2. 70,Sarah received a total of $37.80 in the mail.

Sarah received a total of 14 envelopes, and each envelope had $2.70. To find out how much money she received in total, we can multiply the number of envelopes by the amount of money in each envelope:

Total money = 14 × $2.70

We can simplify the expression by first multiplying the whole number, 14, by the tenths value of $2.70, which is $0.70:

Total money = $37.80

This amount of money is the sum of all the money in the 14 envelopes she received. It can be useful to double-check the answer by adding up the amounts in each envelope manually, but in this case, it is not necessary since we have already calculated the total.

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Answer:

4 or ≈ 12.6

Step-by-step explanation:

L = r * θ

r = 12

θ = 60 = (/3) when converted to radians by multiplying (/180)

then multiply

(/3)*12 = 4 or ≈ 12.6

The intercepts of the graph of y = x²- 25 are (-5, 0), (5, 0), and (0, -25).

Data can also be presented as a table. However, when the information is presented graphically, it is much easier to understand. There are many types of charts and each of them serves specific purposes in different fields.  

To find the x-intercepts of the graph, we need to set y = 0 and solve for x:

0 = x²- 25

Adding 25 to both sides gives:

25 = x²

Taking the square root of both sides gives us:

x = ±5

So the x-intercepts are (-5, 0) and (5, 0).  To find the y-intercept, we need to set x = 0 and solve for y:

y = 0²-25

y = -25

So the y-intercept is (0, -25).  

Therefore, the intercepts of the graph of y = x² - 25 are (-5, 0), (5, 0), and (0, -25).

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Given statement: For log normally distributed returns, the annual geometric average return is always greater than the arithmetic average return.

The given statement is true.

This is because log normal distribution assumes that the rate of return is compounded continuously, which leads to a higher final value of the investment.

For lognormally distributed returns, the geometric average return is greater than the arithmetic average return.

This is because the lognormal distribution has a positive skew, meaning that there are more small positive returns and fewer large negative returns.

This leads to compounding effects over time, which favor the geometric average return.

The geometric average return is calculated by taking the nth root of the product of (1+Ri),

where Ri is the return for the ith period.

The arithmetic average return is calculated by taking the average of the returns over a period.

Therefore, for lognormally distributed returns, the geometric average return is greater than the arithmetic average return.

The geometric average return takes into account the compounding effect, whereas the arithmetic average return does not.

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Answer:

input output

3 7

8 16

n blank

Step-by-step explanation:

we can see that the function's output is twice the input plus one. Therefore, when the input is 6, the output will be 2 * 6 + 1 = 13. When the input is 14, the output will be 2 * 14 + 1 = 29. However, since the output for the input value "n" is not given in the table, we cannot determine the output for that input.

I hope it helps you

a) The length of the hypotenuse AB is 15.

b) The angle ∠A is approximately 53 degrees.

c) The angle ∠C is 90 degrees.

d) The angle ∠B is approximately 37 degrees.

a) To find the length of the hypotenuse AB, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the legs is equal to the square of the hypotenuse. In this case, we have:

AB² = AC² + CB²

AB² = 12² + 9²

AB² = 144 + 81

AB² = 225

AB = √225

AB = 15

Therefore, the length of the hypotenuse AB is 15.

b) To find the angle ∠A, we can use trigonometry. The sine of an angle is the ratio of the opposite side to the hypotenuse. In this case, we have:

sin(∠A) = AC/AB

sin(∠A) = 12/15

sin(∠A) = 0.8

Taking the inverse sine of 0.8, we get:

∠A = sin⁻¹(0.8)

∠A ≈ 53

Therefore, the angle ∠A is approximately 53 degrees.

c) Since angle ∠C is the right angle, its measure is 90 degrees.

d) To find the angle ∠B, we can use the fact that the sum of the angles in a triangle is 180 degrees. Therefore:

∠B = 180 - ∠A - ∠C

∠B = 180 - 53 - 90

∠B ≈ 37

Therefore, the angle ∠B is approximately 37 degrees.

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Answer: 33.375 feet

Step-by-step explanation:

To find the maximum height, we need to find the vertex of the parabolic function h = 16t² + 12t + 30.

The vertex of a parabola with equation y = ax^2 + bx + c is located at x = -b/2a and y = c - b^2/4a.

In this case, a = 16, b = 12, and c = 30.

So,

t = -b/2a = -12/(2*16) = -3/8

h = 16(-3/8)² + 12(-3/8) + 30 = 33.375

Therefore, the maximum height reached is 33.375 feet.

Answer: 24 inches.

Step-by-step explanation:

We can use the formula for the area of a triangle to solve for the length of the base:

A = (1/2)bh

where:

A = the area of the triangle (in this case, 72 square inches)

b = the length of the base (what we're trying to find)

h = the height of the triangle (in this case, 6 inches)

Plugging in the values we know, we get:

72 = (1/2)b(6)

72 = 3b

b = 24

Therefore, the length of the base of the triangle is 24 inches.

Answer:

1) f(-2) = -2 + 3

2) f(-2) = 1