Sue deposited $1,500 into two different accounts.
- She deposited $600 into an account that pays 7.5% simple interest.
- She deposited $900 into an account that pays 6% compounded annually.
If Sue does not deposit additional money into the accounts and she doesn't withdraw any
money from the accounts, which is closest to the total balance she will have in the two
accounts at the end of 5 years?
F $2,029.40
G $2,005.68
H $529.40
J $1,995.00

The quadratic equation in the given graph can be written in the vertex-form as:

y = -2(x - 1)² + 4

We can see the graph of a quadratic equation. Remember that a quadratic equation with a vertex (h, k) and a leading coefficient a can be written as:

y = a*(x - h)² + k

in the graph we can see that the vertex is (1, 4), replacing that we will get:

y = a*(x - 1)² + 4

In the graph we also can see that the curve passes through the point (0, 2), replacing thesevalues in the equation we will get:

2 = a*(0 - 1)² + 4

2 = a + 4

-2 = a

Then the quadratic is:

y = -2(x - 1)² + 4

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It will take around 3.72 months to pay off the credit card debt.

The formula for APR is:

A = P * [tex](1 + r/n)^{nt}[/tex]

In which,

A = amount after compounding.

P = balance amount

r = rate of interest.

n = number of time compounded.

Initial balance: $30,000.

Payments per month = $200.

Expenses = $100

Balance amount = 30,000 - 12 *(200 - 100)

Balance amount = $28800

So, time taken for paying off credit card debt.

30,000 = 28800  [tex](1 + 0.24/1)^{1*t}[/tex]

[tex](1.24)^{t}[/tex] = 30,000 / 28800

[tex](1.24)^{t}[/tex] = 1.04

Solve by using logarithmic function.

t = ln (1.04) / 1.24

t = 0.31  year

t = 3.72 months

Thus, it will take around 3.72 months to pay off the credit card debt.

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The variance of the number of citizens favoring the supermarket is 6.

To find the variance of the number of citizens favoring the supermarket, we need to use the binomial distribution formula:

Variance = n × p × (1 - p)

where n is the number of trials (25 in this case), p is the probability of success (0.6 in this case), and (1 - p) is the probability of failure.

Plugging in the values, we get:

Variance = 25 × 0.6 × (1 - 0.6)

Variance = 25 × 0.6 × 0.4

Variance = 6

The binomial distribution is a probability distribution that models the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes, success or failure. In this case, the trials are the 25 citizens who were chosen, and the success is the event of favoring the supermarket, which has a probability of 0.6.

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Answer:

Step-by-step explanation:

(x+3)^2=49

x+3=√(49)

x+3=√(7^2)

x+3=7

x+3-3=7-3

x+3=-√(49)

x+3=-7

x+3-3=-7-3

x = 4,-10

Answer:

19.2 ft

Step-by-step explanation:

Expression equivalent to 5x - 4 are 5(x - 4/5), 5x - 20/5, 10x/2 - 8/2 and 3(5x/3) - 4

To create an expression equivalent to 5x - 4, we need to use arithmetic operations such as addition, subtraction, multiplication, and division, along with numbers and variables. The goal is to manipulate the numbers and variables in a way that results in the same value as 5x - 4.

Here are some examples of how we can do this:

5(x - 4/5)

In this expression, we start with x and subtract 4/5 from it. Then we multiply the result by 5. This is equivalent to distributing the 5 to x and -4/5, which gives us 5x - 4.

5x - 20/5

Here, we simply subtract 20/5 (which simplifies to 4) from 5x. This gives us 5x - 4.

(25x - 20)/5

In this expression, we start with 25x and subtract 20 from it. Then we divide the result by 5. This is equivalent to simplifying the expression to 5x - 4.

10x/2 - 8/2

This expression might look a bit different, but it's still equivalent to 5x - 4. Here, we start with 10x and divide it by 2, which gives us 5x. Then we subtract 8/2 (which simplifies to 4) from it, giving us 5x - 4.

3(5x/3) - 4

In this expression, we start with 5x and divide it by 3. Then we multiply the result by 3, which gives us 5x. Finally, we subtract 4 from it, giving us 5x - 4.

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Step-by-step explanation:

To find the percentage that $4250 represents of $6500, we can use the following formula:

percentage = (part / whole) x 100%

where "part" is $4250 and "whole" is $6500.

Substituting these values into the formula, we get:

percentage = (4250 / 6500) x 100%

percentage = 0.6538 x 100%

percentage = 65.38%

Therefore, $4250 represents 65.38% of $6500.

Answer: It is approximately 65%

Step-by-step explanation: Divide $4,250 by $6,500 and your answer without rounding is 65.3846%

The probability of rolling an even number on a single die is 1/2, or 50%. This can be calculated by considering the possible outcomes of rolling the die.

There are six possible outcomes, and three of these are even numbers (2, 4, and 6). Therefore, there is a 3/6, or 1/2, chance of rolling an even number. In terms of probability, this can be expressed as a fraction, percentage, or decimal. As a fraction, the probability of rolling an even number on a single die is 3/6, or 1/2. As a percentage, the probability of rolling an even number on a single die is 50%. As a decimal, the probability of rolling an even number on a single die is 0.5. No matter how it is expressed, the probability of rolling an even number on a single die is 1/2, or 50%. This can be easily remembered by considering that there are six possible outcomes, and three of them are even numbers.

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Algebraic expressions are useful for solving different and complex equations in mathematics, as well as for modelling real-life situations such as revenue, cost, inference, etc

The algebraic expression is: [tex]6x - 9[/tex].

To represent the sentence as an algebraic expression, we can follow these steps: Identify the variable. In this case, “a number” is x. Identify the operation. In this case, “less than” means subtraction and “times” means multiplication.

An algebraic expression is an expression that contains variables, constants and mathematical operations. Algebraic expressions are useful because they can help us solve different and complex equations.

For example, if you want to calculate the area of a rectangle with length x and width y, you can use the algebraic expression xy to represent the area.

Write the expression using the order of operations. In this case, we need to multiply six by x first, then subtract nine from the result.

Therefore, The algebraic expression is: [tex]6x - 9[/tex]

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The expressions can be written as  :a. log5.625 ≈ 0.75.

                                                             b. log6.4 + log6.12 ≈ 1.67.

                                                             c. log3.9^{4} ≈ 2.47.

What is logarithm function?

A logarithm function is a mathematical function that determines the power to which a fixed number, called the base, must be raised to produce a given value and The logarithm function is the inverse of the exponential function. The most commonly used base for logarithmic functions is 10 (log base 10), but other bases such as 2 (log base 2) and the natural logarithm base e (ln) are also used.

a. Since there is no base specified, we assume the base to be 10 by default. Therefore, we can write:

log5.625 = log(5625/1000)

Using the property log(a/b) = log(a) - log(b), we can simplify this expression to:

log5.625 = log(5625) - log(1000)

Using the change of base formula, we can convert the logs to a common base, such as 2 or e:

log5.625 = log(5625)/log(10) - log(1000)/log(10)

Evaluating the logs using a calculator or by simplifying, we get:

log5.625 ≈ 0.75

Therefore, log5.625 ≈ 0.75.

b. Using the property log(a) + log(b) = log(ab), we can simplify the expression:

log6.4 + log6.12 = log(6.4 × 6.12)

Using the change of base formula, we can convert this to a common base:

log6.4 + log6.12 = log(6.4 × 6.12)/log(10)

Evaluating the log using a calculator or by multiplying 6.4 and 6.12 and simplifying, we get:

log6.4 + log6.12 ≈ 1.67

Therefore, log6.4 + log6.12 ≈ 1.67.

c. Using the property log(a^{n}) = n log(a), we can simplify the expression:

log3.9^{4} = 4 log3.9

Using the change of base formula, we can convert this to a common base:

log3.9^{4} = 4 log(3.9)/log(10)

Evaluating the log using a calculator or by simplifying, we get:

log3.9^{4} ≈ 2.47

Therefore, log3.9^{4} ≈ 2.47.

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The calculated value of the force of the resistance is 15.62 N

We can use Newton's Second Law of Motion to solve this problem. The formula is:

F = m*a

where F is the net force, m is the mass of the object, and a is the acceleration.

In this case, the brick is falling through water, so there are two forces acting on it:

The net force is the difference between these two forces:

F_net = F_gravity - F_resistance

The weight of the object is:

F_gravity = m*g

So, we have

F_gravity = 2 kg * 9.81 m/s^2 = 19.62 N

Now we can use the formula for net force to find the force of water resistance:

F_net = F_gravity - F_resistance

F_resistance = F_gravity - F_net

F_resistance = 19.62 N - m*a

This gives

F_resistance = 19.62 N - 2 kg * 2 m/s^2 = 15.62 N

Therefore, the force of water resistance is 15.62 N.

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The sum of the given fractions is (2x + 10)/x.

What is fraction ?

A fraction is a way of representing a part of a whole or a ratio between two quantities. It is written in the form of a numerator and a denominator separated by a horizontal line. The numerator represents the number of equal parts under consideration, while the denominator represents the total number of equal parts that make up the whole. For example, the fraction 3/4 represents three equal parts out of a total of four equal parts. Fractions can be added, subtracted, multiplied, and divided to perform various mathematical operations.

According to the question:
The given fractions can be added if they have a common denominator. In this case, the common denominator is 9x.

So, we need to write the fractions with 9x as the denominator:

2/1 * (9x/9x) = 18x/9x

10/1 * (9/9x) = 90/9x

Now, we can add these two fractions:

18x/9x + 90/9x = (18x + 90)/9x = 9(2x + 10)/9x = 2x + 10/ x

Therefore, the sum of the given fractions is (2x + 10)/x.

Q: Find K by Adding the fractions and simplify if possible k=(2*(9x))+(10*(9x))

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Answer:

147

Step-by-step explanation:

A= h^b b=21*14= 147

A square is not created when a plane slices through a cone.

What is square?

A square is a geometrical shape that has four equal sides and four equal angles of 90 degrees.

What is cone?

A cone is a three-dimensional geometric shape that tapers smoothly from a flat base to a pointed top or apex. It looks like a funnel or an ice cream cone.

When a plane intersects or slices through a cone, it creates a variety of different shapes depending on the angle of the plane and the position of the cone.

If the plane intersects the cone at an angle perpendicular to its base, it will create a circle. If the plane intersects the cone at an angle that is not perpendicular to its base, it will create an ellipse.

If the plane intersects the cone at an angle that is parallel to one of its generators (the lines that can be drawn from the vertex of the cone to any point on its base), it will create a parabola. If the plane intersects the cone at an angle that is not parallel to one of its generators, it will create a hyperbola.

Therefore, a square is not created when a plane slices through a cone.

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The formula that could help Jim find Ann’s number, n as soon as he is given the result, r is n = (r - 7) / 5.

Formula 1;

Let the unknown number Ann thought of = n

(n × 5) + 7 = r

5n + 7 = r

If Jim is given Ann's number n if given the results, r

This means Jim will make Ann's number n the subject of the formula;

5n + 7 = r

Subtract 7 from both sides

5n = r - 7

divide both sides by 5

n = (r - 7) / 5

Therefore, the formula written in terms of n is n = (r - 7) / 5

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Finally, express the solution as an interval of real numbers or as a set of values that make the inequality. x<10.4, x>3.3, x≥32 and x≤-15.

To solve an inequality, you need to find the set of values that make the inequality true. The process for solving an inequality depends on the type of inequality and the variables involved. Here are the general steps:

Finally, express the solution as an interval of real numbers or as a set of values that make the inequality true. If the inequality is strict (> or <), use an open interval (e.g., (a, b)). If the inequality includes equality (≥ or ≤), use a closed interval (e.g., [a, b]).

by the question.

a. x-3.5>6.9

x>6.9+3.5

x>10.4

b. 6.4>x+3.1

x[tex]\geq 32[/tex]

c. x/4≤8

x≤32

d. 2/3x≤-10

x≤-15

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Therefore, if Jane had left a message on every call, you would have gotten 670 voicemails. The solution is 670.

Since "percent" is a slang term for "per hundred," when we discuss percentages, we are speaking to a fraction of a hundred. In a variety of contexts, including math, science, finance, and daily living, percentages are used. The percent sign (%) is commonly used to denote percentages. As an illustration, to determine what proportion of 50 apples are red, you would split the number of red apples by the total number of apples and multiply the result by 100.

given

If Jane had phoned 1,000 times and you had allowed 67% of those calls to go to voicemail, then 67% of those calls would have left voicemails for you.

You can multiply the overall number of calls by the proportion of calls that went to voicemail to determine how many voicemails you would have received:

1000 x 67% = 670

Therefore, if Jane had left a message on every call, you would have gotten 670 voicemails. The solution is 670.

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The complete question is :-  

Jane called one thousand times to tell you she's sorry. If you saw she was calling and let your phone go to voicemail 67% of the time, how many voicemails would you have received if she left one each time?

Possible Answers:

3,700

57,000

67

None of the given answers

670

Answer:

"Undefined slope"

Step-by-step explanation:

The line is vertical on the graph.

Every point on the line has the same x-coordinate.

If the line crosses the x-axis where x=-7, then the

x-coordinate of every point on the line is -7, and the

equation of the line is

                                     x = -7 .

Answer:

The product of two numbers is 21.

Step-by-step explanation:

If the first number is -3, which equation represents this situation and what is the second number? A. The equation that represents this situation is x − 3 = 21.

Answer:

0.9973 or 364/365

Step-by-step explanation:

Assuming that every day of the year is equally likely to be someone's birthday, the probability that a randomly selected person has a birthday on the 1st day of the month is 1/365, since there are 365 possible birthdays in a year.

Therefore, the probability that a randomly selected person does not have a birthday on the 1st day of the month is:

P(not on 1st day) = 1 - P(on 1st day)

P(not on 1st day) = 1 - 1/365

P(not on 1st day) = 364/365

So, the probability that a randomly selected person does not have a birthday on the 1st day of the month is 364/365 or approximately 0.9973.

The product of the fraction 1/4 x5/3 is 4/12

Fractions are defined as the part of a whole number, variable or element.

The different types of fractions in mathematics are;

Examples of simple fraction; 1/4, 2/3

Examples of improper fractions; 3/2. 4/3

Examples of proper fractions; 1/2, 2/3

From the information given, we have that;

1/4 x5/3

To determine the product, we need to multiply the numerator, then multiply the denominator

5/12

We can no longer divide the values as there is no common divisor.

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The resulting number is 12/5

Arithmetic operations is a branch of mathematics, that involves the study of numbers, operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication and Division.

Given that we need to, increase the number 15/16 by 3/5 of it, then increase the resulting number by 3/5 of it

So, performing the operations,

15/16+15/16×3/5

= 15/16(1+3/5)

= 15/16(8/5)

= 120/80

= 3/2

Now,

3/2+3/2×3/5

= 3/2(1+3/5)

= 3/2(8/5)

= 24/10

= 12/5

Hence, the resulting number is 12/5

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Answer: 160

Step-by-step explanation: The straight line or line X is 180 degrees. So subtracted 20. This is because X is intersected by another line which makes the upper notch 20 degrees.

The correct answer is E (-1,-3). Reflection across the x-axis is a transformation that flips the object across an imaginary line that runs through the center of the x-axis.

Transformation in mathematics is the process of changing an object or figure in some way. This includes changing the size, position, rotation or reflection of an object. Transformations can also be used to move a figure from one coordinate system to another. Common transformations include translation, rotation, reflection and scaling.

In this case, the x-axis is the line y = 0. The figure ABCD is reflected across this line, resulting in point A being reflected to E.

When a figure is reflected, the x-coordinates remain the same, while the y-coordinates change sign. This means that the x-coordinate of point A (-1) remains the same, but the y-coordinate (3) changes to its opposite (-3). Therefore, the resulting coordinates of point A are (-1,-3).

Reflection across the x-axis is an example of a transformation. Transformations involve changing the position, size or orientation of a figure, but not its shape. This means that the figure ABCD is still the same shape after being reflected, but its position has changed. After being reflected, the figure is now located on the opposite side of the x-axis.

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Step-by-step explanation:

lol sorry for untidy work

Answer:

First, we need to find the radius of the base of the cone. We can see from the grid that the diameter is 8 units, so the radius is 4 units (or 4 feet).

Next, we can use the formula for the volume of a cone to find the height:

V = (1/3)πr^2h

Substituting the given volume and radius, and using 3.14 for π, we get:

200.96 = (1/3) x 3.14 x 4^2 x h

Simplifying and solving for h, we get:

h = 200.96 / (1/3 x 3.14 x 4^2)

h = 200.96 / 53.02

h ≈ 3.79 feet (rounded to two decimal places)

To construct the cone vertically on the grid with respect to the center of the base, we can draw a circle with radius 4 units (or 4 feet) centered at the point (4,4) on the grid. Then, we can draw a line from the center of the circle (point (4,4)) up to a point above the circle that is 3.79 units (or 3.79 feet) away from the center. This line represents the height of the cone. Finally, we can connect the endpoint of the line to the points where the circle intersects the grid to complete the cone.

answer: x= 20x

Step-by-step explanation: 2+2 is 4, 4+4 is 8, quick maths

Answer: 90.32%

Step-by-step explanation:

To calculate your updated grade after receiving a 75% on a quiz that counts 7% of your overall grade, you can use the following formula:

New grade = (Old grade * (100 - weight of quiz)) + (Quiz grade * weight of quiz)

Plugging in your values, we get:

New grade = (97 * (100 - 7)) + (75 * 7)

New grade = (97 * 93) + (5.25)

New grade = 903.16

Therefore, your new grade is 90.32%.

Answer:  The sum of the weight of all your coursework plus your final is equal to 14.00

Step-by-step explanation:

not sure