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 total balance after four years when compounded continuously is $12,615.24.

A technique of calculating interest on a loan or investment where interest is compounded an endless number of times annually is called continuous compounding. Continuous compounding is a method of growing an investment or debt over time by continually adding interest earned over a relatively brief period of time to the principal. In financial computations where interest is earned or charged continuously, such in the bond or mortgage markets, continuous compounding is frequently utilised.

The compound interest is given as:

[tex]A = Pe^{(rt)}[/tex]

Substituting the values:

[tex]A = 12000 * e^{(0.0125 * 4)}\\A = 12000 * e^{(0.05)}[/tex]

A = 12000 * 1.05127

A = 12615.24

Therefore, the total balance after four years is $12,615.24.

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To be able to determine the size of the space for the photograph from the frame area, we need to know the area of the frame and the dimensions of the photo frame (length and width). The given information is insufficient.

Most ideally, we determine the size of an object using different measurements and units of measurement. The most common measurement used for size is length or distance, which refers to the distance between two points on an object.

The other measurements used for size include area, volume, mass, weight, and density, which provide additional information about the object's characteristics. In order to determine the size of an object mathematically, we must understand the units of measurement being used and the appropriate formulas or equations for calculating size.

Translated question "Patricia designed the photo frame on the right. She makes frames of different measurements, but keeping its thickness, which is 4 cm, as shown in the drawing. How can you determine the size of the space for the photograph from the frame area?

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The derivative of f(x) is (1/2)(9x - sin²(2x))^(-1/2) * (9 - 4sin(2x)cos(2x)).

What is a derivative?

A derivative is a mathematical concept used in calculus to determine the rate at which a function changes with respect to its input variable. It measures the instantaneous rate of change of the function at a specific point, and is calculated as the limit of the rate of change as the input variable approaches zero. The derivative is represented by the notation f'(x) or dy/dx, and can be used to find important information about the function, such as its slope, maxima and minima, and points of inflection.

What are expression?

In mathematics, an expression is a combination of numbers, symbols, and/or variables that are combined in some way using mathematical operations such as addition, subtraction, multiplication, division, or exponentiation.

To find the derivative of f(x) = √[9x - sin²(2x)], we can use the chain rule and the power rule of differentiation:

f(x) = √[9x - sin²(2x)]

f'(x) = (1/2)(9x - sin²(2x))^(-1/2) * (9 - 4sin(2x)cos(2x))

Using the chain rule, we first take the derivative of the expression inside the square root, which is 9x - sin²(2x), and then multiply it by the derivative of the expression inside the square root. The derivative of the expression inside the square root is:

(1/2)(9x - sin²(2x))^(-1/2) * (d/dx)(9x - sin²(2x))

Using the chain rule and the power rule of differentiation, we can find the derivative of 9x - sin²(2x) as:

d/dx (9x - sin²(2x)) = 9 - 4sin(2x)cos(2x)

Substituting this into the expression for f'(x), we get:

f'(x) = (1/2)(9x - sin²(2x))^(-1/2) * (9 - 4sin(2x)cos(2x))

So, the derivative of f(x) is (1/2)(9x - sin²(2x))^(-1/2) * (9 - 4sin(2x)cos(2x)).

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The derivative of f(x) is: f'(x) = (9 - 4sin(2x)cos(2x)) / [2√(9x - sin²(2x))].

Differentiation is a mathematical concept used to calculate the rate at which one quantity changes with respect to another. In calculus, it refers to the process of finding the derivative of a function, which gives the slope of the tangent line at any point on the function.

In the given question,

To find the derivative of f(x), we can use the chain rule and the power rule of differentiation.

f(x) = √[9x - sin²(2x)]

Let's first simplify the expression under the square root:

g(x) = 9x - sin²(2x)

Taking the derivative of g(x) gives:

g'(x) = 9 - 2sin(2x) * cos(2x) * 2

g'(x) = 9 - 4sin(2x)cos(2x)

Now we can use the chain rule to find f'(x):

f'(x) = [1/2(9x - sin²(2x))^(-1/2)] * g'(x)

f'(x) = [1/2√(9x - sin²(2x))] * [9 - 4sin(2x)cos(2x)]

Therefore, the derivative of f(x) is:

f'(x) = (9 - 4sin(2x)cos(2x)) / [2√(9x - sin²(2x))]

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Answer:

180

Step-by-step explanation:

The survey results, it can be estimated that approximately 17.93% of adult Americans have seen a ghost at some point in their lives[tex] (718/4,005 = 0.1793)[/tex].

However, it is important to note that this estimate is based on a sample and there may be some degree of error or variability.

Additionally, the term "supernatural experiences" may encompass a wide range of phenomena beyond just seeing ghosts, so the estimate may not accurately reflect the prevalence of all types of supernatural experiences in the population.

In the given survey on supernatural experiences, 718 out of 4,005 adult Americans reported having seen a ghost. Assuming this sample is representative of the adult American population, you can calculate the proportion of adults who have seen a ghost.

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Answer:

Step-by-step explanation:

Given g(x) = 8x2 − x + 5, find the following.

(a). g(0) = 5

(b). g(−1) = 14

(c). g(r) = ?

(d). g(x + h) = ?

The gravitational waves would have traveled through a volume of approximately 3.244 x 10⁷⁴ cubic light-years.

The space-time continuum is subject to gravitational waves, which move at the speed of light. They are caused by the acceleration of large objects that distort space-time around them, such as neutron stars or black holes.

The bending of space-time brought on by the existence of mass and energy is what Einstein's theory of general relativity refers to as gravity rather than a force.

The radius of the sphere can be determined using the formula:

R = Distance / Time

For 1.3 billion light years we have:

R = Distance / Time = 1.239 x 10²⁵ meters

Substituting the value in the volume:

V = (4/3) x π x R³ = 3.244 x 10⁷⁴ cubic light-years (approx)

Hence, the gravitational waves would have traveled through a volume of approximately 3.244 x 10⁷⁴ cubic light-years.

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Answer:

Lion area: 60

Lion Perimeter: 34

Tiger Area: 60

Tiger perimeter: 64

Step-by-step explanation:

Argon is the gas who would work best for something that needs a steady, nonreactive gas. (Ar).

When a neutral environment is required, argon is frequently used. In this manner, titanium and other volatile metals are produced. Additionally, it is used in the manufacture of incandescent bulbs to prevent air from corroding their filaments and by welders to safeguard the weld region.

A chemical substance in the periodic table's 18th group is argon. It is an expensive gas and the third most common gas in the atmosphere of the planet. Aside from nitrogen and oxygen, argon is the most prevalent gas in the atmosphere.

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Step-by-step explanation:

To solve the given equation, we can start by taking the square root of both sides of the equation:

(x – 7)^2 = 36

√((x – 7)^2) = ±√36

x – 7 = ±6

Now, we can solve for x by adding 7 to both sides of the equation for each case:

x – 7 = 6 or x – 7 = -6

x = 13 or x = 1

Therefore, the values of x that satisfy the equation are x = 13 and x = 1. The other values, x = -29 and x = 42, do not satisfy the equation.

Answer:

Option C would likely produce the most representative sample of the population of smartphones made by the company. By testing every 500th smartphone off the production line, the manufacturer can ensure that they are selecting a random sample of smartphones from throughout the production process. This can help to account for any variations or changes that may occur in the manufacturing process over time.

Option A, testing the first smartphone off the production line each day, may not be representative of the entire production run since the first smartphone may not be representative of the rest of the batch. Similarly, option B, testing the last 1000 smartphones produced each month, may not be representative of the entire production run as there may be variations in quality and safety standards throughout the month.

Option D, testing every smartphone made on Wednesday, would likely not produce a representative sample as it may not account for any variations or changes that occur during other days of the week.

Answer:

Step-by-step explanation:

Area of one base:

  [tex]A=\pi r^2=\pi (3.2)^2 =10.24\pi cm^2[/tex]

Perimeter of circle base:

  [tex]P=2\pi r=2\times \pi \times 3.2 =6.4 \pi cm[/tex]

Height of cylinder:

  [tex]h=8.7cm[/tex]       (given in question)

Total surface area:

[tex]SA=[/tex] area 2 circles + area rectangle

     [tex]=(2\times 10.24 \pi) +(6.4\pi\times 8.7)[/tex]           (Area rectangle = cylinder height x

                                                              circle perimeter)

     [tex]=239.26cm^2[/tex]

We will use sine function, and length of the opposite side is [tex]\frac{25\sqrt{3}}{2}$[/tex] feet.

To solve for the opposite side of the right triangle, we would use the sine function. In a right triangle, the sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse.

In this problem, we are given that one angle of the right triangle is 60 degrees and the hypotenuse is 25 feet. Let's label the opposite side as x and the adjacent side as y. Then we can use the sine function:

[tex]$\sin 60^\circ = \frac{x}{25}$[/tex]

Simplifying the left side, we have:

[tex]$\frac{\sqrt{3}}{2} = \frac{x}{25}$[/tex]

Multiplying both sides by 25, we get:

[tex]$x = \frac{25\sqrt{3}}{2}$[/tex]

Therefore, the length of the opposite side is [tex]\frac{25\sqrt{3}}{2}$[/tex] feet.

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The domain of the function R(x) is (-∞, -4) U (-4, 3) U (3, ∞).

The vertical asymptote is x = -4 and x = 3

The horizontal asymptote is y = 1.

In Mathematics, a domain refers to the set of all real numbers (x-values) for which a particular function is defined.

In Mathematics, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached below, we can logically deduce the following domain:

Domain = {0, ∞}.

In conclusion, an asymptote is a line which the graph of any given function approaches but would never cross or touch;

Vertical asymptote is x = -4 and x = 3

Horizontal asymptote is y = 1.

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Complete Question:

Analyze the graph of the function.

[tex]R(x)=\frac{x^2}{x^2+x-12}[/tex]

a. What is the domain of R(x)?

b. What is the vertical and horizontal asymptote?

The chain rule is used when a function is composed of two or more functions, where one function is applied to the output of the other. In other words, it is used when a function is "nested" inside another function. Thus, option A is correct.

We can solve this problem by applying the chain rule and the product rule of differentiation. Let's begin by simplifying the expression inside the parentheses:

[tex]y = ex (e^-2x + 7)[/tex]

Now, let's apply the product rule:

[tex]dy/dx = (ex)'(e^-2x + 7) + ex(e^-2x + 7)'[/tex]

Using the chain rule, we can find (ex)':

[tex](ex)' = ex[/tex]

And using the chain rule again, we can find [tex](e^-2x + 7)':[/tex]

[tex](e^-2x + 7)' = (-2e^-2x)[/tex]

Substituting these values back into the original equation, we get:

[tex]dy/dx = ex(e^-2x + 7) + ex(-2e^-2x)[/tex]

Simplifying, we get:

[tex]dy/dx = ex(e^-2x + 7 - 2e^-2x)[/tex]

[tex]dy/dx = ex(e^-2x - e^-2x + 7)[/tex]

[tex]dy/dx = ex(7)[/tex]

Therefore, the answer is A) 7.

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Answer:

f(x) = (x+3)^2 + 5

Step-by-step explanation:

Hope this is right :)

Answer:

Step-by-step explanation:

The simple interest formula is:

I = Prt

where I is the interest earned, P is the principal or initial investment, r is the annual interest rate as a decimal, and t is the time in years.

Substituting the given values:

P = $2,926

r = 0.64% = 0.0064 (as a decimal)

t = 19 years

I = 2,926 * 0.0064 * 19

I = $353.21

Therefore, Elisabeth will have earned $353.21 in interest after 19 years.

Answer:

X = 61,  Angle 57 and 123

Step-by-step explanation:

If you could provide the exact question that would be great, but from the information given what we know is that the entirety of half of a circle is 180 degrees so the angle at x-4 and the angle and 2x+1 must be equal to 180 degrees.

Therefore:

x-4  +  2x+1 = 180 degrees

X = 61,    Therefore:

x-4 -->  61 -4 = 57 degrees

2x+1 ---> 2(61) +1  = 123 degrees

So:

The angles are 57 degrees for x-4 and 123 for 2x+1 .

Answer:

The total number of fruits Halston can choose is 3 + 4 + 2 = 9.

The number of ways she can choose two fruits without restrictions is 9C2 = (98)/(21) = 36.

The number of ways she can choose two fruits where both are bananas is 2C2 = 1.

Therefore, the number of ways she can choose two fruits that are not bananas is 36 - 1 = 35.

So, the probability that Halston chooses two fruits that are not bananas is:

35/36

Therefore, the probability that Halston chooses two fruits that are not bananas is 35/36.

To assess the reasonableness of Cameron's statement that he spent about $215 on a gaming system and video games, we can use mental math to estimate the total cost.

We know that he spent $130 on a gaming system and $80 on video games. If we round $80 up to $100 and add it to $130, we get:

$130 + $100 = $230

So based on this estimate, it seems like Cameron's statement of spending about $215 is not entirely accurate. However, it is close to the actual total cost, which is within 10% of the estimated total.

Therefore, we can say that while Cameron's statement may not be entirely precise, it is reasonably close to the actual total cost and can be considered reasonable.

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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With the help of proportions in the given similar triangles we know that the value of x is 3.5 units.

Euclidean geometry states that two objects are comparable if they have the same shape or the same shape as each other's mirror image.

One can be created from the other more precisely by evenly scaling, possibly with the inclusion of further translation, rotation, and reflection.

These three theorems—Angle-Angle (AA), Side-Angle-Side (SAS), and Side-Side-Side (SSS)—are reliable techniques for figuring out how similar triangles are to one another.

So, in the given situation:

TR and WY are as follows:
TR/WU

24/2

2/1

Similarly,

TS/WV

2/1

7/x

7/3.5

Therefore, with the help of proportions in the given similar triangles we know that the value of x is 3.5 units.

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The length of the base is 6 inches.

What is triangle?

A triangle is a three-sided polygon, which is a flat shape with straight sides. It is a basic shape in geometry and has many interesting properties that are useful in mathematics and other fields.

The formula for the area of a triangle is A = 1/2 * b * h, where A is the area, b is the length of the base, and h is the height of the triangle.

In this case, we know that the area of the triangle is 21 in² and the height is 7 in. So we can substitute these values into the formula and solve for the base:

21 = 1/2 * b * 7

Multiplying both sides by 2:

42 = b * 7

Dividing both sides by 7:

6 = b

Therefore, the length of the base is 6 inches.

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Complete question : The area of the triangle is 21 in² ad the height is 7 in. what is the length of the base?

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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Answer: it depends; if exam day, no

Step-by-step explanation:

275 miles can be driven in one day on a budget of $100.

an inequality is defines as a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on either sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

The rental car costs $45 a day and $0.20 a mile. So, for a budget of $100, the inequalities can be written as

45+.20m≤ 100

Where m= no.of miles

No.of miles can be travelled in 100

.2m=100-45

m=55/.2

m=275miles

Hence,275 miles can be driven in one day on a budget of $100.

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The expressions in a single exponent are 9³/9⁹ = 9⁻⁶ and 14⁻³ * 14¹² = 14⁹

Diego's mistake is multiplying the expressions, wrongly

Expression 1

Given that

9³/9⁹

To solve, we make use of the law of indices

So, we have

9³/9⁹ = 9⁻⁶

Expression 2

Here, we have

14⁻³ * 14¹²

Using the law of indices, we have

So, we have

14⁻³ * 14¹² = 14⁹

Diego's expression is given as

6⁴ * 8³ = 48⁷

The mistake in Diego's expression is that he multiplied 6 and 8, and then add the exponents

This is incorrect, and the actual solution is

6⁴ * 8³ = 1296* 512

6⁴ * 8³ = 2¹³ × 3⁴

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Answer:

The geometric mean of 9 and 6 is 4/3

Step-by-step explanation:

The geometric mean of 8 and 6 is [tex]4\sqrt{3}[/tex]

The geometric mean of two numbers [tex]x_1[/tex] and [tex]x_2[/tex] is given by the formula:

[tex]GM=\sqrt{x_1\times x_2}[/tex]

The two given numbers are 8 and 6

That is, [tex]x_1=8[/tex] and [tex]x_2=6[/tex]

Substitute [tex]x_1=8[/tex]  and [tex]x_2=6[/tex] into the formula [tex]GM=\sqrt{x_1\times x_2}[/tex]

[tex]GM=\sqrt{8\times 6}[/tex]

Simplifying further:

[tex]GM=\sqrt{48}[/tex]

[tex]GM=4\sqrt{3}[/tex]

Therefore, the geometric mean of 8 and 6 is [tex]4\sqrt{3}[/tex]

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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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