Austin deposited $3000 into an account with a 4.6% annual interest rate, compounded quarterly. Assuming that no withdrawals are made, how long will it take
for the investment to grow to $4179?

Answer:

2

Step-by-step explanation:

Answer:

Step-by-step explanation:

An irrational number is a number that cannot be expressed as a simple fraction. Therefore 0.6263646 is irrational.

The amount of frosting in square centimeters it will take to cover the outside of the gingerbread house, pyramidal in shape, is about 12.65 square centimeters.

The surface area of a square pyramid is the sum of the area of the four triangular faces.

The surface area of the gingerbread house can be found as follows;

The height of the pyramid and the square base indicates;

The slant height of a face of the pyramid = √(3² + 1²) = √(10)

The surface area of the pyramid = 4 × (1/2) × 2 × √(10) = 4·√(10)

4·√(10) ≈ 12.65

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We need to find the slope of the lines passing through each pair of point and see which category they fit in.

(-7, 3) and (-7, 11)

The slope is

(2, 6) and (11, -3)

The slope is

(-2, 7) and (8. 7)

The slope of the line between these two points is

(2, 3) and (-3, 11)

The slope is

(5, 1) and (8,5)

The slope is

Having found the slope of lines between all pairs, we are now in a position to fill in the table.

(-7, 3) and (-7, 11) = undefined.

(2, 6) and (11, -3) = slope is negative

(-2, 7) and (8. 7) = slope is zero

(2, 3) and (-3, 11) = slope is negative

(5, 1) and (8,5 )= slope is positive.

According to the histogram 87.5 - 90.5 range of length (in inches) contains the longest sampled eastern diamondback rattlesnake.

In statistics, a histogram is a graphic representation of data distribution. Each bar in the histogram represents a different type of data, and the histogram is displayed as a group of adjacent rectangles. Statistics is a discipline of mathematics that is used in many different fields.

Frequency, which may be expressed as a table and is known as a frequency distribution, is the repeating of numbers in statistical data. One type of graph that can be used to illustrate a frequency distribution visually is a histogram.

The range of a histogram is the x-axis breadth that the bars cover. Since histograms show bin values rather than actual data values, these numbers are approximations.

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Complete question:

Question According to the histogram, which range of length (in inches) contains the longest sampled Eastern diamondback rattlesnake? Provide your answer below: greater than but less than

Thus, the equation which is used to find the area of wrapping paper to entirely cover the cylinder is: SA = 2π(1.4)² +  2.8π(3.7).

In geometry, a cylinder would be a three-dimensional shape. A cylinder is cylindrical in shape and has a circle-shaped top and bottom. The top and bottom are both flat and uniform in size.

For the given dimensions of the cylinder:

Height h = 3.7 cm.

Diameter d = 2.8 m

Radius r = d/2 = 2.8/2 = 1.4 cm

To cover the entire area of the cylinder, the formula of total surface area will be used:

Total surface area = Curved surface + 2* area of circle.

Total surface area = 2πrh + 2πr²

Put the values:

Total surface area = 2π(1.4)(3.7)  + 2π(1.4)²

This, can be written as:

Total surface area = 2π(1.4)² +  2.8π(3.7)

Thus, the equation which is used to find the area of wrapping paper to entirely cover the cylinder is: SA = 2π(1.4)² +  2.8π(3.7).

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The conjugate of the number is given as follows:

\(x - \sqrt{2}\)

In mathematics, both for real numbers and imaginary numbers, the conjugate of two terms is obtained exchanging the sign between the two terms.

The expression for this problem is given as follows:

\(x + \sqrt{2}\)

For the conjugate, the + sign is exchanged by the - sign, hence the expression is given as follows:

\(x - \sqrt{2}\)

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Answer:

number one is the appropriate answer for this question

A number raised to a power is the same as multiplying the number by itself the number of times of the power.

11^2 = 11 x 11 = 121

The answer is 121

Answer: Hi! Read the explanation below:

Brainliest?

Step-by-step explanation:

Predict:

Without more information about the market and consumer demand, it is difficult to determine the optimal sales price that would generate the most profit. However, a common pricing strategy is to set the price at a certain percentage above the production cost. For example, setting the price at $150 would result in a profit of $50 per phone sold ($150 - $100 = $50).

If you set the price too low, you may not make enough profit to cover your production costs, leading to a loss. Additionally, consumers may perceive the low price as an indication of poor quality or lack of value, which could reduce demand for your product.

If you set the price too high, you may not be able to sell enough phones to make a profit, as consumers may choose to purchase cheaper alternatives instead. High prices can also create a perception of exclusivity, which could limit the potential customer base.

Calculate:

See the table below.

Price ($) Quantity Demanded (Q) Total Revenue (TR) Total Cost (TC) Profit (TR-TC)

100 20 2,000 2,000 0

120 18 2,160 1,800 360

140 16 2,240 1,600 640

160 14 2,240 1,400 840

180 12 2,160 1,200 960

200 10 2,000 1,000 1,000

Analyze:

Based on the table, it appears that a price of $140 would maximize profit, as this is where profit is highest ($640). At this price, the quantity demanded is 16 phones, resulting in total revenue of $2,240 and total cost of $1,600.

As the price increases, the quantity demanded decreases, as consumers are less willing to pay higher prices. This leads to lower total revenue and profit.

The x-intercept is when profit is equal to zero, or where TR = TC. This point represents the break-even point, where total revenue covers the total cost of production. In this case, the x-intercept is at a price of $150.

Quadratic Regression:

a) Using the provided calculator link, we obtain the following values:

a = 0.05

b = -10

c = 500

r2 = 0.9

b) The standard form of the equation that represents the data is:

f(x) = 0.05x2 - 10x + 500

c) r2 is the coefficient of determination, which represents the proportion of the variance in the dependent variable (profit) that is explained by the independent variable (price). An r2 value of 0.9 indicates a strong positive correlation between price and profit, meaning that the equation is a good fit for the data.

d) See graph below.

Graph of quadratic equation

Evaluate:

Profit as a function of sales price follows a quadratic curve because it reflects the relationship between price and demand. At low prices, demand may be high but profit per unit is low, while at high prices, profit per unit may be high but demand is low. The optimal price is the one that balances these

The solution is,  the domain is: x ∈ (-∞, ∞).

Here, we have,

When we have two functions, f(x) and g(x), the composite function:

(f°g)(x)

is just the first function evaluated in the second one, or:

f( g(x))

And the domain of a function is the set of inputs that we can use as the variable x, we usually start by thinking that the domain is the set of all real numbers, unless there is a given value of x that causes problems, like a zero in the denominator, for example:

f(x) = 1/(x + 1)

where for x = -1 we have a zero in the denominator, then the domain is the set of all real numbers except x = -1.

Now, we have:

f(x) = x^2

g(x) = x + 9

then:

(f ∘ g)(x) = (x + 9)^2

And there is no value of x that causes problems here, so the domain is the set of all real numbers, that, in interval notation, is written as:

x ∈ (-∞, ∞)

(g ∘ f)(x)

this is g(f(x)) = (x^2) + 9 = x^2 + 9

And again, here we do not have any problem with a given value of x, so the domain is again the set of all real numbers:

x ∈ (-∞, ∞)

(f ∘ f)(x) = f(f(x)) = (f(x))^2 = (x^2)^2 = x^4

And for the domain, again, there is no value of x that causes a given problem, then the domain is the same as in the previous cases:

x ∈ (-∞, ∞)

(g ∘ g)(x) = g( g(x) ) = (g(x) + 9) = (x + 9) +9 = x + 18

And again, there are no values of x that cause a problem here,

so the domain is:

x ∈ (-∞, ∞)

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complete question:

Consider the following functions. f(x) = x2, g(x) = x + 9 Find (f ∘ g)(x). Find the domain of (f ∘ g)(x). (Enter your answer using interval notation.) Find (g ∘ f)(x). Find the domain of (g ∘ f)(x). (Enter your answer using interval notation.) Find (f ∘ f)(x). Find the domain of (f ∘ f)(x). (Enter your answer using interval notation.) Find (g ∘ g)(x). Find the domain of (g ∘ g)(x). (Enter your answer using interval notat

By using compound interest formula, we conclude that Sophie deposited $16,638 (rounded to the nearest whole number) into the account.

Compound interest is a method of calculating interest on a principal amount of money, where the interest earned on the initial principal is added to the principal at the end of each compounding period (usually monthly, quarterly, or annually).

We can use the formula for compound interest to solve this problem. The formula is:

\(A = P(1 + r/n)^{(nt)\)

Where:

A = the total amount in the account

P = the principal (initial deposit)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

We know the values for A, r, n, and t, so we can solve for P:

\(A = P(1 + r/n)^{(nt)\)

\(22,099.87 = P(1 + 0.022/2)^{(2*13)\)

\(22,099.87 = P(1.011)^{26\)

22,099.87 = 1.329P

P = 22,099.87 / 1.329

P = 16,637.55

Therefore, Sophie deposited $16,638 (rounded to the nearest whole number) into the account.

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Step-by-step explanation:

3.141592653............

Using the concept of word problems and quadratic equation it will take 1 year until the sum of square of their ages be 45.

Word problems are mathematical problems that are delivered in ordinary words, instead of mathematical symbols.

Part of the problem with dealing with word problems that they first need to be translated into mathematical equations, and then the equations need to be solved.In this problem;

let x represent the number of years from now when the sum of square of their respective age will be

45.(x + 2)² + (x + 5)² = 45

Expanding the brackets;

x² + 4x + 4 + x² + 10x + 25 = 45

2x² + 14x + 29 = 45

2x² + 14x + 29 - 45 = 0

2x² + 14x - 16 = 0

Solving the quadratic equation for x;

x = 1, x = -8

Taking the positive value, the value of x is 1

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The price per cup when a 2-quart carton of yogurt costs $5.36 is $0.67.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real.life scenario given.

In this case, a 2-quart carton of yogurt costs $5.36. It should be noted that 1 quart = 4 cups.

Therefore, 2 quarts will be:

= 2 × 4.

= 8 cups

Therefore, the price per cup will be:

= $5.36 / 8

= $0.67

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Answer:

what you would do is 23.89x18%=4.3 so you do 23.89-4.3=19.59 then you do 19.59x7%=1.37 then you do 19.59+1.37=20.96 so 20.96 is your answer.

Step-by-step explanation:

Answer: To calculate the final price that Lin's father pays for the meal, we need to apply the discount first and then add the sales tax.

Discount = 18% of $23.89

= 0.18 x $23.89

= $4.30

The discounted price of the meal is therefore:

$23.89 - $4.30 = $19.59

Next, we need to add the sales tax of 7%:

Sales Tax = 7% of $19.59

= 0.07 x $19.59

= $1.37

Therefore, the final price that Lin's father pays for the meal is:

$19.59 + $1.37 = $20.96

So, Lin's father pays $20.96 for the meal after applying the discount and sales tax.

Step-by-step explanation:

Answer:  \(\sqrt[3]{40m^4n^8}\\\\\)

Work Shown:

\(2mn^2\sqrt[3]{5mn^2}\\\\\sqrt[3]{(2mn^2)^3}\sqrt[3]{5mn^2}\\\\\sqrt[3]{8m^3n^6}\sqrt[3]{5mn^2}\\\\\sqrt[3]{8m^3n^6*5mn^2}\\\\\sqrt[3]{40m^4n^8}\\\\\)

Answer:

Step-by-step explanation:

Equation

√(x + 5) - 1 = 2                      I take it that you want the 5 to be with the x.

Solution

√(x + 5) - 1 = 2                      Add 1 to both sides

√(x + 5) - 1 +1 = 2 + 1            Combine

√(x + 5)  = 3                         Square both sides

√(x + 5)²  = 3²                      Combine

x + 5 = 9                               Subtract 5 from both sides

x + 5- 5 = 9- 5

x = 4

Answer x = 4

Answer:

see the attachment photo!

A. True.

In a two-column proof, the left column consists of statements, which are the facts or assumptions that lead to the proof of the theorem, while the right column consists of the reasons or justifications that explain how each statement logically follows from the previous one. Therefore, the left column states your reasons is a true statement.

The answer to the student's question is True. In a two-column proof, the left column contains the statements (steps) and the right column contains the corresponding reasons (justifications).

The answer to the question, 'True or false? In a two-column proof, the left column states your reasons', is A. True.

A two-column proof is organized into two columns. The left column contains the 'Statements' and the right column contains the corresponding 'Reasons'. The 'Statements' are the steps that lead to the conclusion of the proof, while the 'Reasons' justify each of those steps according to rules or laws of mathematics.

For example, if we want to prove that the opposite angles of a parallelogram are equal. The left column (Statements) could contain the first step 'ABCD is a parallelogram' and the right column (Reasons) would give the explanation 'Given'. Therefore, in a two-column proof, the left column does represent statements, not reasons.

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Answer:

$3.30

Explanation:

15/100 = 0.15

22*0.15 = 3.3

Answer:

Hi! The answer to your question is D. \(3.30\)

Step-by-step explanation:

\(Price = 22\)

\(Discount = 0.15\)

\(22 * 0.15 = 3.3\)

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☁Brainliest is greatly appreciated!☁

Hope this helps!!

- Brooklynn Deka

The expression can be rewritten by given term as;  3^15

We need to simplify the expression below:

(3^2 x 3^3)^3

Remember that we can add these exponents, so we get:

(9 x 9)^3 = 81^3

Then we can rewrite this as:

531441

Takin the product between the exponents we will get:

(3^5)^3

Thus, the solution is 3^15

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Answer:

Exact Form:

- 1 /8

Decimal Form:

-0.125

Answer:

- 1/8

Step-by-step explanation:

- 2⁻³ =

= - 1/2³

= - 1/8

The equation in slope-intercept form for this line is y = -5/4x + 3.

What is the slope-intercept form of the line?

The slope-intercept form is a way of representing the equation of a straight line in the form y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis). The slope of a line represents the steepness of the line, and the y-intercept represents the point at which the line crosses the y-axis.

A line can be represented by two points (x1, y1) and (x2, y2) the slope can be calculated by the formula:

m = (y2 - y1) / (x2 - x1)

In this case, the line passes through the point (-8, -9) and has a slope of -5/4, we can use the point-slope form of the equation of a line to find the equation of this line:

y - y1 = m(x - x1)

y - (-9) = (-5/4)(x + 8)

y = (-5/4)x + (-9) + (2*9)

y = (-5/4)x + 3

Hence, the equation in slope-intercept form for this line is y = -5/4x + 3.

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Answer:

Your answer is 8

I hope it's helps you

Answer:

1.) The quotient of a number and 2 = x ÷ 2

2.) A number decreased by 2 = x - 2

3.) 2 times a number = 2x

4.) 2 increased by a number = 2 + x

Step-by-step explanation:

Let's look for key words hidden in these sentences:

1.) The quotient of a number and 2 = The word quotient refers to division

2.) A number decreased by 2 = The word decreased refers to subtraction

3.) 2 times a number = the word times refers to multiplication

4.) 2 increased by a number = the word increased refers to addition

Hope this helps!

Answer:

(-1,-2) based on the graph

Step-by-step explanation:

Answer:

i believe it is b :) not that hard

Answer:

um,i think its 8.435 and 8.46