If f(x) = 3^x + 10 and g(x) = 2x - 4, find (f-g)(x)

The interest rate of the account is 2%

From the question, we are to determine the interest rate of the account

From the compound interest formula, we have that

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

Where A is the amount

P is the principal

r is the rate

n is the number of times compounded

t is the time in years

From the given information,

A = $1,325.71

P = $1,130

n = 6

t = 8 years

Thus,

1325.71 = 1130(1 + r/6)⁶⁽⁸⁾

1325.71 = 1130( 1 + r/6)⁴⁸

1325.71/1130 = ( 1 + r/6)⁴⁸

Take the 48th root of both sides

1.003333 = 1 + r/6

1.003333 - 1 = r/6

0.003333 = r/6

r = 6 × 0.003333

r = 0.019998

r ≈ 0.02

r ≈ 2%

Hence, the interest rate of the account is 2%.

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Answer:

198 months

Step-by-step explanation:

12 months in a year times 16 years plus 6 months is 198

If a hospital medical unit has 50 beds and the unit provided 1,420 days of service, the average daily census for the medical unit in May is 28.4.

To find the average daily census for a medical unit in May, we divide the total number of days of service provided by the number of beds in the unit. Here's how we do it:

According to the question, Total number of beds = 50 and Total number of days of service = 1,420

Average daily census = Total number of days of service / Total number of beds

Average daily census = 1,420/50

Average daily census = 28.4

Therefore, the average daily census for the medical unit in May is 28.4.

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The graph for y = 4(1/4)ˣ is B)

Explain graphs.

A graph is a visual representation of a set of data, typically in the form of a diagram or a chart. A graph is made up of points, called vertices or nodes, that are connected by lines or curves, called edges. Graphs can be used to display various types of information, including mathematical functions, relationships between variables, and patterns in data. They are commonly used in fields such as science, engineering, economics, and social sciences to convey complex information in a simple and easy-to-understand manner.

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Answer:

This is the graph. Hope the pic loads.

Answer:

y = 5x+18

Step-by-step explanation:

y - 3 = 5(x + 3)

Distribute

y -3 = 5x+15

Add 3 to each side

y - 3+3 = 5x + 15 +3

y = 5x+18

This is slope intercept form (y = mx+b) where m is the slope and b is the y intercept

Answer:

A regular dog has 4 legs so it has 4 paws. If each paw needs one wipe Jen will need 4 wipes.

Jen will need 4 wipes for each paw

x=2/3

6(2/3) + 4 9/10 =4 + 4 9/10 = 8 9/10

Answer:

2x-1=y,2y+3=x

Step-by-step explanation:

no explanation

Answer:

Step-by-step explanation:

0.5^(t/5600) = 0.08

2^(-t/5600) = 0.08

-t/5600 = log₂0.08

t = -5600 log₂0.08 ≈ 20406 years

The percent increase from the wholesale price of one sweater to the store's selling price of one sweater is 25.9%.

To calculate the percent increase, we need to find the difference between the selling price and the wholesale price, and then divide it by the wholesale price.

The wholesale price of 20 sweaters is $260, which means the wholesale price of one sweater is $260/20 = $13.

The selling price of one sweater is $17.55.

To find the percent increase, we subtract the wholesale price from the selling price: $17.55 - $13 = $4.55.

Then, we divide the difference by the wholesale price: $4.55 / $13 ≈ 0.3504.

To express this as a percentage, we multiply by 100: 0.3504 * 100 ≈ 35.04%.

Rounded to the nearest tenth, the percent increase is approximately 35%.

Therefore, the correct answer is (J) 35%.

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Answer:

Step-by-step explanation:

We can use trigonometry to solve this problem. Let's draw a right triangle to represent the situation:

        |\

        | \

   h    |  \   9 ft

        |   \

        |    \

        |     \

        -------

        6 ft

Here, h represents the height on the wall where the ladder touches. We want to find the angle of elevation θ.

Using the right triangle, we can write:

sin(θ) = h / 9

cos(θ) = 6 / 9 = 2 / 3

We can solve for h using the Pythagorean theorem:

h^2 + 6^2 = 9^2

h^2 = 9^2 - 6^2

h = √(9^2 - 6^2)

h = √45

h = 3√5

So, sin(θ) = 3√5 / 9 = √5 / 3. We can solve for θ by taking the inverse sine:

θ = sin^-1(√5 / 3)

θ ≈ 37.5 degrees

Therefore, to the nearest tenth of a degree, the angle of elevation the ladder makes with the ground is 37.5 degrees.

The measures of the angles are ∠1 = 127°, ∠2 = 53°, ∠3 = 127°, ∠4 = 37°, ∠5 = 53°, ∠6 = 90°, ∠7 = 37°, ∠8 = 143°, ∠9 = 37° and ∠10 = 143°

From the question, we have the following parameters that can be used in our computation:

The transversal lines and the other lines

So, we have

∠1 = 180 - 53

Evaluate

∠1 = 127°

Also, we have

∠5 = 53°

By vertical angles, we have

∠2 = 53°

∠3 = 127°

Next, we have

∠4 = 127 - 90°

∠4 = 37°

Solving further, we have

∠6 = 90°

By corresponding angles, we have

∠7 = 37°

∠9 = 180 - 90 - 53°

∠9 = 37°

∠10 = 90 + 53°

∠10 = 143°

∠8 = 143°

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Answer:

1000000

Step-by-step explanation:

I'm not sure what you meant by "scientific notation". So uhh, I only solved the 1.0 times 10^6,

10^6=10×10×10×10×10×10

10^6=1000000

(Fun fact. If you ever see a power of 10, you don't actually need to solve it. Look at the power, and add the same amount of 0's. For example 10^2. Power sign is 2. 2 trailing 0's.)

Answer:

Is Square Root of 25 Rational or Irrational?  

Step-by-step explanation:

A rational number can be expressed in the form of p/q. Because √25 = 5 and 5 can be written in the form of a fraction 5/1. It proves that √25 is rational.

The answer is:

Work/explanation:

What are rational numbers?

Rational numbers are integers and fractions.

Irrational numbers are numbers that cannot be expressed as fractions, such as π.

Now, \(\bf{\sqrt{25}}\) can be simplified to 5 or -5; both of which are rational numbers.

The Lagrange polynomial basis L = {l0(t), l1(t),..., ln(t)} is a set of polynomials with specific properties: li(t_i) = 1 for all i = 0, 1,..., n, and li(t_j) = 0 for all i, j = 0, 1,..., n, where i ≠ j. This basis allows you to represent any polynomial p(t) in Pr by a linear combination of the Lagrange polynomials in the basis L.

Polynomials are mathematical expressions consisting of variables and coefficients, often used in algebra and calculus. In this context, we are considering polynomials of degree n or less, denoted by Pr.

Lagrange polynomials are a type of polynomial that form a basis for Pr. This means that any polynomial in Pr can be expressed as a linear combination of the Lagrange polynomials. The Lagrange polynomial basis is formed from a set of n + 1 distinct points in R, denoted {to, t1, ..., tn}.

Each Lagrange polynomial, denoted li(t), has the following properties:
- li(ti) = 1 for all i = 0, 1,..., n
- li(tj) = 0 for all i, j = 0, 1,..., n, i + j.

In other words, each Lagrange polynomial is equal to 1 at its corresponding point ti, and is equal to 0 at all other points. These properties ensure that the Lagrange polynomials are linearly independent and form a basis for Pr.

Hope this helps! Let me know if you have any further questions.
Hi! I'd be happy to help you with your question. Polynomials are mathematical expressions involving a sum of powers in one or more variables multiplied by coefficients. The Lagrange polynomial is a specific type of polynomial that provides a way to interpolate a polynomial function using a set of n + 1 distinct points in R, {t0, t1, ..., tn}.

The Lagrange polynomial basis L = {l0(t), l1(t),..., ln(t)} is a set of polynomials with specific properties: li(t_i) = 1 for all i = 0, 1,..., n, and li(t_j) = 0 for all i, j = 0, 1,..., n, where i ≠ j. This basis allows you to represent any polynomial p(t) in Pr by a linear combination of the Lagrange polynomials in the basis L.

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A real-world example of how piecewise functions can be used is in:

Piecewise functions are tools that are often used for representing ways where the connection between variables alters under varying intervals or conditions.

To demonstrate the application of piecewise functions, consider the following example such as  calculating taxes on income. where a different nations implement an income tax system that make use of a segmented function to determine tax rates based on various income brackets.

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Answer:

2c+7

Step-by-step explanation:

Jessica is 7 more than 2x Cory's age.

Given that Cory is c years old,

then Jessica is

2c+7

I hope this helps! :)

At an airport, the length of time for both the shaded and open parking that a lost parking ticket would be an advantage depends on the parking policy of the airport.

Typically, airports have a maximum daily rate for parking, and the longer you park, the cheaper the daily rate becomes. However, most airports also charge an hourly rate for short-term parking. If you lose your parking ticket, you may have to pay the maximum daily rate, regardless of how long you parked your vehicle. In some cases, if you lose your parking ticket, the airport may charge you based on the amount of time you were parked, but this may require verification such as providing proof of payment, license plate number or other details that can help airport staff determine the length of time you parked. This may take some time and inconvenience on your part. It's important to note that deliberately losing a parking ticket to save money is not advisable as it may be considered a violation of the airport's parking policies and could result in additional fees or even legal consequences. It's always best to keep your parking ticket in a safe place to avoid any potential issues or extra costs.

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Answer:

x=3y-29/y-8

Step-by-step explanation:

3(y-10)+1=x(y-8)

xy-8x=3y-29

x(y-8)=3y-29

/y-8        /y-8

x=3y-29/y-8

the capacity of the largest container that can measure the contents of each drum an exact number of times is 36 liters.

To find the capacity of the largest container that can measure the contents of each drum an exact number of times, we need to determine the greatest common divisor (GCD) of the volumes of the drums.

The GCD is the largest positive integer that divides each of the given numbers without leaving a remainder. In this case, we want to find the GCD of 36, 45, and 72.

First, let's find the prime factorizations of these numbers:

36 = 2^2 * 3^2,

45 = 3^2 * 5,

72 = 2^3 * 3^2.

To find the GCD, we take the product of the common prime factors raised to the lowest powers they appear in the factorizations:

GCD(36, 45, 72) = 2^2 * 3^2 = 4 * 9 = 36.

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Answer:

x = 4, -2 1/2

Step-by-step explanation:

factors:

(2x + 5) (x - 4)

set each factor equal to zero:

2x + 5 = 0

2x = -5

x = -5/2

x - 4 = 0

x = 4

The value of the unknown number x is 8.

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

The given numbers include:

The sum of the given numbers is calculated as follows:

\(2 + 4 + \text{x} + 6 = 12 + \text{x}\)

The mean of the given 4 numbers is calculated as follows:

\(\dfrac{12+\text{x}}{4} =5\)

\(12+\text{x}=20\)

\(\text{x}=20-12\)

\(\text{x}=8\)

Thus, the value of the unknown number x is 8.

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Answer:

i think it would be sprint cause it is lest money and the mintues is 450 but the other is just 50 more mintues and you have to pay 22 more dollor for verizion  so i pick sprint have a nice day

Step-by-step explanation:

Answer:

what are we soposed to do?

Step-by-step explanation:

Answer:

Answer: $11,942.29

Step-by-step explanation:

Let the value after 9 years be y

y = 22400 (0.9325)^9

y = 11,942.29Step-by-step explanation:

Answer:

with what nothing here to help you with. so is there an actual question you need help with?

Answer:

y = -3/4x + 7/4

Step-by-step explanation:

First you move to get y by itself

4y = -3x + 7

then you divide by 4

this may be a messy answer

then you get y = -3/4x + 7/4

a) The amount of water in the pool after 2 hours can be calculated using the equation.

Water in pool = 10L/hour × 2 hours = 20L.

b) The pool will be 80L when the equation is satisfied: 80L = 10L/hour × Time.

Solving for Time, we find Time = 8 hours.

c) Part b) is linear.

a) To calculate the amount of water in the pool after 2 hours, we can use the equation:

Water in pool = Water filling rate × Time

Since the pool gets filled up with 10L of water per hour, we can substitute the values:

Water in pool = 10 L/hour × 2 hours = 20L

Therefore, after 2 hours, there will be 20 liters of water in the pool.

b) To determine the number of hours it takes for the pool to reach 80 liters, we can set up the equation:

Water in pool = Water filling rate × Time

We want the water in the pool to be 80 liters, so the equation becomes:

80L = 10 L/hour × Time

Dividing both sides by 10 L/hour, we get:

Time = 80L / 10 L/hour = 8 hours

Therefore, it will take 8 hours for the pool to contain 80 liters of water.

c) Part b) is linear.

The equation Water in pool = Water filling rate × Time represents a linear relationship because the amount of water in the pool increases linearly with respect to time.

Each hour, the pool fills up with a constant rate of 10 liters, leading to a proportional increase in the total volume of water in the pool.

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