If the rate of inflation is 3.4% per year, the future price p(t) (in dollars) of a certain item can be modeled by the following exponential function, where t is the number of years from today. p(t)=25000(1.034)^t. Find the current price of the item and the price 10 years from today.

The minimum of P is 16 and the maximum of P is 24.

Calculating the value of P for these points, we get:


P(2,6) = 4*2 + 2*6 = 20


P(0,8) = 4*0 + 2*8 = 16


P(4,2) = 4*4 + 2*2 = 24


P(3,3) = 4*3 + 2*3 = 18


Therefore, the minimum of P is 16 and the maximum of P is 24.

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The solution to this equation 9ˣ - 1 = 2 is 1/2.

The correct option is A.

What is an equation?

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

Given:

An equation:

9ˣ - 1 = 2

Simplifying,

9ˣ  = 3

3²ˣ = 3

Comparing, we get,

2x = 1

x = 1/2

Therefore, the solution is x = 1/2.

Answer:

It’s a right triangle

Step-by-step explanation:

15 squared plus 8 squared equals 17 squared which 289=289

Answer:

  32°

Step-by-step explanation:

You want the measure of the smaller angle of the linear pair marked (3g+23) and (7g+127).

The angles of a linear pair total 180°, so we have ...

  (3g +23) +(7g +127) = 180

  10g = 30 . . . . . . . . . subtract 150

  g = 3 . . . . . . . . . divide by 10

The smaller angle is ...

  ∠PKT = (3·3 +23)°

  ∠PKT = 32°

A rectangular prism actually has three pairs of bases. Each pair of bases is a set of two opposite and parallel faces on the rectangular prism.

The first pair of bases is the two opposite and parallel rectangles on the top and bottom of the prism. The second pair of bases is the two opposite and parallel rectangles on the front and back of the prism. The third pair of bases is the two opposite and parallel rectangles on the left and right sides of the prism.

Each pair of bases is congruent, meaning they have the same shape and size. This is because a rectangular prism is a type of polyhedron with six rectangular faces, and each pair of opposite faces is parallel and congruent to each other.
In conclusion, a rectangular prism has three pairs of bases, each consisting of two opposite and parallel rectangular faces.
I hope this helps! Let me know if you have any further questions.

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Answer:

Step-by-step explanation:

30x453.6=13608 grams

The cost of 5 pounds of bananas in 1939 would have been $2.709.

According to the US Bureau of Labor Statistics, the cost of 1 pound of bananas is $0.63/lb. In 1939, the cost of bananas was 14% lower. Therefore, to find the cost of bananas in 1939, we need to calculate 14% of $0.63/lb and then subtract it from $0.63/lb.

Calculate 14% of $0.63/lb
0.14 * $0.63/lb = $0.0882/lb

Subtract $0.0882/lb from $0.63/lb to get the cost of bananas in 1939
$0.63/lb - $0.0882/lb = $0.5418/lb

Multiply the cost of bananas in 1939 by the number of pounds Pam buys
$0.5418/lb * 5 lb = $2.709

Therefore, the cost of 5 pounds of bananas in 1939 would have been $2.709.

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Given:

What is the interest earned when $46,230 is invested for 9 years at 7.8% p.a?

To find:

The interest

Solution:

Answer:

218.88

Step-by-step explanation:

We can conclude that the measure of length AB is 23.46 ft and the measure of length BC is 9 ft.

Sine formula is used to calculate the sine angle of a right-angled triangle which is the ratio of the opposite side and the hypotenuse.

Given is that a 40-ft-wide house has a roof with a 6-12 pitch (the roof

rises 6 ft for a run of 12 ft). The owner plans a 14-ft-wide addition that will

have a 3-12 pitch to its roof.

We can write the measure of length AB as -

AB = 6 + √(9 + 296)

AB = 6 + 17.46

AB = 23.46 ft

We can write the measure of length BC as -

BC = 6 + 1/4 x 12

BC = 6 + 3

BC = 9 ft

Therefore, we can conclude that the measure of length AB is 23.46 ft and the measure of length BC is 9 ft.

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Answer:

312 square inches

Step-by-step explanation:

To find the surface area of a cake baked in a rectangular pan with an 8-inch by 12-inch base and a volume of 288 cubic inches, we need to find the dimensions of the pan. We can do this by dividing the volume by the area of the base, which gives us the height of the pan. Once we know the height, we can use the dimensions of the base and the height to find the surface area of the cake.

The exponential functions y=1.2ˣ  shows exponential growth and y=0.71ˣ shows exponential decay.

What exactly are exponential functions?

Exponential functions are functions that involve a variable exponent. They are of the form f(x) = aˣ, where "a" is a positive constant base and "x" is the variable exponent.

Exponential functions exhibit rapid growth or decay, depending on the value of "a" and the sign of "x". For example, if "a" is greater than 1, the function grows rapidly as "x" increases, while if "a" is between 0 and 1, the function decays rapidly as "x" increases.

Now,

As stated above that for exponential function y=aˣ

when a>1 it shows exponential growth

and when a<1 it shows decay.

hence,

          The exponential functions y=1.2ˣ  shows exponential growth and y=0.71ˣ shows exponential decay.

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Answer:

There are different methods to express a two logarithm into a single logarithm, depending on the specific form of the logarithms involved. Here are some examples:

Logarithms with the same base:

If you have two logarithms with the same base, you can use the following logarithmic identity:

log_a(x) + log_a(y) = log_a(xy)

Using this identity, you can express a sum or difference of logarithms with the same base as a single logarithm:

Example 1: log_2(3) + log_2(5) = log_2(3*5) = log_2(15)

Example 2: log_5(7) - log_5(2) = log_5(7/2)

Logarithms with different bases:

If you have two logarithms with different bases, you can use the following change of base formula to express them with a common base:

log_a(x) = log_b(x) / log_b(a)

Using this formula, you can rewrite a logarithm with a base a as a logarithm with a base b:

Example 1: log_2(7) = log_10(7) / log_10(2)

Example 2: log_5(2) = log_2(2) / log_2(5)

Once you have expressed both logarithms with the same base, you can apply the logarithmic identity from method 1 to simplify them into a single logarithm.

The two linearly independent solutions are y₁(x) = 1 - (x²/3) + (x⁴/81) - (x⁶/2187) + … and y₂(x) = x - (x³/9) + (x⁵/405) - (x⁷/21870) + ...

We can use the power series method to find the two solutions of the given differential equation:

Let y = ∑anxn be a power series solution. Then, we have:

y' = ∑nanxn-1

y'' = ∑nan(n-1)xn-2

Substituting these into the differential equation and equating coefficients of like powers of x, we get:

3x∑nan(n-1)xn-1 + ∑anxn = 0

Simplifying, we obtain:

∑[3nan(n-1) + an-1]xn = 0

Since x ≠ 0, the coefficients of like powers of x must be zero. This gives us the recurrence relation:

an = -an-1/(3n(n-1)), n ≥ 1

Using this recurrence relation and the initial condition y(0) = 1, we can find the power series solution:

y₁(x) = 1 - (x²/3) + (x⁴/81) - (x⁶/2187) + ...

To find a second linearly independent solution, we can use the method of reduction of order. Let y₂(x) = v(x)y₁(x). Then, we have:

y₂' = v'y₁ + vy₁'

y₂'' = v''y₁ + 2v'y₁' + vy₁''

Substituting these into the differential equation and simplifying, we get:

v''y1x + (2v'y1' + vy1'')x + 3vy1 = 0

Since y₁(x) is a solution, we have:

y₁'' + (1/3x)y₁ = 0

Multiplying by y1 and integrating, we obtain:

(y₁')² + y₁²/3 = C

where C is a constant of integration. Using the initial condition y₂(0) = 0, we can find the second solution:

y₂(x) = x - (x³/9) + (x⁵/405) - (x⁷/21870) + ...

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(5g^(2)+6g-10)-(2g^(2)+2g+9) = 3g^(2) + 4g - 19

To subtract the two polynomials, we will use the vertical form. This means that we will line up the like terms and subtract them.

Step 1: Line up the like terms in the vertical form.

5g^(2) + 6g - 10

- (2g^(2) + 2g + 9)

Step 2: Distribute the negative sign to each term in the second polynomial.

5g^(2) + 6g - 10

- 2g^(2) - 2g - 9

Step 3: Subtract the like terms.

5g^(2) - 2g^(2) = 3g^(2)

6g - 2g = 4g

-10 - 9 = -19

Step 4: Write the final answer.

3g^(2) + 4g - 19

Therefore, the answer is 3g^(2) + 4g - 19.

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 x = 4/3 and y = 2/3

To solve this system of linear equations using a matrix equation, we first need to construct a matrix by writing the coefficients of the variables and the constants from the equation in a rectangular array.

The matrix for the given equations will be:

Now, we can solve the system by multiplying the inverse of the matrix of coefficients with the matrix of constants. To find the inverse of the matrix, we can use the following equation:

where |A| is the determinant of the matrix, and adj(A) is the adjoint of the matrix.

We can use this equation to find the inverse of the matrix, which is:

We can then multiply this inverse by the matrix of constants to get the solution for the system:

Therefore, the solution for the system is x = 4/3 and y = 2/3.

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The volume of the rectangular prism whose surface area is 250 cm square is 250cubic centimeters.

The surface area of a rectanular prism is calculates by the formula

= 2( length*width + length*height + width*height ) square units

Let the length of the given prism be l centimeters.

Given, width is 5 centimeters and height is 10 centimeters of the rectangular prism.

The surface area of the rectangular prism is 250 cm square.

Thus by the above formula,

250 = 2 ( l*5 + l*10 +10*5)

⇒250 = 2 (15*l +50)

⇒ 250= 30*l + 100

⇒ 150 = 30*l

⇒l = 150/30 = 5 (centimeters)

Thus the volume of the given rectangular prism is calculated as

= ( length*width*height) cubic units

= (5*5*10) cubic centimeters

= 250 cubic centimeters

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2x2 - 9xy - 1 is the expression for how much money the buddies still need to gather to reach their objective.

A mathematical expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations. This mathematical procedure makes it possible to multiply, divide, add, or subtract quantities.

The total of what they have already raised towards the overall fundraising target.

The total contribution goal is given as: 7x² - 4xy + 8

The amount Martin has already collected is: 5xy + 16

The amount Tyreese has already collected is: x²

The amount Braydon has already collected is: 4x² - 7

Adding the amounts already collected:

= (5xy + 16) + x² + (4x² - 7)

= 5xy + x² + 4x² + 16 - 7

= 5xy + 5x² + 9

By deducting the total of the contributions from the overall contribution target:

= (7x² - 4xy + 8) - (5xy + 5x² + 9)

= 2x² - 9xy - 1

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Answer: A

Step-by-step explanation: i wish other people would just put the letter, but here ya go c:

Yes

Yes, \( W \) is a subset of \( R^{2} \) since it consists of vectors of the form
\[ \mathbf{x}=\left[\begin{array}{l} x_{1} \\ x_{2} \end{array}\right] \]. Therefore, for Exercises \( 1-8 \), the answer is yes.

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Step-by-step explanation:

addition and subtraction:

y + z - z = y

b. multiplication and division:

When y ≠ 0:

yz / y = z

When z ≠ 0:

y / z * z = y

The correct answer is b. 81°F.

On a certain day, the temperature of the pool rose at a constant rate from 76°F at 10 A.M. to 91°F at 1 P.M. To find the temperature at 11 A.M., we need to find the rate of change in temperature and then use it to calculate the temperature at 11 A.M.

The rate of change in temperature can be found by dividing the difference in temperature by the difference in time:

Rate of change = (91°F - 76°F) / (1 P.M. - 10 A.M.) = 15°F / 3 hours = 5°F per hour

Now, we can use this rate of change to find the temperature at 11 A.M.:

Temperature at 11 A.M. = 76°F + (5°F per hour)(1 hour) = 81°F

Therefore, the correct answer is b. 81°F.

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The value of the model expression when simplified is (d)

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

Using the above as a guide, we have the following:

The given expression is

3 * Black triangle + 2 * White triangle + 2 * Black square + 1 * White square

This gives

-3x + 2x - 2 + 1

Evaluate the like terms

-x - 1

This means

1 Black triangle and 1 Black square

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Answer:

2:35

Step-by-step explanation:

The simplified expression of (1)/(13)(13y)  is 169y.

To simplify the expression (1)/(13)(13y) using the commutative or associative property, we can rearrange the terms and group them together.

Using the commutative property, we can rearrange the terms so that the two 13's are next to each other:

(1)(13)(13y) = (13)(13y)(1)

Now, using the associative property, we can group the two 13's together and simplify:

(13)(13y)(1) = (13*13)(y)(1) = (169)(y)(1)

Finally, we can simplify further by multiplying the 169 and 1 together:

(169)(y)(1) = (169y)(1) = 169y

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Answer:

5,6 and 7.

Step-by-step explanation:

I am not sure what the three step method is, but here is how I solved it.

Consecutive integers means integers in a row.  For example, 5,6 7 are consecutive integers or -4,-3,-2 are consecutive integers.

Integers are all the whole numbers (0,1,2,3...) and their opposites (..., -3, -2, -1)  1/2 or -.23 are not integers.

Let x = the first number

Let x + 1 = the second number

Let x + 2 = the third number

x + (x + 1) + (x + 2) = 18  I do not need the parentheses, but I want you to see that  the first number, plus the second number, plus the third number equals 18.

x + x + 1 + x + 2  = 18  Combine like terms

3x + 3 = 18  Subtract 3 from both sides of the equation

3x + 3 - 3 = 18 - 3

3x = 15  Divide both sides by 3

[tex]\frac{3x}{3}[/tex] = [tex]\frac{15}{3}[/tex]

x = 5

The first number is 5.  The second number is 6 and the last number is 7.

Check:

5 + 6 + 7 = 18

18 =18 Checks.

Helping in the name of Jesus.

Answer:

X: 45° Y:16°

Step-by-step explanation:

by help of teacher

The trigonometric value of sin 14° to 4 decimal places is sin 14° = 0.241.

The value of sin 14° to 4 decimal places is 0.2419.

An angle is the measure that determines two straight lines, which when joined together create a point of origin, which is called the vertex of the angle.

The unit of measurement associated with angles is degrees.

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The value of the constant of variation for the direct variation is k = -1/2.

Variation depicts the relationship between two variables and how it changes. Often, a ratio is used to illustrate this connection. When we remark that a variation is continuous, we are referring to how consistently the ratio changes. Hence, whenever you read the phrase "constant of variation," just keep in mind that it refers to the stability of the relationship between the variables.

The direct variation is given by the following relations:

y = kx

Now, using the table substitute the value of y = f(x) and x:

y = kx

-2 = k(4)

k = -2/4

k = -1/2

Hence, the value of the constant of variation for the direct variation is k = -1/2.

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The answer are LCD (least common denominator) of the set of fractions (7)/(20) and (9)/(40) is 40.

Here is a step-by-step explanation on how to find the LCD:

1. Find the multiples of each denominator.

- Multiples of 20: 20, 40, 60, 80, 100, 120, 140, 160, 180, 200...

- Multiples of 40: 40, 80, 120, 160, 200, 240, 280, 320, 360, 400...

2. Compare the multiples of each denominator and find the smallest number that appears in both lists.

- The smallest number that appears in both lists is 40.

3. The smallest number that appears in both lists is the LCD.

- Therefore, the LCD of the set of fractions (7)/(20) and (9)/(40) is 40.

So the answer to the question "Find the LCD (least common denominator) of the set of fractions. Do not combine the fractions; only find the LCD. (7)/(20) and (9)/(40)" is 40.

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Answer: 20 gallons of red paint and 30 gallons blue paint

Step-by-step explanation: