I REALLY NEED YOUR HELP!!! PLEASE!!!!!

A store is selling two mixtures of nuts in 20-ounce bags. The first mixture has 15 ounces of peanuts combined with five ounces of cashews, and costs $4.25. The second mixture has five ounces of peanuts and 15 ounces of cashews, and costs $6.75. How much does one ounce of peanuts and one ounce of cashews cost?

Select one:
a. $0.40 for peanuts and $0.15 for cashews
b. $0.15 for peanuts and $0.40 for cashews
c. $0.12 for peanuts and $0.49 for cashews
d. There is no solution.

The properties of exponents and logarithms allow for simplifying and solving exponential equations by manipulating exponents, such as multiplying and dividing quantities, raising a power to another power, and using the inverse relationship between exponents and logarithms.

The properties of exponents are essential for solving exponential equations because they allow for the manipulation of the equations into forms that are easier to solve. The exponential and natural logarithm are inverse functions, meaning ln (e^x) = x and e^(ln x) = x. By using this relationship, any base number b can be expressed as e^(ln b), making complex calculations more manageable.

When multiplying exponential quantities, we can apply the rule where the exponents are added together, such as in (a^m) × (a^n) = a^(m + n). If we raise an exponent to another power, we multiply the exponents, which is depicted in the example of (5^3)^4 = 5^(3×4) = 5^12. Similarly, dividing exponential quantities involves subtracting exponents, and an exponential raised to a negative exponent signifies an inversion.

The logarithmic properties also come into play when working with exponents. The logarithm of a product is the sum of the logarithms: log(xy) = log(x) + log(y). This is useful when solving exponential equations since logarithms can help linearize them, making it easier to isolate the variable and find the solution.

Answer-

The inequality that models this situation is,

[tex]\boxed{\boxed{B.\ 6x+3\leq 27}}[/tex]

Solution-

The total money Charlie has = $27

He wants to order 6 sandwiches and a kid's meal of $3

Let us assume the price of each sandwiches is x.

So, the amount he will be spending for sandwiches is $6x

The total amount he will be spending is $(6x+3)

As he has only $27, so he can spend any amount less than or equal to 27

So the inequality becomes,

[tex]\Rightarrow 6x+3\leq 27[/tex]

Therefore, the inequality that models this situation is [tex]6x+3\leq 27[/tex]

Answer:  The correct option is (B) 1.28 radians.

Step-by-step explanation:  We are given that for an angle A :

[tex]\cos A=0.29.[/tex]

We are to find the measure of angle A in radians.

We know that the relation between degree and radians is given by

[tex]80^\circ=\pi~\textup{radians}\\\\\\\Rightarrow 180^\circ=\dfrac{22}{7}~\textup{radians}.[/tex]

Now, we have

[tex]\cos A=0.29\\\\\Rightarrow A=\cos^{-1}(0.29)\\\\\\\Rightarrow A=73.14^\circ.[/tex]

Again,

[tex]180^\circ=\dfrac{22}{7}\\\\\Rightarrow 1^\circ=\dfrac{22}{7\times180}\\\\\Rightarrow 73.14^\circ=\dfrac{22}{1260}\times73.14=1.277=1.28~\textup{radians}.[/tex]

Thus, the measure of angle A in radians is 1.28 radians.

Option (B) is CORRECT.

If we equate the two given equations y = m^4 and y = n^3, we can express mn as m^(7/3) or as n^(7/4). This is done by taking the cube root and square root on both sides of the equated equation to isolate m and n.

If we have two equations, y = m^4 and y = n^3, where y > 1, we can equate these two equations since they are both equal to same value 'y'. So the equation will be m^4 = n^3. To find the value of mn, we want to express it in terms of 'y'. So we take cube root on both sides, it will be m = (n^3)^(1/4) = n^(3/4). And square root on both sides will give n = (m^4)^(1/3) = m^(4/3). Now mn = m * m^(4/3) = m^(1 + 4/3) = m^(7/3). Similarly, mn = n * n^(3/4) = n^(1 + 3/4) = n^(7/4). Hence, mn can be expressed either as m^(7/3) or n^(7/4).

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Answer:

The answer is $3.75

Step-by-step explanation:

P = $500

r = 3%   = 0.03

n = 4

t =[tex]3/12=1/4[/tex]

Now compound interest formula is :

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

Putting the values in formula we get,

[tex]A=500(1+\frac{0.03}{4})^{4*1/4}[/tex]

[tex]A=500(1.0075})^{1}[/tex]

= $503.75

Now, withdrawal fee = amount paid - principle

=> [tex]503.75-500=3.75[/tex] dollars.

So, the answer is $3.75.

Answer:

{–2, 1, 2, 5}

Step-by-step explanation:

i got it right on the test lol

The rate of change of radius of the circle when the radius is 10 cm is

dr / dt = 1/2π cm / sec

What is implicit differentiation?

In mathematics, differentiation is the process of determining the derivative, or rate of change, of a function. Differentiation is a technique for determining a function's derivative. Differentiation is a mathematical procedure that determines the instantaneous rate of change of a function based on one of its variables. The process of finding the derivative of dependent variable in an implicit function by differentiating each term separately

Given data ,

Oil is poured on a flat surface and it spreads out forming a circle

The area of the circle is increasing at a rate of 10 cm²/sec

Let the area of the circle be = A

So , the equation is dA² / dt² =  10 cm²/sec

The area of the circle = πr²

So , dA² / dt² = 2π dr / dt

2πr dr / dt = 10 cm²/sec

Substituting the value of r in the equation , we get

2π x 10 dr / dt = 10 cm²/sec

20π dr / dt = 10 cm²/sec

Divide both sides of the equation be 20π

dr / dt = ( 1/2π ) cm / sec

Therefore , the rate of change of radius of the circle is ( 1/2π ) cm / sec

Hence , The rate of change of radius of the circle when the radius is 10 cm is dr / dt = 1/2π cm / sec

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The derivative of f(x) at x = -1 is -8.

Derivative is the rate of change of a function with respect to a variable. Derivatives are fundamental to the solution of problems in calculus and differential equations.

According to the given problem,

f(x) = [tex]\frac{8}{x}[/tex]

Derivative of f(x),

⇒ f'(x) = [tex]-\frac{8}{x^{2} }[/tex]

At x = -1,

⇒ f'(-1) =  [tex]-\frac{8}{(-1)^{2} }[/tex]

          = -8

Hence, we can conclude, the derivative of f(x) at x = -1 is -8.

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area of yard = 41 x 60 = 2460 square feet

walk is 4 feet wide

 41-4 =37, 60-4 = 56

37*56 = 2072

2460-2072 = 388

 area of walk is 388 square feet

Answer:

simplified answer: its letter c

Step-by-step explanation:

Answer:

1 + 1 = 2

2 - 1 = 1

The line's slopes are cute

Step-by-step explanation:

I hope your lines enjoy their equations, you are a great parent to your lines. =D

The gravitational potential energy of a 3 kg toy car resting at the top of a 0.45-meter ramp is calculated using the formula PE = mgh, giving us a result of 13.2385 Joules.

The calculation of gravitational potential energy for a 3 kg toy car at the top of a 0.45-meter ramp. Gravitational potential energy (PE) is calculated using the formula PE = mgh, where m stands for mass, g is the acceleration due to gravity (usually 9.81 m/s² on Earth's surface), and h is the height above the reference point. In this case, PE = 3 kg × 9.81 m/s² × 0.45 m, which gives us a gravitational potential energy of 13.2385 Joules. As the car is at rest on the top of the ramp and has not yet moved, its potential energy is at its maximum at that point.