Find each value or measure.

The decomposition of Substance A is proportional to the amount of A present. An equation can be written to relate the amount of A remaining to the initial amount A₀ and the time t. Using this equation, we can determine the time it takes for the amount of A to reduce to a specific value.

The decomposition of Substance A can be described by the following differential equation:

dA/dt = -kA,

where dA/dt represents the rate of change of A with respect to time t, k is the proportionality constant, and A is the amount of A present at time t.

To solve this differential equation, we can separate variables and integrate:

∫(1/A) dA = -∫k dt.

This simplifies to:

ln(A) = -kt + C,

where C is the constant of integration.

By applying initial conditions, we can determine the value of the constant C. In this case, we are given that 8 grams of A reduces to 4 grams in 3 hours. Using A = 8 and t = 3 in the equation, we can solve for C.

Once C is determined, we can rearrange the equation to solve for t when A = 1 gram. This gives:

ln(A) = -kt + C,

ln(1) = -k(t') + C,

where t' represents the time it takes for the amount of A to reduce to 1 gram. Solving for t' will give us the answer to how long it takes for there to be only 1 gram of A left.

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Answer:

105

Step-by-step explanation:

1,000 divided by 3.5% is 35

35 x 3 is 105

Since you are just asking for just the interest and not the total the answer is 105

The interest that Amy should pay is $105.

Given that,

Based on the above information, the calculation is as follows:

\(= 1000 \times 3.5\% \times 3\)

= 105

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Answer:

I think it's 6 or 0.6

The explanation of using Literal equations to solve for a given variable is as explained below.

How to solve Literal Equations?

Literal equations are equations containing two or more variables; at least one independent variable and one dependent variable

To solve a literal equation means to rewrite the equation so a different variable stands alone on one side of the equals sign. We have to be told for which variable we want to solve.

Linear equations in one variable may take the form ax + b = 0  and are solved using basic algebraic operations.

We begin by classifying linear equations in one variable as one of three types: identity, conditional, or inconsistent. An identity equation is true for all values of the variable.

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ATQ

\(\\ \sf\longmapsto m+m+4+m+6=37\)

\(\\ \sf\longmapsto 3m+10=37\)

\(\\ \sf\longmapsto 3m=27\)

\(\\ \sf\longmapsto m=9\)

Answer:

279.000000028

Step-by-step explanation:

correct

Answer:

C

Step-by-step explanation:

The total population of Deer's in the given span area is 5852 Deer's.

Population density is defined as the total number of humans presence

per unit square miles. Mathematically, we can write -

Population density = (Total human population)/(Total span area)

Given is that a county in north Carolina spans 532 square miles. the population density of deer in the county is 11 deer per square mile

We can write the total population of Deer's in the given span area as -

Population = Deer's population density x total area span

Population = 11 x 532

Population = 5852

Therefore, the total population of Deer's in the given span area is 5852 Deer's.

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Answer:

-74

Step-by-step explanation:

The coefficient of static friction between the coin and the turntable is 0.085.

(a) The centripetal force required to keep the coin moving in a circular path is provided by the force of static friction between the coin and the turntable.

When the coin is stationary relative to the turntable, the centripetal force is equal to the maximum static friction force.

The centripetal force is given by:

\(\(F_c = \frac{mv^2}{r}\)\)

In this case, the coin is stationary relative to the turntable, so the centripetal force is equal to the maximum static friction force:

\(\(F_c = f_{\text{static max}}\)\)

Therefore, we can write:

\(\(f_{\text{static max}} = \frac{mv^2}{r}\)\)

(b) The maximum static friction force can be expressed as:

\(\(f_{\text{static max}} = \mu_{\text{static}} \cdot N\)\)

Where:

\(\(f_{\text{static max}}\)\) is the maximum static friction force,

\(\(\mu_{\text{static}}\)\) is the coefficient of static friction, and

\(\(N\)\) is the normal force.

Since the coin is on a horizontal surface, the normal force \(N\) is equal to the weight of the coin, which is \(mg\), where \(g\) is the acceleration due to gravity.

Setting the equations for the maximum static friction force equal to each other, we have:

\(\(\frac{mv^2}{r} = \mu_{\text{static}} \cdot mg\)\)

Simplifying, we can solve for the coefficient of static friction:

\(\(\mu_{\text{static}} = \frac{v^2}{rg}\)\)

Now substitute

v = 50.0

r = 30.0 cm

g = 9.8 m/s²

Now we can calculate the coefficient of static friction:

\(\(\mu_{\text{static}} = \frac{(0.5 \, \text{m/s})^2}{(0.3 \, \text{m})(9.8 \, \text{m/s}^2)}\)\)

= 0.085

Therefore, the coefficient of static friction between the coin and the turntable is approximately 0.085.

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The question attached here seems to be incomplete, the complete question is:

A coin placed 30.0cm from the center of a rotating, horizontal turntable slips when its speed is 50.0cm/s.

(a) What force causes the centripetal acceleration when the coin is stationary relative to the turntable? (b) What is the coefficient of static friction between coin and turntable?

Answer:

Step-by-step explanation:

C

3 7/10 is less than 3 4/5

turn the mixed numbers into improper fractions and you get 37/10 and 19/5 yoy make the 19/5s denominator 10 and you get 38/10

38/10 is greater than 37/10

The function f(x) = 10(3)2x – 2 is given. We need to find the value of f(0) without using a calculator.To find f(0), we need to substitute x = 0 in the given function f(x).

The given function is f(x) = 10(3)2x – 2 and we need to find the value of f(0) without using a calculator.

To find f(0), we need to substitute x = 0 in the given function f(x).

f(0) = 10(3)2(0) – 2

[Substituting x = 0]f(0) = 10(3)0 – 2 f(0) = 10(1) / 1/100 [10 to the power 0 is 1]f(0) = 10 / 100 f(0) = 1/10

Thus, we have found the value of f(0) without using a calculator. The value of f(0) is 1/10.

Therefore, we can conclude that the value of f(0) without using a calculator for the given function f(x) = 10(3)2x – 2 is 1/10.

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Answer:

(2(y-2)+3) (2(y-2)-3)

Step-by-step explanation:

In mathematics, the difference of two squares is a squared number subtracted from another squared number. Every difference of squares may be factored according to the identity a^2-b^2 = in elementary algebra.

The given series diverges for all values of the variable since the absolute value of the common ratio (3/2) is greater than 1.

The sum of a finite geometric series is given by the formula:S=ar(r^n -1)/(r -1)where S is the sum, a is the first term, r is the common ratio and n is the number of terms. If we take the limit of this formula as n approaches infinity and as r is between -1 and 1 (inclusive), then we have the sum of an infinite geometric series:S=a/(1-r)The sum of the given infinite series will converge if and only if the absolute value of the common ratio is less than 1. Therefore, to find the values of the variable for which the series converges, we must find the absolute value of the common ratio and ensure that it is less than 1.Sum of series:S = 1 + 3/2 + 9/4 + ...+ [3^(n-1)]/[2^(n-2)] + ...The first term is a = 1.The common ratio is r = 3/2.Therefore, we can write:S = 1 + 3/2 + 9/4 + ...+ [3^(n-1)]/[2^(n-2)] + ...= a/(1-r) = 1/[1 - (3/2)] = 1/(1/2) = 2.For what values of the variable does the series converge to this sum?As the common ratio is 3/2 and the absolute value of this ratio is greater than 1, the given series diverges for all values of the variable.

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Answer:

Theres not enough information

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

\((-3)^3\) \(=(-3)(-3)(-3) = 9(-3)= -27\)

Answer:

Y/6 = x

Step-by-step explanation:

Y = 6x

Y/6 = x

Hicksian demand functions are:x1** = 2P₁x₂ ; x₂** = P₂²

Utility function: u(x1+x2) = .5ln(x1) + .25ln(x₂) .The Marshallian demand functions are: x1* = - and x₂* = P₂.

The indirect utility function is found by substituting Marshallian demand functions into the utility function and solving for v(P₁, P₂, Y).u(x1*,x2*) = v(P₁,P₂,Y) ⇒ u(-, P₂) = v(P₁,P₂,Y) ⇒ .5ln(-) + .25ln(P₂) = v(P₁,P₂,Y) ⇒ v(P₁,P₂,Y) = - ∞ (as ln(-) is not defined)

Thus the indirect utility function is undefined.

Minimum expenditure function can be derived from the Marshallian demand function and prices of goods:

Exp = P₁x1* + P₂x2* = P₁(-) + P₂P₂ = -P₁ + P₂²

Minimum expenditure function is thus:

Exp = P₁(-) + P₂²

Hicksian demand functions can be derived from the utility function and prices of goods:

H1(x1, P1, P2, U) = x1*H2(x2, P1, P2, U) = x2*

Hicksian demand functions are:

x1** = 2P₁x₂

x₂** = P₂²

If there are no restrictions on the amount of money the consumer can spend, the Hicksian demand functions for x1 and x2 coincide with Marshallian demand functions.

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The area of rectangle bounded by the x-axis and the semicircle is 72.

Let us name the semicircle with center (0, 0) and radius 6 to have the equation y = √36 – x² and the rectangle to be R.

The objective is to evaluate the area of the rectangle.

A graph of the semicircle and the rectangle are shown below:

Graph of the semicircle and the rectangle

The rectangle is bounded by the x-axis and the semicircle y = √36 – x²;

therefore, we know that the base of the rectangle is from x = -6 to x = 6.

Since the equation for the semicircle is y = √36 – x², the top corner of the rectangle should be y = √36 – 6² = √0 = 0 (that is when x = 6) and the bottom corner of the rectangle should be y = √36 – (-6)² = √0 = 0 (that is when x = -6).

We know that the base of the rectangle is 2(6) = 12 (from x = -6 to x = 6) and the height of the rectangle is 6 (from y = 0 to y = 6).

Therefore, the area of the rectangle is 72.

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Answer:

12345678

Step-by-step explanation:

gtrhtgkyikguko

Answer:

500,000,000,000,000,000,000

Step-by-step explanation:

The number of bottles will be 24 bottles.

It should be noted that 1 pound = 16 ounces.

Since he bought 1 pound of each color, the total pounds will be:

= 1 × 9 = 9 pounds.

The number of sand art will be:

= 9 pounds / 6 ounce

= (9 × 16) / 6

= 24 bottles

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7000 milliters are = to 7 liters

The cost of one apple is $0.70.

Let's assume that the cost of one apple is "a" dollars and the cost of one banana is "b" dollars. We can create two equations based on the information given:

4a + 9b = 12.70 ...(1)

8a + 11b = 17.70 ...(2)

To solve for "a", we can use elimination method by multiplying equation (1) by 8 and equation (2) by -4, so that the coefficients of "a" in both equations will be equal and opposite:

32a + 72b = 101.60

-32a - 44b = -70.80

Adding these two equations, we get:

28b = 30.80

Simplifying and solving for "b", we get:

b = 1.10

Now, we can substitute the value of "b" in equation (1) and solve for "a":

4a + 9(1.10) = 12.70

4a + 9.90 = 12.70

4a = 2.80

a = 0.70

Therefore, the cost of one apple is $0.70.

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Answer:

I've done this before, I think it was C.

Step-by-step explanation:

Answer: The answer is C

Step-by-step explanation:

Answer:

A- 95.53 $         B- 47.35 $     C- 48.18 $

Step-by-step explanation:

45.00+35.75=80.75 (The money Sergio Pappas earned by working.)

80.75+14.78=95.53 (Sergio Pappas money earned by working + initial money.)

25.23+22.12=47.35 (Total money lost by Sergio Pappas.)

95.53-47.35=48.18 (Total money left by Sergio Pappas over the weekend.)

Anais, who bought a ribbon of length \(2 \dfrac 12 \) yards, and she trimming a curtain from it. From substraction, length of ribbon used in curtain is equals to 72 inches.

Word problems express in mathematical form. In subtraction, keywords that could signal the operation are lesser, less than, removed from. However, there are times when the idea of subtraction or taking away is inferred from the problem itself. In the problem, total length of ribbon Anais bought

= \(2 \dfrac 12 \) yards

The length of ribbon left after trimming some curtains = 1 feet 6 inches

We have to determine inches of ribbon Anais use to trim the curtains. Let it will be equal to x inches . We may notice in the provide values that they all have different units. We can convert the all different units into inches. Using uint conversation, 1 yard = 36 inches

=> \(2 \dfrac 12 \)

yards =\( 36 × \frac{ 5}{2} \)

= 90 inches

Similarly, 1 feet = 12 inches, then 1 feet + 6 inches = 12 + 6 = 18 inches

Thus, the left ribbon length = 18 inches

Using substraction method, the length in inches of ribbon that anais use to trim the curtains = total length - left length of ribbon = 90 - 18

= 72 inches.

Hence, required value is 72 inches.

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Complete question:

Anais bought

\(2 \dfrac 12 \)

yards of ribbon. She had 1 feet 6 inches of ribbon left after trimming some curtains. How many inches of ribbon did Anais use to trim the curtains?

The formula to calculate the volume of the brick is given to be:

We have the following dimensions, converted to meters, as follows:

Therefore, the volume is:

Answer

Multiply the sticks of butter by 8. You need 2 sticks of butter for 16 cookies, and you need 5 sticks of butter for 40 cookies.

Step-by-step explanation:

Answer:

2 and 40

Step-by-step explanation: