Solve the equation for x: 4x+1=29

The population size at t = 10 can be determined using the equation P(t) = 200ekt, given that P(2) = 100.

1. Start with the given equation: P(t) = 200ekt.

2. We are given that P(2) = 100. Substitute t = 2 and P = 100 into the equation: 100 = 200e2k.

3. Simplify the equation by dividing both sides by 200: e2k = 0.5.

4. Take the natural logarithm (ln) of both sides to isolate the exponent: ln(e2k) = ln(0.5).

5. Use the logarithmic property ln(e2k) = 2k to rewrite the equation: 2k = ln(0.5).

6. Divide both sides by 2 to solve for k: k = ln(0.5)/2.

7. Now that we have the value of k, substitute t = 10 into the original equation: P(10) = 200e( ln(0.5)/2 * 10).

8. Calculate the population size: P(10) = 200e( ln(0.5)/2 * 10) ≈ 20.180.

9. Therefore, the population size at t = 10 is approximately 20,180.

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The exact area of the bounded region between the parabolas is -4/3.

To find the area of the bounded region between the two parabolas y = x^2 + 3x - 5 and y = -3x^2 - 5x + 7, we need to find the points of intersection of the two curves and then integrate the difference of the two functions over that interval.

To find the points of intersection, we set the two equations equal to each other:

x^2 + 3x - 5 = -3x^2 - 5x + 7

Combining like terms and moving all terms to one side, we get:

4x^2 + 8x - 12 = 0

Dividing the equation by 4, we have:

x^2 + 2x - 3 = 0

Factoring the quadratic equation, we get:

(x + 3)(x - 1) = 0

This gives us two possible values for x: x = -3 and x = 1.

To determine the area between the two parabolas, we need to integrate the difference between the upper and lower functions with respect to x over the interval from x = -3 to x = 1.

The area can be calculated as follows:

Area = ∫[from -3 to 1] [(x^2 + 3x - 5) - (-3x^2 - 5x + 7)] dx

Simplifying the integrand:

Area = ∫[from -3 to 1] (4x^2 + 8x - 12) dx

Integrating each term separately:

Area = [4/3 * x^3 + 4x^2 - 12x] [from -3 to 1]

Substituting the limits of integration:

Area = [4/3 * (1)^3 + 4(1)^2 - 12(1)] - [4/3 * (-3)^3 + 4(-3)^2 - 12(-3)]

Calculating the values:

Area = [4/3 + 4 - 12] - [-4/3 - 36 + 36]

Area = [16/3 - 8] - [-4/3]

Area = (16/3 - 8) + (4/3)

Area = 16/3 - 24/3 + 4/3

Area = -4/3

Therefore, the exact area of the bounded region between the parabolas is -4/3.

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Answer:

240 cubic cm

Step-by-step explanation:

Volume of a cone = 1/3(nr^2h)

volume of a cylinder = nr^2h

n = 22/7

r = radius

The volume of a cone is 1/3 that of a cylinder

to determine the volume of the cylinder with the same parameters as a cylinder, multiply the volume of the cone by 3

80 x 3 = 240 cubic cm

Answer:

The function is decaying exponentially at a rate of 9% every month.

Step-by-step explanation: there you go bro

Answer:

Answer:

Step-by-step explanation:

You graph it

Answer:

C

Step-by-step explanation:

U fisrt find the y intercept where x=0 and deferentiate to find gradient

We re-write the system of equations by using the fact that we need the y-values to be the same, so we equal them:

- 10 x + 7/3 = - 10 x + 1/10

We notice then, as we try to solve for the one unknown left (x), that as we add 10 x on both sides of our new equation, all the terms in "x" go away, as shown below:

- 10 x + 10 x + 7/3 = - 10 x + 10 x + 1/10

combine like terms:

7/3 = 1/10

so we notice we have ended up with a ridiculous solution, a statement that tells us that 7/3 equals 1/10 which is mathematically a FALSE statement. Therefore, we conclude that the system has NO solutions, given that there are no possible x or y values that can ever produce a logical answer.

We select therefore the option No solution, among the list of answers.

Considering that each input is related to only one output, the correct option regarding whether the relation is a function is:

A. yes.

A relation represents a function when each value of the input is mapped to only one value of the output.

For this problem, we have that:

There are no repeated inputs, hence the relation is a function and option A is correct.

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Correct Answer:

y = -1/3x

Step-by-step explanation:

I see what you were tying to do and you did a good job at trying but the slope is negative 1/3, not negative 1. To find the slope, you have to divide the y by the x for example point (3, -1)

-1 ÷ 3 = -1/3

Remember the phrase Rise over Run where the Rise is y and Run is x

Hope you have a good day and luck in finding good memes!

Answer:

CHINA

Step-by-step explanation:

Answer:

\( \frac{1}{ {5}^{15} } \)

Answer:

j=|x|

Step-by-step explanation:

x = 6 and x = -2

Step-by-step explanation:

Put the 12 to the other side

x^2 - 4x - 12 = 0

Now factor this out:

(x - 6)(x + 2) = 0

Therefore, the roots of this equation are

x = 6 and x = -2

\(∫f(x)dx = 5\\∫f(x)dx = 8\\∫t(x)dx = 5\\∫t(x)dx = -3\)The answers to the integrals are:

\(∫(9x)dx = g(x)dx = -3x + C\\∫4g(x)dx = 4(-3)dx = -12x + C\)

Starting with the given information:

\(∫f(x)dx = 5\\∫f(x)dx = 8\\∫t(x)dx = 5\\∫t(x)dx = -3\)

We can rearrange these equations to solve for\(f(x), t(x),\)and \(g(x)\)separately:

\(f(x) = 5/dx = 5\\f(x) = 8/dx = 8\\t(x) = 5/dx = 5\\t(x) = -3/dx = -3\)

Thus, we have:

\(f(x) = 5\\t(x) = 5\\g(x) = -3\)

Now we can evaluate the given integrals:

\(∫(9x)dx = g(x)dx = -3x + C\), where C is the constant of integration

\(∫4g(x)dx = 4(-3)dx = -12x + C\), where C is the constant of integration

Therefore, the answers to the integrals are:

\(∫(9x)dx = g(x)dx = -3x + C\\∫4g(x)dx = 4(-3)dx = -12x + C\)

Note: the constant of integration C is added to both answers since the integrals are indefinite integrals.

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The optimal solution for the given linear programming problem using the graphical solution procedure is at (A, B) = (6, 2) with the objective function value of -4.

To find the optimal solution graphically, we plot the feasible region determined by the constraints. In this case, the feasible region is a polygon bounded by the lines 2A + 3B = 12, A + 4B ≤ 21, 2A + B ≥ 7, 3A + 1.5B ≤ 21, and -2A + 6B ≥ 0. We then evaluate the objective function -2A - B at the vertices of the feasible region to determine the optimal solution. The vertex that gives the minimum value of the objective function is the optimal solution. By calculating the objective function at each vertex, we find that the minimum value of -4 is obtained at (A, B) = (6, 2). This means that the optimal solution is to set A = 6 and B = 2, and the objective function value at this point is -4. For part (b), to determine the amount of slack or surplus for each constraint, we evaluate the constraints at the optimal solution (A, B) = (6, 2). For the constraint 1A + 4B ≤ 21, the left-hand side is 1(6) + 4(2) = 14, which indicates a slack of 7 (21 - 14). For the constraint 2A + 1B ≥ 7, the left-hand side is 2(6) + 1(2) = 14, which indicates a surplus of 7 (14 - 7). For the constraint 3A + 1.5B ≤ 21, the left-hand side is 3(6) + 1.5(2) = 20, which indicates a slack of 1 (21 - 20). Lastly, for the constraint -2A + 6B ≥ 0, the left-hand side is -2(6) + 6(2) = 4, which indicates a surplus of 4 (4 - 0). These slack and surplus values represent the amount by which the left-hand side of each constraint falls short or exceeds the right-hand side at the optimal solution. A positive slack indicates that the constraint is not fully utilized, while a positive surplus indicates that the constraint is exceeded.

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Answer:

gemma gets 6 and zac gets 12

Step-by-step explanation:

zac gets double the about

Answer:

170.25

Step-by-step explanation:

I made 15% into a decimal. The decimal, being 0.15, was multiplied to 1135 to get the answer 170.25

1135 x 0.15 = 170.25

The value of the percentage is,

→ 15 ÷ 100

→ 0.15

We have to find,

→ 15% of 1135

Let's find the solution,

→ 1135 × 0.15

→ 170.25

Hence, the answer is 170.25.

Answer:

105.37

Step-by-step explanation:

The composite function N(T(t)) = 20082.The time when the bacteria count reaches 20082 is approximately 30.28 hours.

To find the composite function N(T(t)), we need to substitute the expression for T(t) into the function N(T).

Given:

N(T) = 307² - 112T + 75

T(t) = 3t + 1.7

Substituting T(t) into N(T), we get:

N(T(t)) = 307² - 112(3t + 1.7) + 75

Simplifying:

N(T(t)) = 307² - 336t - 190.4 + 75

N(T(t)) = 307² - 336t - 115.4

Now let's find the time when the bacteria count reaches 20082.

N(T(t)) = 20082

307² - 336t - 115.4 = 20082

Taking 115.4 to the other side:

\(307^2\) - 336t = 20082 + 115.4

307² - 336t = 20197.4

336t = 307² - 20197.4

Dividing by 336:

t = (307² - 20197.4) / 336

Calculating the value of t:

t ≈ 30.28

Therefore, the time when the bacteria count reaches 20082 is approximately 30.28 hours.

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Therefore, the solution to the equation is x = 3.

A logarithmic equation is an equation in which a variable appears inside a logarithmic function. In other words, it is an equation in which the unknown quantity appears in the argument of a logarithm.

Logarithmic equations are often used to solve problems involving exponential growth or decay, as well as in various areas of mathematics, science, engineering, and finance.

A general logarithmic equation can be written in the form:

\(log(base a)(x) = b\)

where a is the base of the logarithm, x is the unknown variable, and b is a constant.

To solve a logarithmic equation, you would typically use properties of logarithms to simplify the equation and isolate the variable. Then, you would use algebraic techniques to solve for the variable.

using the properties of logarithms, we can simplify the equation as follows:

log₂(4x²) - log₂(6x) = 2

log₂[(4x²)/(6x)] = 2

log₂(2x/3) = 2

Now we can rewrite the equation in exponential form:

2^2 = 2x/3

\(4 = 2x/3\)

Multiplying both sides by 3/2, we get:

\(x = 6/2 = 3\)

Therefore, the solution to the equation is x = 3.\(2^2 = 2x/3\)

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The mean amount of snow per day is equal to 19 cm snow per day.

In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:

Mean = [F(x)]/n

For the total amount of snow based on the frequency, we have;

Total amount of snow (s cm), F(x) = 5(8) + 15(10) + 25(7) + 35(2) + 45(3)

Total amount of snow (s cm), F(x) = 40 + 150 + 175 + 70 + 135

Total amount of snow (s cm), F(x) = 570

Now, we can calculate the mean amount of snow as follows;

Mean = 570/30

Mean = 19 cm snow per day.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The force required to keep a hockey puck sliding at a constant velocity, neglecting ice friction and air resistance, is equal to its weight. The correct option is "equal to its weight."

When a hockey puck is set in motion across a frozen pond and there is no ice friction or air resistance, the only force acting on the puck is its weight, which is the force due to gravity pulling it downward. According to Newton's first law of motion (the law of inertia), an object at a constant velocity will continue to move at that velocity unless acted upon by an external force.

Since the puck is already in motion and we want to maintain its constant velocity, the force required to counteract its weight and keep it sliding is equal to its weight. This is because the weight of an object is the force exerted on it by gravity, and in the absence of other forces, an equal and opposite force is needed to maintain the object's motion without acceleration.

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Answer:

Step-by-step explanation:

yeah your answer was wrong so you clearly need help

8b-1=24b+4

subtract 4 from both sides

8b-5=24b

subtract 8b from both sides

-5=16b

divide by 16

b=-5/16

Answer:

b = -5/16

Step-by-step explanation:

8b - 1 = 24b + 4

8b - 24b = 4 + 1

-16b = 5

16b = -5

b = -5/16

Answer:

(C) 7 * 0.001

Step-by-step explanation:

There are 3 digits to the right of the decimal point, meaning it goes into the thousandths. One to the right of the decimal point is tenths, and two is hundredths. We know by looking at the expression, that the '7' is located 3 digits to the right of the decimal point, meaning it is in the thousandths. In a regular fraction, this would be 7/1000, hence the name thousandths. Converting this to standard form, it would be 7*0.001 as using the trick whereas, in a division problem, flipping the divisor (not the dividend) or in more advanced terms, getting the reciprocal then multiplying both factors gets you the same thing. This proves that (C) 7 * 0.001 is the correct answer.

Answer:

first option

Step-by-step explanation:

Answer:

Volume of a right prism = 65 cubic inches

Its height is increased by a factor of 20.

To find:

The new volume of the prism if the other dimensions do not change.

Solution:

The volume of a prism is:

\(Volume=Bh\)

Where, B is the base area and h is the height.

A right prism has a volume of 65 cubic inches.

\(65=Bh\)

The height of prism is increased by a factor of 20. So, the new volume is:

\(Volume=B(20h)\)

\(Volume=20(Bh)\)

\(Volume=20(65)\)

\(Volume=1300\)

The volume of the new prism is 1300 in³.

Therefore, the correct option is B.

Answer:

A

Step-by-step explanation:

Hope this helps :)

Answer:

A

Step-by-step explanation:

Answer: 13.79%

Step-by-step explanation:

Amount spent on broadcast TV advertisement = $10000

Amount spent on cable TV advertisement = $15000

Amount spent on radio advertisement = $4000

Total amount spent advertisement = $10000 + $15000 + $4000 = $29000

The Percentage of radio advertisement done will be:

= (Amount spent on radio advertisement / Total amount spent advertisement ) × 100

= (4000 / 29000) × 100

= 13.79%