5 of 12
Work out the percentage change when a price of £1 is increased to £1.50.
1 %
I

The exact solution to the given IVP is: y(t) = ±\(e^(-20t)\) * 10.

To solve the given initial value problem (IVP):

dy/dt + 20y = 0,

y(0) = 10,we can separate the variables and integrate both sides.

Separating the variables, we have:

dy/y = -20dt.

Integrating both sides:

∫(1/y) dy = ∫(-20) dt.

The left side integrates to ln|y|, and the right side integrates to -20t, giving us:

ln|y| = -20t + C,

where C is the constant of integration.

Now, applying the initial condition y(0) = 10, we can solve for C:

ln|10| = -20(0) + C,

ln(10) = C.

Thus, the particular solution to the IVP is:

ln|y| = -20t + ln(10).

Taking the exponential of both sides, we obtain:

|y| = \(e^(-20t) * 10.\)

Finally, since we have an absolute value, we consider two cases:

Case 1: y > 0,

\(y = e^(-20t) * 10.\)

Case 2: y < 0,\(y = -e^(-20t) * 10.\)

Therefore, the exact solution to the given IVP is:

y(t) = ±\(e^(-20t)\) * 10.

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Answer:

A vesting period is the time an employee must work for an employer in order to own outright employee stock options, shares of company stock or employer contributions to a tax-advantaged retirement plan.

Answer:

m = -90 - 6d

Step-by-step explanation:

18 ÷ 3 = 6 { She needs to memorize six measures a day. }

m = 90 - 6d { She has memorized bd measures }

This means that approximately 68% of women's heights fall within the range of 62 to 68 inches, which is centered around the mean of 65 inches.

The mean is a measure of central tendency that represents the average value of a set of data. In this case, we are interested in the mean of women's heights. The standard deviation is a measure of variability that describes how much the data points deviate from the mean.

The normal distribution curve is a bell-shaped curve that represents a set of data that follows a normal distribution pattern. The curve is symmetrical around the mean, and approximately 68% of the data points fall within one standard deviation of the mean. This interval of values is commonly referred to as the "68% confidence interval."

To find an interval of values that is centered at the mean and includes approximately 68% of the women's heights, we need to calculate the mean and standard deviation of the data set. Then, we can use the formula:

mean ± (standard deviation)

To calculate the interval of values that includes approximately 68% of the data points.

For example, let's say the mean height of women is 65 inches, and the standard deviation is 3 inches. Then, the interval of values that includes approximately 68% of the women's heights would be:

65 ± (3) = 62 to 68 inches

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Answer:

X= -0.1290 (bar line on top of the 90)

Hope this helps!

Step-by-step explanation:

Answer:

X= -0.1290

Step-by-step explanation:

Answer: the first one is x=19/7+2y/7

the second one is y=x/2+21/2

hope this help :)

The complex numbers -2.7e^(√7) + 4.3e^(√5) can be expressed as approximately -6.488 - 0.166i in rectangular form and approximately 6.494 ∠ -176.14° in polar form.

To express the given complex numbers in rectangular form and polar form, we need to understand the representation of complex numbers using exponential form and convert them into the desired formats. In rectangular form, a complex number is expressed as a combination of a real part and an imaginary part in the form a + bi, where 'a' represents the real part and 'b' represents the imaginary part.

In polar form, a complex number is represented as r∠θ, where 'r' is the magnitude or modulus of the complex number and θ is the angle formed with the positive real axis.

To convert the given complex numbers into rectangular form, we can use Euler's formula, which states that e^(ix) = cos(x) + isin(x), where 'i' is the imaginary unit. By substituting the given values, we can calculate the real and imaginary parts separately.

The real part can be found by multiplying the magnitude with the cosine of the angle, and the imaginary part can be obtained by multiplying the magnitude with the sine of the angle.

After performing the calculations, we find that the rectangular form of -2.7e^(√7) + 4.3e^(√5) is approximately -6.488 - 0.166i.

To express the complex numbers in polar form, we need to calculate the magnitude and the angle. The magnitude can be determined by calculating the square root of the sum of the squares of the real and imaginary parts. The angle can be found using the inverse tangent function (tan^(-1)) of the imaginary part divided by the real part.

Upon calculating the magnitude and the angle, we obtain the polar form of -2.7e^(√7) + 4.3e^(√5) as approximately 6.494 ∠ -176.14°.

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Substituting this value into the exponential equation, we can represent the growth for Ingrid's business. k = ln(25) / 3.

Our current growth rate is k. When this quantity is substituted into the exponential equation,

We may use the standard exponential equation to illustrate Ingrid's company's exponential growth:

P(t) = P₀ *\(e^{(kt)\),

, where P(t) is the population or the number of employees at time t, P0 is the starting population or the number of employees, e is the natural logarithm's base (about 2.71828), k is the growth rate, and t is the amount of time in years.

Ingrid had 2 employees when she began her business in 2000 (t = 0), and she had 50 employees in 2003 (t = 3), therefore we can enter these numbers into the equation to determine the growth rate, k.

Using P0 = 2 and P(3) = 50, we have

50 = 2 * \(e^{(3k)\).

Dividing both sides by 2:

25 = \(e^{(3k).\)

Taking the natural logarithm (ln) of both sides to isolate the exponent:

ln(25) = 3k.

At last, we find k: k = ln(25) / 3.

Our current growth rate is k. This amount can be used to indicate the growth of Ingrid's company in the exponential equation.

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a) The probability after 3 years is calculated using geometric Brownian motion and the standard normal distribution. b) The expected value of the stock price after 3 years is found by geometric Brownian motion.

a) To find the probability that the stock price is more than $80 after 3 years, we first need to calculate the standardized value of S(3) - $80.

Using the formula for geometric Brownian motion, we have S(3) = $75 * \(e^{(0.05-(0.25^{2} )/3} *3+0.25\) * W(3)), where W(3) represents a standard Brownian motion.

Let Z be the standardized value:

Z = (ln(S(3)/$75) - ((0.05 - (\(0.25^{2}\))/2) * 3))/ (0.25 * \(\sqrt{\)(3))

To calculate the probability, we need to find P(Z > z), where z is the standardized value corresponding to $80. We can look up this probability in a standard normal distribution table or use a calculator to find the cumulative distribution function (CDF) of the standard normal distribution for the given value of z.

b) To find the expected value of the stock price after 3 years, we use the formula for geometric Brownian motion: E[S(t)] = S(0) * e^(μt).

Plugging in the values, we have E[S(3)] = $75* \(e^{0.05*3}\) Evaluating this expression will give us the expected value of the stock price after 3 years.

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The required difference when (-5x + 4y) is subtracted from (7x + 9y) in simplest terms is 12x + 5y.

Given that,
To find an expression that represents the difference when (-5x + 4y) is subtracted from (7x + 9y) in simplest terms.

In mathematics, it deals with numbers of operations according to the statements.

The process in mathematics to operate and interpret the function to make the function simple or more understandable is called simplifying and the process is called simplification.

= 7x + 9y - (-5x + 4y)
= 7x +9y + 5x - 4y
= 7x + 5x + 9y -4y
= 12x + 5y

Thus, the required difference when (-5x + 4y) is subtracted from (7x + 9y) in simplest terms is 12x + 5y.

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So, the volume of the can in cubic centimeters is 61.99 cm^3. If we round to the nearest tenth, the volume of the can is 62 cm^3.

A can of soda can be modeled as a right cylinder, which is a three-dimensional geometric shape with two circular bases that are connected by a curved surface. The volume of a cylinder can be calculated using the formula:

V = πr^2h

Where V is the volume, π is a constant (approximately equal to 3.14), r is the radius of the base and h is the height of the cylinder.

Given that the radius of the can is 2.6 cm and the height is 9.2 cm, we can substitute these values into the formula:

V = π (2.6 cm)^2 (9.2 cm)

To get the area of the base we need to square the radius and multiply by π, and then multiply it by the height to get the volume.

V = π * 6.76 * 9.2 = 61.99 cm^3

So the volume of the can in cubic centimeters is 61.99 cm^3. If we round to the nearest tenth, the volume of the can is 62 cm^3. This means that the can can hold 62 cubic centimeters of liquid.

It's worth noting that this is an approximation and the real value of π is not 3.14. Also, this answer is based on the assumption that the can is a perfect cylinder with no other gaps or spaces.

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Answer:

i need the answer

Step-by-step explanation:

Answer:

m<DCB=34

Step-by-step explanation:

90-56=34

The m<DCA would be 56, not the m<DCB

Answer: B = 1.9

Step-by-step explanation:

A=5

C=12

B=x

Pythagorean Theorem: 5^2 + x^2 = 12^2  

25+x^2=144

x^2=119

\(\sqrt{19}\)≈10.9

Answer:

-p^3

Step-by-step explanation:

( p - 2 p ) ^ 3

combine p and 2p to get -p

》expand (-p)^3

》(-1)^3p^3

calculate -1 to the power of 3 and get -1

and this equals -p^3

Answer:

Tonga trench Elevation = 35,702ft

South sandwich trench elevation = 23,737ft

Step-by-step explanation:

Given the following:

Tonga trench Elevation = 35,702 Feets

South sandwich trench elevation = 23,737 Feets

Expressing both numbers as rational numbers :

Both the Tonga trench Elevation and South sandwich trench elevation are already stated as rational numbers because all integers are rational numbers, be it expressed as a quotient or proportion of integer numbers ( that is numbers that are expressed without decimal components.

Therefore, rational expression for both are :

Tonga trench Elevation = 35,702ft

South sandwich trench elevation = 23,737ft

The FV is $107 for the simple interest.

The formula to calculate simple interest is given as:

I = P × R × T

Where,I is the simple interest, P is the principal or initial amount, R is the rate of interest per annum, T is the time duration.

Formula to find FV:

FV = P + I = P + (P × R × T)

where,P is the principal amount, R is the rate of interest, T is the time duration, FV is the future value.

Given that P = $100, R = 7%, and T = 1 year, we can find the FV of the investment:

FV = 100 + (100 × 7% × 1) = 100 + 7 = $107

Therefore, the FV of $100 invested at 7% for one year (simple interest) is $107.

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lim sin(pi/3+h) - sin(pi/3)/ h as h approaches 0 is  Non existent. The correct answer is option e.

To evaluate the limit, we can use the formula for the derivative of sin(x), which is:

lim f(x+h) - f(x) / h as h approaches 0 = f'(x)

where f(x) = sin(x).

So, in this case, we have:

lim sin(pi/3+h) - sin(pi/3) / h as h approaches 0

which can be rewritten as:

lim [sin(pi/3+h) - sin(pi/3)] / h as h approaches 0

Using the identity for the difference of two sines, we can simplify this expression to:

lim [2cos(2pi/6+h/2)sin(h/2)] / h as h approaches 0

Now, we can cancel out the factor of sin(h/2) in the numerator and denominator, and we are left with:

lim 2cos(2pi/6+h/2) / h as h approaches 0

We can evaluate the limit using direct substitution, and we get:

2cos(pi/3) / 0

Since the denominator is 0, the limit does not exist. Therefore, the answer is option E: Nonexistent.

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Answer:

i alr answered this correctly

Step-by-step explanation:

3 4/5

If the weight of the elephant on Earth is 4100 pounds and the ratio of Earth weight to Jupiter weight is 2:5,.The weight of the elephant on Jupiter is approximately 10280 pounds.

Now, let's explain the calculation in more detail:

We are given that the ratio of the weight on Earth to the weight on Jupiter is 2:5. This means that for every 2 units of weight on Earth, there are 5 units of weight on Jupiter. We can set up a proportion to find the weight on Jupiter:

2 units (Earth weight) / 5 units (Jupiter weight) = 4100 pounds (Earth weight) / x pounds (Jupiter weight).

Cross-multiplying, we have:

2x = 4100 * 5.

Simplifying further:

2x = 20500.

Dividing both sides by 2:

x = 20500 / 2 = 10250.

Therefore, the weight of the elephant on Jupiter is approximately 10280 pounds.

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Answer:

Step-by-step explanation:

There are number of 170 seats with folding arm tablets that are not designed for wheelchair users.

1. First we need to identify the total number of seats in the lecture hall which is 200.

2. Then we need to identify the number of seats with folding arm tablets that are designed for wheelchair users which is 30.

3. To find the number of seats with folding arm tablets that are not designed for wheelchair users, we can subtract the number of seats designed for wheelchair users from the total number of seats.

4. Therefore, 200 - 30 = 170, which means there are 170 seats with folding arm tablets that are not designed for wheelchair users.

The lecture hall in question has a total of 200 seats, with 30 of those seats having folding arm tablets that are designed for wheelchair users. To find the number of seats with folding arm tablets that are not designed for wheelchair users, we can subtract the number of seats designed for wheelchair users from the total number of seats. This means that 200 - 30 = 170, which means there are number of 170 seats with folding arm tablets that are not designed for wheelchair users.

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For the above question by using inequalities she must buy atleast 8 tickets.

What are inequalities?

Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal.

So according to question

    One plan costs =$110

    Extra of $25 per ticket

 let the tickets be x, so the quation will be

                                   =>          110 + 25x ≤ 40x

                                    =>         110 ≤ 15x

                                     =>7 1/3 ≤ x

So, if she must  at least buy 8 tickets, the first plan saves money.

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Answer:

Option C

Step-by-step explanation:

First, knowing that two angles on a horizontal line split by a vertical line at any angle is equal to 180 degrees, I try to find which of the combinations of angle x and z equal 180.

A. x = 63, and z = 104 and together they equal 170, so not A

B. x = 76 and z = 63 and together they equal 139 so not B

C. x = 76 and z = 104 and together they equal 180 so it could be C, but we must check D to make sure.

D. x = 63 and z = 76 and together they equal 139 so not D.

From all of this it must be option C

Answer:

Step-by-step explanation:

If the solutions are x = -3 and x = -1, then (x - 3) (x - 1) will give us our answer. Using the FOIL method,

(x - 3) (x - 1)

x^2 - x - 3x + 3

x^3 - 4x + 3 = 0

Your answer is 3

Answer:

14

Hope this helps

Answer:

14

Step-by-step explanation:

2 x 7 = 7 + 7

7+7=14

There are a few different ways you can determine whether a function is always positive:

1. Analyze the function's formula: If the function's formula includes only positive terms or is a product of positive factors, it is likely that the function will be positive for all input values.

2. Graph the function: Plotting the function on the coordinate plane can give you a visual understanding of the function's behavior. If the graph always lies above the x-axis, the function is always positive.

3. Consider the function's domain: If the domain of the function consists only of positive numbers, the function will be positive for all input values in its domain.

4. Use the function's properties: If the function is increasing, continuous, and has no zeros in its domain, it will always be positive. Similarly, if the function is decreasing, continuous, and has no zeros in its domain, it will always be negative.

5. Test the function for specific input values: You can also test the function for specific input values to see if the output is always positive. For example, if the function is defined for all real numbers, you could test it for a few small positive and negative values to see if the output is always positive.

Thus, above mentioned are used to determine if a function is always positive.

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Answer:

I guess it would be 36?

Step-by-step explanation: