the price of an item has been reduced by $4.07. the new sale price is 82.09. what was the original price

Answer:

Step-by-step explanation:

To find the normal plane and osculating plane, we first need to find the required derivatives.

x = 5t, y = t^2, z = t^3

dx/dt = 5, dy/dt = 2t, dz/dt = 3t^2

So, the velocity vector v and acceleration vector a are:

v = <5, 2t, 3t^2>

a = <0, 2, 6t>

Now, let's evaluate them at t = 1 since the point (5, 1, 1) is given.

v(1) = <5, 2, 3>

a(1) = <0, 2, 6>

The normal vector N is the unit vector in the direction of a:

N = a/|a| = <0, 1/√10, 3/√10>

Using the point-normal form of the equation for a plane:

normal plane equation = 0(x-5) + 1/√10(y-1) + 3/√10(z-1) = 0

Simplifying this equation we get:

5x + 2y + 3z = 30

The osculating plane can be found using the formula:

osculating plane equation = r(t) · [(r(t) x r''(t))] = 0

where r(t) is the position vector, and x is the cross product.

At t = 1, the position vector r(1) is <5, 1, 1>, v(1) is <5, 2, 3>, and a(1) is <0, 2, 6>.

r(1) x v(1) = <-1, 22, -5>

r(1) x a(1) = <12, -6, -10>

v(1) x a(1) = <-12, 0, 10>

Substituting these values into the formula, we get:

osculating plane equation = (x-5, y-1, z-1) · <12, -6, -10> = 0

Simplifying this equation we get:

3x - 15y + 5z = 5

Therefore, the equations for the normal plane and osculating plane at (5, 1, 1) are:

(a) 5x + 2y + 3z = 30

(b) 3x - 15y + 5z = 5

A. To determine if an integral is convergent, we analyze the function's behavior, integrability, apply integration techniques, and examine its limits, ensuring they are finite, leading to a finite result.

B. To determine if an integral is divergent, we look for infinite limits, vertical asymptotes, and erratic behavior within the integration interval, indicating the lack of a finite value for the integral.

A. To determine if an integral is convergent, we need to consider several approaches. First, we check for basic convergence criteria such as infinite limits or vertical asymptotes.

Then, we examine integrability, ensuring the function is continuous or has a finite number of discontinuities. Next, we simplify the integral using integration techniques.

Finally, we analyze the behavior of the function at infinity and apply comparison tests if necessary to establish convergence.

B. To determine if an integral is divergent, we follow a series of steps. First, we check for basic divergence criteria such as infinite limits or vertical asymptotes.

Then, we examine integrability, looking for discontinuities that prevent integration. Next, we simplify the integral using integration techniques. Finally, if the integral does not converge, it is deemed divergent.

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Answer:

a=2/5

Step-by-step explanation:

1.7((2)/(5))+0.3((2)/(5)) = 0.8=80/100=4/5

Answer:

the answer is a=2/5

Step-by-step explanation:

combine like terms 1.7+0.3=2

get the varliable alone 2/4/5

answer 2/5

Answer:

x = –2

Step-by-step explanation:

– 6(1+4x) = –x +40

–6 – 24x = –x +40

24x –x = –6 –40

23x= – 46

x= – 46 / 23

x= – 2

I hope I helped you‌^_^

The bottleneck time is 18.18%. Therefore, option A is the correct answer.

In economics terms, the bottleneck is a chain of supply of resources that wants the most extended time in the supply chain operation for specific demand. It also evaluated to estimate the supply chain throughput.

Through put time = Sum of all times=1+2+3+4+5+6+7+8+9+10=55

Given,

Assembly line has 10 stations

Throughput time is 55

The formula for bottleneck time is:

Bottle neck time = Total stations/Throughput time ×100

= 10/55 ×100

= 18.18%

The bottleneck time is 18.18%. Therefore, option A is the correct answer.

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"Your question is incomplete, probably the complete question/missing part is:"

An assembly line has 10 stations with times of 1, 2, 3, 4,...,10, respectively. What is the bottleneck time?

a. 18.18% of the throughput time

b. 100% of the throughput time

c. 550% of the throughput time

d. 50% of the throughput time

e. 1.82% of the throughput time

Answer:

480

Step-by-step explanation:

12 x 60 = 720

1200 - 720 = 480

Answer: 1,920

Step-by-step explanation:

12ft per second, so to find out his elevation after one minute you would have to convert from seconds to minutes. (60 sec = 1 min). So you would do 12*60 to get 720. And since he already started at 1,200 feet, you add 720. So 1,200+720 = 1,920 ft.

Answer:

r=C2

Step-by-step explanation:

C=2r is the equation to find circumference

She needs to work backwards in this case, so:

r=C2

r=The circumference she knows x 2 x 3.14(or 3.14159265359)

-----------------------------------------------------------------------------------------------------------------

I hope this helped!

Answer:

consider the < as = signs

and take -5 to the other side making it a +

x<0+5

x<5

Answer:

110 pounds

Step-by-step explanation:

Let the weight of Sandra, Peter and Martin be S, P and M pounds respectively.

S +P= 275 -----(1)

S +M= 245 -----(2)

S +P +M= 410 -----(3)

(3) -(1):

S +P +M -(S +P)= 410 -275

S +P +M -S -P= 135

M= 135

Substitute M= 135 into (2):

S +135= 245

S= 245 -135

S= 110

Thus, Sarah weighs 110 pounds.

Joel would have to work for 15 weekends.

The number of weekends that Joel has to work to earn the same as Sue is represented by X.

Joel earnings per weekend: $40

Sue earnings per weekend: $30

To get number of weekends Joel needs to work, we will set up the equation:

40x = 150 + 30x

40x - 30x = 150

10x = 150

x = 150/10

x = 15

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This means that we can be 95% confident that the true population means difference lies between 1.7075 and 10.2925.

Confidence interval = Mean difference ± (t-value × standard error)

Substituting the given values into the formula, we get:

Confidence interval = 6 ± (2.045 × 2.1)

Confidence interval = 6 ± 4.2925

A confidence interval is a statistical concept used to estimate the range of values in which a population parameter is likely to fall. It is calculated using sample data and is used to provide an estimate of the true population parameter.

The confidence interval is a range of values that is constructed around a point estimate, such as the sample mean or proportion. This range is based on the level of confidence chosen by the researcher, typically 90%, 95%, or 99%. For example, a 95% confidence interval means that if we were to repeat the sampling process many times, we would expect the true population parameter to fall within the range of values calculated for 95% of those samples.

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To find the number of pounds of salt in the tank at time t, we need to determine the rate of change of salt in the tank. The amount of salt remains constant over time.

Let's define A(t) as the number of pounds of salt in the tank at time t.

Initially, the tank is filled with 600 gallons of pure water, which means there is no salt present. So, A(0) = 0 pounds.

Now, let's consider the rate of change of salt in the tank.

Every minute, 6 gallons of brine containing 2 pounds of salt per gallon is pumped into the tank. This means that the rate at which salt is added to the tank is 6 * 2 = 12 pounds per minute.

At the same time, 6 gallons of the well-mixed solution is pumped out of the tank. Since the solution is well-mixed, the concentration of salt remains constant throughout the tank. Therefore, the rate at which salt is removed from the tank is also 6 * 2 = 12 pounds per minute.
Hence, the net rate of change of salt in the tank is 12 - 12 = 0 pounds per minute.

This means that the amount of salt in the tank remains constant over time.

Therefore, A(t) = 0 pounds for all values of t.

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The  Trigonometric Identity sin² x + cos²x = 1 is: A. Pythagorean Identity.

The Pythagorean Identity which  tend to asserts that for every angle x, the sum of the squares of the sine and cosine of x is equal to one  is known as or called a  trigonometric identity.

The  Pythagorean identity can be expressed as:

sin² x + cos² x = 1

This identity is crucial to understanding trigonometry and tend to have several uses in numerous branches of science and engineering.

Therefore the correct option is A.

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Answer:

2x + 5

Step-by-step explanation:

Let x represent the number

Twice the number will be represented by 2x, since that multiplies the number by 2

Then, add 5 to this:

2x + 5

So, 2x + 5 is the expression that will represent this situation

Answer:

35,000,000 km

Step-by-step explanation:

1.4 x 10^9 = 1,400,000,000

2.5% = 0.025

1,400,000,000 x 0.025 = 35,000,000

Answer:

The 2 values that makes the function equal to 18 is 3 and -6

Step-by-step explanation:

First you can convert the quadratic equation from standard form to root form

Step 1: Substitute f(g) = 18

Step 2: Move 18 to the other side to create

0 = g² + 3g - 18

Step 3: Now we rearrange equation from standard form into root form

Step 4: Find what adds to 3 and multiples to -18

-3 and 6 adds to 3 and multiples to -18

Step 5: Now we substitute -3 and 6 into the root equation

0 = (g-3)(g+6)

Step 6: Set the brackets to 0 and solve

g - 3 = 0

g = 3

g + 6 = 0

g = -6

Answer:

There are 70 stones in the bucket.

Step-by-step explanation:

If there are 40 seashells in the bucket and the ratio of stones to seashells is 7:4, then there are 70 stones, because  4 x 10 = 40, and 7 x 10 = 70

Hope this helps!

The arc length is D) 3.14 meters.

What is arc length?

In mathematics, an arc is a portion of a curve that can be thought of as a segment of the curve. An arc is a connected set of points on a curve, usually a portion of a circle.

It is defined by two endpoints and all the points along the curve between them. The length of an arc is the distance along the curve between its two endpoints.

The distance along the curved line that forms the arc (a section of a circle) is measured using the arc length formula.

                                      \(A_L=\frac{\theta}{360\textdegree}2\pi r\)

Here the give circle Radius PR = 3m and θ=60°.

Now using arc length formula then,

=> Arc length \(A_L=\frac{\theta}{360\textdegree}2\pi r\)

=> \(A_L=\frac{60}{360} \times2\times3.14\times3\)

=> \(A_L=\frac{1}{6}\times2\times3.14\times3\)

=> \(A_L\) = 3.14 m.

Hence the arc length is D) 3.14 meters.

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Answer:

C, 11

Step-by-step explanation:

Answer

linear

nonproportional

Step-by-step explanation:

Since for each equal change in time (1 week), there is an equal change in weight (5 lb), the situation is linear.

At time zero, the first week, the weight was not zero. It was 60 lb, so it is not proportional.

Answer:

linear

nonproportional

Answer:

6 (I believe).

Step-by-step explanation:

The explicit formula for population (Pr) according to given exponential growth model is: Pr = 27 * (1 + 5.0568)^(r-1)

To find the recursive formula for the exponential growth model, we can use the given information.

Let's first consider the given values:

P3 = 27

P7 = 136.6875

The recursive formula for an exponential growth model is given by:

Pn = x * Pn-1

We need to determine the value of x in order to complete the recursive formula.

To find x, we can use the given values of P3 and P7:

P7 = x * P6 (substituting n = 7 and n-1 = 6)

136.6875 = x * P6

Similarly,

P6 = x * P5

P5 = x * P4

P4 = x * P3

Substituting the given value P3 = 27, we have:

P4 = x * 27

P5 = x * P4

P6 = x * P5

P7 = x * P6

Now, let's substitute these equations into the expression for P7:

136.6875 = x * (x * (x * (x * 27)))

Simplifying the equation, we have:

136.6875 = x^4 * 27

To solve for x, we divide both sides by 27:

136.6875 / 27 = x^4

x^4 ≈ 5.0568

Now, to find the explicit formula for Pr, we can use the general form of the explicit formula for exponential growth:

Pr = P0 * (1 + r)^n

In this case, since the growth model is exponential, we have P0 as the initial population, r as the growth rate, and n as the number of time periods.

Given that P0 is the population at time 0, we can substitute P0 = 27 into the explicit formula.

Thus, the explicit formula for Pr is:

Pr = 27 * (1 + 5.0568)^(r-1)

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Answer:

117 in²

Finding the area of the trapezoid:

First, we need to find the area of the trapezoid formed by the dotted lines. The formula for finding the area of the trapezoid is "(a₁ + a₂)h/2".

[Where, a₁ = shorter parallel side; a₂ = longer parallel side]

⇒ (a₁ + a₂)h/2 = Area of trapezoid

⇒ (14 + 26)15/2 = Area of trapezoid

⇒ Area of trapezoid = (40)15/2 = (20)15 = 300 in²

Reviewing on how to find the area of the unshaded region:

To find the area of the shaded region, we need to subtract the area of the unshaded region from the area of the trapezoid. In this case, the unshaded region is a triangle whose base is 26 inches. To find the area of the triangle, we need to use the formula 1/2 x Base x Height. We are given the base, but the height is unknown.

Determining the height:

We are given a small side length "6 inches" and the height of the trapezoid "15 inches". If we subtract the small side length from the height of the trapezoid, we will obtain the height of the triangle.

⇒ Height of trapezoid - Small side length = Height of triangle

⇒ 15 - 6 = Height of triangle

⇒ 9 in = Height of triangle

Determining the area of the unshaded region:

Now, let's substitute the base and the height in the formula to find the area of the triangle

⇒ 1/2 x Base x Height

⇒ 1/2 x 26 x 9

⇒ 13 x 9

⇒ 117 in²

Determining the area of the shaded region:

Finally, let's subtract the area of the unshaded region from the area of the trapezoid to obtain the area of the shaded region.

⇒ Area of trapezoid - Area of unshaded region = Area of shaded region

⇒ 300 - 117 = Area of shaded region

⇒ 183 in² = Area of shaded region

The expected instantaneous rate of change, denoted as r, for a geometric Brownian motion stock price (St) represents the average rate at which the stock price is expected to change at any given point in time. It is typically expressed as a constant or a deterministic function.

On the other hand, the expected return, denoted as r - 0.5σ^2, on the stock ln(St) over an interval of time [0,t] represents the average rate of growth or change in the logarithm of the stock price over that time period. It takes into account the volatility of the stock, represented by σ, and adjusts the expected rate of return accordingly.

The key difference between the two is that the expected instantaneous rate of change (r) for the stock price represents the average rate of change at any given moment, while the expected return (r - 0.5σ^2)t on the stock ln(St) over an interval of time considers the cumulative effect of volatility on the rate of return over that specific time period.

In other words, the expected instantaneous rate of change focuses on the average rate of change at a specific point in time, disregarding the impact of volatility. On the other hand, the expected return over a given interval of time accounts for the volatility in the stock price and adjusts the expected rate of return to reflect the effect of that volatility.

The expected instantaneous rate of change (r) for a geometric Brownian motion stock price represents the average rate of change at any given moment, while the expected return (r - 0.5σ^2)t on the stock ln(St) over an interval of time considers the cumulative effect of volatility on the rate of return over that specific time period.

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The price that Maura sell each scarf would be =$33. Maura sells each scarf for $33. That is option A.

To calculate the amount of money that Maura spends on each scarf the following is carried out.

The amount of money that she spends on the scarf material = $5.50

The percentage selling price of each scarf = 600% of $5.50

That is ;

= 600/100 × 5.50/1

= 3300/100

= $33.

Therefore, each price that is sold by Maura would probably cost a total of $33.

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