Business Calculus CRN 21116 Save = Homework: 6.5 Related Rates Question 4, Bus Econ 6.5-9 HW So 0%, 15 ports O Pontoft A manufacturer of andered wito nick minst cost to producent per morgen by C-047.000 How fast is het per month we do not the one of 19 per month and the production levels out? Costs are of the rate of per month at the production eded) Round to Decreasing COSTO Find the rate of change of total revenue, cost, and profit with respect to time. Assume that R(x) and C(x) are in dollars. R(x) = 45x -0.5x? C(x) = 3x + 15, when x = 25 and dx/dt = 15 units per day The rate of change of total revenue is $ per day

On a postsynaptic membrane, the opening of K+ ion channel induces an IPSP (Inhibitory Postsynaptic Potential).

The potential changes in a neuron after the receptor and ion channel activation is called synaptic potential. This potential can be either an Excitatory Postsynaptic Potential (EPSP) or an Inhibitory Postsynaptic Potential (IPSP).EPSP is a depolarizing potential that results from the opening of the Na+ ion channel. It causes a change in the potential of the neuron towards threshold level that may trigger an action potential.Ion channels and pumps in a postsynaptic neuron regulate the internal potential of the cell. In a typical postsynaptic cell, the resting potential (Vrest) is -70 mV, the threshold value is -55 mV, the reversal potential for Cl- ion (Ec) is -63 mV, the reversal potential for K+ ion (Ex) is -90 mV, and the reversal potential for Na+ ion (ENa) is 60 mV.The opening of Cl- ion channel leads to an inward flow of negative ions and thus results in hyperpolarization. The opening of K+ ion channel leads to an outward flow of K+ ions, and the membrane potential becomes more negative. Thus, it also results in hyperpolarization. The opening of a Na+ ion channel leads to inward flow of Na+ ions, which makes the cell more positive, and it is depolarization. Therefore, the opening of K+ ion channel leads to an IPSP, and it hyperpolarizes the neuron.

The postsynaptic potential can be either an Excitatory Postsynaptic Potential (EPSP) or an Inhibitory Postsynaptic Potential (IPSP). The opening of the K+ ion channel leads to an outward flow of K+ ions, which makes the cell more negative and hyperpolarizes it, leading to IPSP.

To learn more about postsynaptic membrane visit:

brainly.com/question/14969022

#SPJ11

Answer:

JL = 70

Step-by-step explanation:

Since K is the midpoint of JL then JK = KL and

JL = JK + KL = 9x - 1 + 2x + 27 = 11x + 26

solve for x using JK = KL

9x - 1 = 2x + 27 ( subtract 2x from both sides )

7x - 1 = 27 ( add 1 to both sides )

7x = 28 ( divide both sides by 7 )

x = 4, hence

JL = 11x + 26 = (11 × 4 ) + 26 = 44 + 26 = 70

Answer:

h = 6

Step-by-step explanation:

\(:\implies\sf\:x-\dfrac{3}{4}=2x-\dfrac{9}{7}\)

\(:\implies\sf\:\dfrac{9}{7}-\dfrac{3}{4}=2x-x\)

\(:\implies\sf\:\dfrac{36-21}{28}=x\)

\(:\implies\boxed{\bf{\red{x=\dfrac{15}{28}}}}\)

Answer: 56%

Probably that it will rain and she goes + probably that it will be sunny and she goes

=     0.4 * 0.2     +           0.6*0.8

=          0.08      +              0.48

=   0.56

56% chance

Answer:

158 in.

Step-by-step explanation:

Surface area of a prism = Area of all the faces added together

So, Face 1 & 2 = 5 x 80 = 40 x 2 = 80

Face 3 & 4 = 8 x 3 = 24 x 2 = 48

Face 5 & 6 = 5 x 3 = 15 x 2 = 30

Therefore, adding them together makes:

80 + 48 + 30 = 158 in.

For, the expression a + 4, where a = 7, the solution is obtained as 11.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The expression is given as a + 4.

The value of a is given as a = 7.

Substitute the value of a in the given expression.

7 + 4

Apply the arithmetic operation of addition -

11

Therefore, the value is obtained as 11.

To learn more about expression from the given link

https://brainly.com/question/24734894

#SPJ1

Evaluate a + 4 when, a = 7.

Answer:

Step-by-step explanation:

a)

The original figure is ABC and the image is A'B'C'.

We can see the image is larger than the original figure.

It indicates that the dilation is an enlargement.

b)

Find the ratio of corresponding sides to find the scale factor.

First get the measure of corresponding line segments.

The scale factor is:

#1

#2

Take two sides of both

Scale factor:-

The ratios that can be used to illustrate how many heads of lettuce,X, he would need to head 275 guests would be = 37/100 = X/275. That is option A.

The number of heads of lettuce needed to feed 100 guest = 37

The number of heads of lettuce that will be needed for 275 guests = X.

Mathematically;

100 guests = 37

275 guests =X

That is,

X * 100 = 37 ×275

Which is the same as = 37/100 = X/275

Learn more about division here:

https://brainly.com/question/25289437

#SPJ1

Answer:

(4, 0) and (3, 0)

Step-by-step explanation:

x - 4 = 0;  x = 4

x - 3 = 0;  x = 3

Answer:

1401.25

Step-by-step explanation:

F(4000)= 1.25+0.35(4000) = 1401.25

I assume you're trying to prove this identity for natural numbers n?

Let P(n) be the statement that

1² + 4² + 7² + … + (3n - 2)² = n (6n² - 3n - 1) / 2

We prove it by induction. First check that P(1) is true:

1² = 1

1 • (6•1² - 3•1 - 1) / 2 = 1 • 2 / 2 = 1

so P(1) is indeed true.

Assume P(k) is true, that

1² + 4² + 7² + … + (3k - 2)² = k (6k² - 3k - 1) / 2

We want to use this hypothesis to show that P(k + 1) is also true, that

1² + 4² + 7² + … + (3k - 2)² + (3 (k + 1) - 2)²

= (k + 1) (6 (k + 1)² - 3 (k + 1) - 1) / 2

= (k + 1) (6k² + 9k + 2) / 2

= (6k³ + 15k² + 11k + 2) / 2

By the induction hypothesis,

1² + 4² + 7² + … + (3k - 2)² + (3 (k + 1) - 2)²

= k (6k² - 3k - 1) / 2 + (3 (k + 1) - 2)²

= k (6k² - 3k - 1) / 2 + (3k + 1)²

= 3k³ + 15/2 k² + 11/2 k + 1

= (6k³ + 15 k² + 11 k + 2) / 2

which is exactly what we needed to show, so P(k + 1) is also true.

Thus P(n) is true for all natural numbers n.

Answer:

distance between 2 cities is 490km

time taken for first trip is 7 hours

Step-by-step explanation:

speed. time

70 x

10. 1

= 10x =70*1

x=70/10

=7 hours

distance= speed*time

=70*7

=490km

Answer: x < -1 or x ≥ 3

Step-by-step explanation:

     First we will look at the left part. The circle is open (not "equal to), arrow is pointing to the left (showing "less than" in this case), and the value is on -1;

         x < -1

     Second, we will look at the right part. The circle is closed (showing "equal to"), the arrow is pointing to the right (showing "greater than" in this case). and the value is on 3;

         x ≥ 3

     Lastly, we will write the final compound inequality. In this case, we use the word "or" because the solution value is either less than -1 or greater than and equal to 3.

     Note: The word "and" is only used when the "arrows point towards each other" creating a segment, so to say. In this case, they "point away" so we use the word or.

The sum of the interior angles of this irregular hexagon is 720

The sum of the interior angles of a polygon is:

Sum = 180 *(n - 2)

A hexagon has 6 sides.

So, we have:

Sum = 180 *(4 - 2)

Evaluate

Sum = 720

Hence, the sum of the interior angles of this irregular hexagon is 720

Read more about polygons at:

https://brainly.com/question/1592456

#SPJ2

Hometown Property Casualty Insurance Company's combined ratio, after dividends, can be calculated as 114%. This means that the company is paying out more in losses, expenses, dividends, and taxes than it is earning in premiums and investment income.

The combined ratio is a key metric used in the insurance industry to assess the overall profitability of an insurance company. It is calculated by adding the loss ratio and the expense ratio. In this case, the loss ratio is 75% and the expense ratio is 30%. Therefore, the combined ratio before dividends would be 75% + 30% = 105%.

To calculate the combined ratio after dividends, we need to consider the dividend ratio and the net investment income. The dividend ratio is 1%, which means that 1% of the company's premium revenue is paid out as dividends to shareholders. The net investment income is 8%, representing the return on the company's investments.

To adjust the combined ratio for dividends, we subtract the dividend ratio (1%) from the combined ratio before dividends (105%). This gives us 105% - 1% = 104%. Then, we add the net investment income (8%) to obtain the final combined ratio.

Therefore, the combined ratio after dividends for Hometown Property Casualty Insurance Company is 104% + 8% = 114%. This indicates that the company's expenses and losses, including dividends and taxes, exceed its premium revenue and investment income by 14%. A combined ratio above 100% suggests that the company is operating at a loss, and in this case, Hometown Property Casualty Insurance Company would need to take measures to improve its profitability.

Learn more about ratio here:

https://brainly.com/question/13419413

#SPJ11

A. The 20th percentile for incubation times is approximately 18.16 days.

B.  The incubation times that make up the middle 97% are approximately between 16.83 days and 21.17 days.

a) To determine the 20th percentile for incubation times, we need to find the value below which 20% of the data falls.

Using the properties of the normal distribution, we know that approximately 20% of the data falls below the z-score of -0.84 (which corresponds to the 20th percentile). We can find this z-score using a standard normal distribution table or a calculator.

Using a standard normal distribution table or calculator, we find that the z-score corresponding to the 20th percentile is approximately -0.84.

Next, we can use the formula for converting z-scores to raw scores to find the incubation time corresponding to this z-score:

x = μ + (z * σ)

where x is the raw score (incubation time), μ is the mean (19 days), z is the z-score (-0.84), and σ is the standard deviation (1 day).

Plugging in the values, we have:

x = 19 + (-0.84 * 1)

x = 19 - 0.84

x = 18.16

Therefore, the 20th percentile for incubation times is approximately 18.16 days.

b) To determine the incubation times that make up the middle 97%, we need to find the range within which 97% of the data falls.

Since the distribution is symmetric, we can split the remaining 3% (1.5% on each tail) equally.

To find the z-score corresponding to the 1.5th percentile (lower tail), we can look up the z-score from the standard normal distribution table or use a calculator. The z-score for the 1.5th percentile is approximately -2.17.

To find the z-score corresponding to the 98.5th percentile (upper tail), we can subtract the 1.5th percentile z-score from 1 (as the area under the curve is symmetrical). Therefore, the z-score for the 98.5th percentile is approximately 2.17.

Now, using the formula mentioned earlier, we can find the raw scores (incubation times) corresponding to these z-scores:

For the lower tail:

x_lower = μ + (z_lower * σ)

x_lower = 19 + (-2.17 * 1)

x_lower = 19 - 2.17

x_lower = 16.83

For the upper tail:

x_upper = μ + (z_upper * σ)

x_upper = 19 + (2.17 * 1)

x_upper = 19 + 2.17

x_upper = 21.17

Therefore, the incubation times that make up the middle 97% are approximately between 16.83 days and 21.17 days.

Learn more about times from

https://brainly.com/question/27894163

#SPJ11

The arrow's motion can be described by parametric equations: x = V₀cosθt and y = -4.9t² + V₀sinθt + h, where V₀ is the initial velocity, θ is the launch angle, t is the time, and h is the initial height. To determine the time the arrow is in the air before touching the ground and the maximum height reached, we need to solve for the corresponding values in the equations.

(a) To find the time the arrow is in the air before touching the ground for the final time, we need to determine the value of t when y equals zero (the ground level). We can set the equation -4.9t² + V₀sinθt + h = 0 and solve for t. This equation represents the vertical motion of the arrow. Once we find the value of t, we can round it to the nearest tenth.

(b) To determine the maximum height reached by the arrow, we need to find the vertex of the parabolic equation -4.9t² + V₀sinθt + h. The maximum height occurs at the vertex of the parabola, which corresponds to the highest point of the arrow's trajectory. We can use the formula t = -b/2a, where a = -4.9 and b = V₀sinθ, to find the time at which the maximum height is reached. Once we find the value of t, we can substitute it into the equation y = -4.9t² + V₀sinθt + h to calculate the maximum height, rounding it to the nearest whole number.

By solving for the time when the arrow touches the ground and finding the maximum height, we can better understand the arrow's motion and trajectory.

Learn more about parabola here:

https://brainly.com/question/29267743

#SPJ11

To calculate the posterior probability P(W|D), we can use Bayes' theorem, which states:

P(W|D) = (P(D|W) * P(W)) / P(D)

Given the information provided:

P(Z) = 0.12

P(C|W) = 0.65

P(D|Z) = 0.95

We need to calculate P(D) using the law of total probability.

P(D) = P(D|W) * P(W) + P(D|Z) * P(Z)

Substituting the given values:

P(D) = (0.95 * P(W)) + (0.12 * P(Z))

Now, we can calculate P(W|D) using Bayes' theorem:

P(W|D) = (P(D|W) * P(W)) / P(D)

P(W|D) = (0.95 * P(W)) / [(0.95 * P(W)) + (0.12 * P(Z))]

To calculate the specific value of P(W|D), we need additional information about the probability distribution of P(W) and P(Z). Without this information, we cannot determine the exact decimal value of P(W|D).

Learn more about probability here:

https://brainly.com/question/31828911

#SPJ11

The length x of JK is 3.6 units

Here, quadrilaterals ABCD and JKLM are similar.

We know that the corresponding sides of similar triangles are in proportion.

So, by definition of similar triangles,

AB/JK = BC/KL = CD/LM = AD/JM

To find:  the length x of JK

So, consider an equation

AB/JK = AD/JM

Substitute the length of each side in above equation.

4/x = 2/1.8

(4 × 1.8)/x = 2

(4 × 1.8)/2 = x

x = 2 × 1.8

x = 3.6

Therefore, the length of JK = 3.6 units

Learn more about an equation here:

https://brainly.com/question/649785

#SPJ4

Answer:

0.75

Step-by-step explanation:

3(0.5^2)-4(0.5)+2=0.75

Answer:

0.75

Step-by-step explanation:

3(0.5²) - 4(0.5) + 2

3(0.25) - 4(0.5) + 2

0.75 - 4(0.5) + 2

0.75 - 2 + 2

0.75 + 0

0.75

Answer:

3w + 8 = 2

Step-by-step explanation:

product of a number and 3 is w * 3

eight more than the above is 3w + 8

which is equal to 2

3w + 8 = 2

Answer: x=1

Step-by-step explanation:

Given: MN || OP, m<MQR = 58-7x, m<QRP = 54-3x

Since we know that lines MN and OP are parallel, we know that m<MQR and m<QRP are equal because of alternate interior angles theorem.

Since those two angles are equation we can create an equation to solve.

58-7x=54-3x

Subtract 54 from both sides, add 7x to both sides

4=4x

Divided by 4

x=1

Hope that helps! :)

Let me know if you need help understanding or a clearer explanation!

Answer:

They are supplementary angles so they add up to make 180°

So you do the reverse

180°-100°=x

80°=x

Step-by-step explanation:

Please give me brainliest

The mass of 3 cans of beans and 2 cans of sausage is 1280 grams

The first step is to calculate the mass of a can of beans and sausage.

The second step is to form a system of equation using the information provided in the question:

b = 2s equation 1

2b + s = 800 equation 2

Where:

b = cost of one can of beans

s = cost of one can of sausage

The substitution method would b used to solve the system of equations:

Substitute for b in equation 2 using equation 1:

2(2s) + s = 800

4s + s = 800

5s = 800

s = 800 / 5

s = 160

Now determine the cost of one can of beans by substituting for s in equation 1 :

b = 2 x 160

b = 320

Mass of 3 cans of beans and 2 cans of sausage = (3 x 320) + (2 x 160)

960 + 320 = 1280 grams

To learn more about system of equations, please check: https://brainly.com/question/25875552

#SPJ1