The rate of change in sales S is inversely proportional to time t(t > 1) measured in weeks. Find S as a function of t if sates after 2 and 4 weeks are 200 units and 350 units respectively.
A. S(t) = 50 [3 ln t/ln2 +1]
B. S(t) = 550 [3 ln t/ln3 +150]
C. S(t) = 50 [3 ln t/ln2 +11]
D. S(t) = 50 [11 ln t/ln2 +1]
E. S(t) = 550 [ln t/ln3 +1]

Answers

Answer 1

Answer:

A. S(t) = 50 [3 ln t/ln2 +1]

Step-by-step explanation:

We are told that the rate of change in sales S is inversely proportional to time.

Thus;

dS/dt = k/t

Where k is the constant of proportionality.

So,

dS = (k/t)dt

Integrating both sides gives us;

S = (kIn t) + C

We are given that after 2 and 4 weeks are 200 units and 350 units respectively.

Thus;

S(2);

(k In 2) + C = 200 - - - (eq 1)

(k In 4) + C = 350 - - - -(eq 2)

To find k, let's subtract eq 1 from eq 2 to get;

(k In 4) - (k In 2) = 350 - 200

(k In 4) - (k In 2) = 150

k(In 4 - In 2) = 150

0.6931k = 150

k = 150/0.6931

k = 216.42

Plugging this for k in eq 1 gives;

(216.42 In 2) + C = 200

C = 200 - 150

C = 50

Thus;

S(t) = (216.42In t) + 50

Now 216.42 can also be expressed as;

150/In 2

Thus;

S(t) = ((150/In 2)In t) + 50

Factorizing out gives;

S(t) = 50 [(3 ln t/ln2) + 1]

Option A is the correct answer


Related Questions

I’ll mark brainliest please help with all and leave a small explanation! :)

Answers

Answer:

A y=6 x= 3

B y=4 x= 2

C y=6 x= 2

D x= 4 y= -2

Step-by-step explanation:

you need to add the numbers on and look how many once u do thag u can see the pattern it makes

Find the angle of N
Will give branialist

Answers

I learned this last year and I Forgot, sorry I couldn’t help but stay safe!

Answer:

n=66

Step-by-step explanation:

6+12x+120+80+19x-1=360

205+31x=360

31x=155

x=5

please solve needed asap

Answers

Answer:

x = 56°

Step-by-step explanation:

Base angles of an isosceles triangle are equal.

This:

The angle of the triangle to our right, which is the third unequal angle = 180 - 2(31)

= 180 - 62

= 118°

The base angle of the triangle to our left = 180 - 118 (angles on a straight line)

= 62°

x = 180 - 2(62)

x = 180 - 124

x = 56°

Match these?

LA
If two angles and the included side of one triangle are equal to two angles and the included side of the other triangle, then the triangles are congruent.
ASA
If the hypotenuse and a leg of one right triangle are equal to the hypotenuse and leg of another right triangle, then the triangles are congruent.
HL
If three sides of one triangle are equal to three sides of anther triangle, then the triangles are congruent.
SAS
If a leg and an acute angle of one right triangle are equal to the corresponding parts of another right triangle, then the triangles are congruent.
SSS
If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.

Answers

Answer:

see below

Step-by-step explanation:

If two angles and the included side of one triangle are equal to two angles and the included side of the other triangle, then the triangles are congruent.

This is angle side angle  ASA

If the hypotenuse and a leg of one right triangle are equal to the hypotenuse and leg of another right triangle, then the triangles are congruent.

This is  hypotenuse leg  HL

If three sides of one triangle are equal to three sides of anther triangle, then the triangles are congruent.

This is side side side  SSS

If a leg and an acute angle of one right triangle are equal to the corresponding parts of another right triangle, then the triangles are congruent.

This is leg angle LA

If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.

This is side angle side SAS

You have measured the systolic blood pressure of a random sample of 25 employees of a company located near you. A 95% confidence interval for the menu systolic blood pressure for the employees of this company is (122, 138). Which of the following statements gives a valid interpretation of the confidence level?a. 95% of the sample of employees have a systolic blood pressure between 122 and 138.b. 95% of tire population of employees have a systolic blood pressure between 122 and 138c. If the procedure were repeated many times, 95% of the resulting confidence intervals would contain the population means systolic blood pressure.d. The probability that the population mean blood pressure is between 122 and 138 is .95

Answers

I have 0 idea sorry

Ehehejejrjrjejejrjrjtjtjrjrje

Answers

Answer:

?

Step-by-step explanation:

shvwhehdjdjdnbddvbxnxjjxjdjdnbdnekskdjdjnebeeekekkenenennenemskkddkejennene hope this helps :3

Help Please, im stuck on this question.

Answers

Answer:

irrational

Step-by-step explanation:

3/4 + sqrt(2)

3/4 is rational

sqrt(2) is irrational

The sum of a rational and an irrational number is irrational

please help me<3
i will give brainliest to the right answer

Answers

Answer:

26.5

Step-by-step explanation:

Because the sales is $530 and the commission rate is 5%, the commission would be 5% of the sales, which would be $26.5

need answer thanks!!!!!!!

Answers

Step-by-step explanation:

Touch and hold a clip to pin it. Unpinned clips will be deleted after 1 hour.Touch and hold a clip to pin it. Unpinned clips will be deleted after 1 hour.Touch and hold a clip to pin it. Unpinned clips will be deleted after 1 hour.Touch and hold a clip to pin it. Unpinned clips will be deleted after 1 hour.Touch and hold a clip to pin it. Unpinned clips will be deleted after 1 hour.Touch and hold a clip to pin it. Unpinned clips will be deleted after 1 hour.

Jenny bought a pair of shoes for $49.76 with a 30% off coupon. How much will she pay in total after 7% sales tax?



Answers

Answer: the final price is $37.26

Step-by-step explanation:

Always when we have an increase in a percentage X%, with an initial amount A, the new amount will be:

A + A*(X%/100%)

And for a decrease, the equation is_

A - A*(X%/100%)

Then if the initial price is $49.76, and there is a decrease of the 30%, the new price will be

$49.75 - (30%/100%)*$49.75 = $34.83

Now we have an increase of the 7% because of the IVA, then the final price is:

$34.83 + (7%/100%)*$34.83 = $37.26

Randy saving for console cost $290 he got a $50 gift card from grandma $15 each week, how many weeks until he get money?

Answers

Answer:

it will take him 16 weeks

Step-by-step explanation:

290 subtract 50 equals 240

240 divided by 15 equals 16

What do I do?????????

Answers

First you need to find out how many people there are. If it is her and her two sisters, this is 3 people.

Divide 21 by 3

21/3

Which gives you

7

This means they each got $7 to spend.
Hope this helps!

Answer:

7

Step-by-step explanation:

So its three girls and each of them get the same amount. All you really have to do is divide 21 by 3 which is 7.

They each get to spend $7.

What is the vertex of the following: y=1/4x^2+2x+6

Answers

Answer:

Yea i definitly just lost brain cells

Step-by-step explanation:

sophia used 1/10 of a liter of water to fill 1/4 of a fish aquarium. How much water, in liter is required to fill the aquarium?​

Answers

Answer:

4/10 of a liter

Step-by-step explanation:

if 1/10 of a liter fills 1/4 of the aqauium then your ratio is .1:.25 out of 100 so

100/25=4

PLEASE HURRY) The graph indicates the running route for Tobias

Which best describes his run

A. From time 0 to 6, he went fast and then slowed down.
B. From time 6 to 10, he was at his slowest.
C. From time 12 to 14, he went very slow.
D. From time 14 to 18, he went toward the starting point.

Answers

Answer: B. From time 6 to 10, he was at his slowest.

Step-by-step explanation: I just took the same quiz so HURRY!!!

Answer:

b

Step-by-step explanation:

The data below gives the mean price (in cents) of a liter of regular gasoline at self-service filling stations at a sample of six urban centers in Canada in May 2011.

Urban area Price/liter
St. John, NL 137.1
Halifax 133.6
Montreal 136.2
Regina 132.3
Saskatoon 132.2
Yellowknife 138.9

Required:
a. Find the sample mean (in cents).
b. Find the sample standard deviation (in cents).
c. Find a 90% confidence interval for the mean gasoline price per liter across urban Canada in May 2011. Provide the lower and upper limits for your confidence interval.
d. Find a 95% confidence interval for the mean gasoline price per liter across urban Canada in May 2011. Provide the lower and upper limits for your confidence interval.

Answers

Answer:

135.05 ; 2.762 ; (133.201, 136.899) ; (132.840, 137.260)

Step-by-step explanation:

Given the data:

Urban area Price/liter

St. John, NL 137.1

Halifax 133.6

Montreal 136.2

Regina 132.3

Saskatoon 132.2

Yellowknife 138.9

Mean = (137.1 + 133.6 + 136.2 + 132.3 + 132.2 + 138.9) / 6

= 810.3 / 6

= 135.05

Standard deviation (σ) : √Σ(X - mean)²/n-1

(137.1 - 135.05)^2 + (133.6 - 135.05)^2 + (136.2 - 135.05)^2 + (132.3 - 135.05)^2 + (132.2 - 135.05)^2+ (138.9 - 135.05)^2 = 38.135

√(38.135 / (6 - 1))

= √7.627

= 2.7617023

= 2.762

C.)

90% confidence interval of the mean :

Mean ± Zcrit * σ/√n

Zcrit at 90% = 1.64

135.05 ± 1.64 * (2.762/√6)

135.05 ± 1.64 * 1.1275817

Lower Value = (135.05 - (1.64 * 1.1275817)) = 133.201

Upper Value = (135.05 + (1.64 * 1.1275817))) = 136.899

Confidence interval = (133.201, 136.899)

D.)

95% confidence interval of the mean :

Mean ± Zcrit * σ/√n

Zcrit at 95% = 1.96

135.05 ± 1.96 * (2.762/6)

135.05 ± 1.96 * 1.1275817

Lower Value = (135.05 - (1.96 * 1.1275817)) = 132.840

Upper Value = (135.05 + (1.96 * 1.1275817)) = 137.260

Confidence interval = (132.840, 137.260)

Jill paid a sales tax of $1.40 when she bought a vest.What was the price of the vest not including the tax?

Answers

Answer:

Price of tne Vest + $40 - 1.40 = $38.6

Step-by-step explanation:

3.5% * n = $1.40

0.035 * n = $1.40

0.035/0.035 * n = $1.40/0.035

n = $40

The price of the vest not including the tax is, $40

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Since, Tax is a sum levied by the government or an agency of the government on goods and services. taxes increases the price of products

Now,

Let p = price of a vest

Hence, from the question, this equation can be formed,

⇒ 35% of p = $1.40

⇒ 0.035 x p = $1.4

divide both sides of the equation by 0.035;

⇒ p = $40

Thus, The price of the vest not including the tax is, $40

Learn more about the percent visit:

https://brainly.com/question/24877689

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Complete question is this;

Jill paid a sales tax of $1.40 when she bought a vest. What was price of vest not including tax? Sales tax = 3.5%

PLZ HELP ME WITH THIS!?!? I WILL MARK BRAINLIEST!!!

Answers

Answer: can it be a bit clearer pls?

Step-by-step explanation:

Suppose a publishing company estimates that its monthly cost is C(x) = 600{x^2} + 300xC(x)=600x 2 +300x and its monthly revenue is R(x) = - 0.4{x^3} + 700{x^2} - 600x + 500R(x)=−0.4x 3 +700x 2 −600x+500, where x is in thousands of books sold. The profit is the difference between the revenue and the cost.
What is the profit function, P(x)?​

Answers

Answer:

the answer is A,

P(x) = -0.4x³+100x²-900x+500

Step-by-step explanation:

monthly cost:

[tex]c(x) = 600x {}^{2} + 300x[/tex]

monthly revenue:

[tex]r(x) = - 0.4 {}^{3} + 700x {}^{2} - 600x + 500[/tex]

profit function:

[tex]p(x) = r(x) - c(x)[/tex]

[tex]p(x) = ( - 0.4x {}^{3} + 700 {x}^{2} - 600x + 500) - (600x {}^{2} + 300x)[/tex]

i) remove the first bracket

[tex]p(x) = - 0.4x {}^{3} + 700x {}^{2} - 600x + 500 - (600 {x}^{2} + 300x)[/tex]

ii) there is a negative sign, '-' in front of the second bracket. so, change the sign of each term of the expression inside the bracket

[tex]p(x) = - 0.4x {}^{3} + 700 {x}^{2} - 600x + 500 - 600x {}^{2} - 300x[/tex]

iii) collect like terms

[tex]p(x) = - 0.4x {}^{3} + 700 {x}^{2} - 600 {x}^{2} - 600x - 300x + 500[/tex]

iv) simply the like terms

[tex]p(x) = - 0. 4{x}^{3} + 100 {x}^{2} - 900x + 500 [/tex]

Lee is making scarfs for a shelter. He purchased 11 skeins of yarns. Each skein has 660 feet of yarn. He needs 200 yards of yarn to make one scarf.

Answers

Answer:

Give me sum

Step-by-step explanation:

Answer:

Most scarves will use one to two skeins of yarn. According to the chart above, you will probably need about 300–650 yards, depending on the weight of yarn, the colors, the stitches, style, and length amongst other factors.

Step-by-step explanation:

|7-8| • 4 + 3 (-1) ???????

Answers

Answer:

1

Step-by-step explanation:

|7-8| • 4 + 3 (-1) =

= |-1| • 4 + (-3)

= 1 • 4 - 3

= 4 - 3

= 1

A company that makes cola drinks states that the mean caffeine content per 12-ounce bottle of cola 40 milligrams. You want to test this claim. During your tests, you find that a random sample of thirty 12-ounce bottles of cola has a mean caffeine content of 39.2 milligrams. Assume the population is normally distributed with a standard deviation of 7.5 milligrams. At α=0.01, can you reject the company’s claim

Answers

Answer:

Claim cannot be rejected

Step-by-step explanation:

We solve this by using hypothesis testing

H0: mean = 40

H1: mean ≠ 40

We have samples of 30, but we were not gives the population standard deviation. We used the t distribution

T score = 39.2-40/(7.5/√30)

= -0.5842

Degree of freedom = 30-1 = 29

Then p value = 0.5636

In conclusion, we fail to reject the null hypothesis since 0.5636 > 0.01 significance level.

So company's claim cannot be rejected

What is the effect on the graph of f(x) = x2 when it is transformed to h(x) = 2 x2 + 15?

Answers

Answer:

B

Step-by-step explanation:

The effect on the graph of f(x)=x² when it is transformed to h(x)=2x²+15 is the graph of f(x) is vertically streched by 2 and moved up by 15 unit.

How does the transformation of a function happen?

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units, y=f(x+c) (same output, but c units earlier)

Right shift by c units, y=f(x-c)(same output, but c units late)

Vertical shift

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given two functions, f(x) and h(x). Also, the function f(x) = x² is transformed to form h(x) = 2x² + 15. Therefore, we can write the transformation as,

f(x) vertically streched by a factor of2  first, Therefore,

g(x) = 2f(x)

      = 2x²

Now, the function g(x) is moved up by 15 units, therefore,

h(x) = g(x) + 15

      = 2x² + 15

Hence, the effect on the graph of f(x)=x² when it is transformed to h(x)=2x²+15 is the graph of f(x) is vertically streched by 2 and moved up by 15 unit.

Learn more about Transforming functions:

https://brainly.com/question/17006186

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How to solve this problem

Answers

Answer:

Solving the radical [tex]\pm\sqrt{-81}[/tex]  we get [tex]\mathbf{\pm9 \ i}[/tex]

Step-by-step explanation:

We need to express the radical [tex]\pm\sqrt{-81}[/tex] using the imaginary unit i

Prime factors of 81 are: 3x3x3x3

and [tex]\sqrt{-1}=i[/tex]

Solving:

[tex]\pm\sqrt{-81}\\=\pm\sqrt{81}\sqrt{-1}\\=\pm\sqrt{3\times3\times3\times3}i\\ =\pm\sqrt{3^2\times3^2}i\\=\pm3\times3\ i\\=\pm9 \ i[/tex]

So, Solving the radical [tex]\pm\sqrt{-81}[/tex]  we get [tex]\mathbf{\pm9 \ i}[/tex]

what's the area of the quadillateral​

Answers

Answer:

The area of the quadillateral is 360 degree.

Step-by-step explanation:

Hope this helped!

Have an amazing day!

Acardboard popcom container is shaped like a cone that is 11 inches high and has a radius of 2.5 inches What is the volume of the container? Use 3 14 for pi Round your answer to the nearest hundredth​

Answers

Answer:

71.99 in³

Step-by-step explanation:

The formula to apply is that of volume of a cone where;

V=π*r²*h/3  --------where V is the volume of the container, r is the radius of the container  and h is the height of the container

Given that : π=3.14 , r is 2.5 inches , h= 11 inches then apply values to the container as;

V= 3.14 * 2.5²* 11/3

V= 3.14 * 6.25 * 3.67

V= 71.9948

V= 71.99 in³

Answer:

Volume of Cone= 71.9583

Step-by-step explanation:

Volume of Cone= (1/3)πr²h

Volume of Cone= (1/3)×3.14×(2.5)²×11

Volume of Cone= 71.9583

Bob needs to read 3 novels each month. Let N be the number of novels Bob needs to read in M months, Write an equation relating N to M. Then use this equation to find the number of novels Bob needs to read in 17 months.​

Answers

Answer:

Equation: n=3m; Bob needs to read 51 novels over 17 months.

Step-by-step explanation:

Since the number of novels Bob needs to read (n) depends on the amount of months (m) we can say that n is the dependent variable and m is the independent. Since x is always independent and y is always independent we can say that m is going to stand for x and n is going to stand for y. Each month Bob reads 3 novels so we can write the equations as n=3m. To find out how many books he needs to read in 17 months plug it into the equation. n=3(17) -------------------> n=51

The data set shows the numbers of flowers that students on a field trip correctly identified. What is the mode of the data set? 0 7 3 9 5 0 10 5 8 6

Answers

Answer:

The mode is the value that appears most frequently in a data set

Step-by-step explanation:

so it will be 0 and 5

Answer:

0 and 5

explanation:


The weighted mean of the variables 2,5,8,10 with weights 1,3,1,2 is...

6.2

O 6.4

O 1.4


which one ?​

Answers

The weighted average of 4 entered numbers is 6.4286 so its b 6.4

Steel is an alloy of iron and carbon (98% iron, 2% carbon). Stainless steel is steel and chromium, (90% steel, 10% carbon). What amount of iron, carbon, and chromium are needed for 500 kg of stainless steel?

Answers

500 kg x 90% = 500x 0.9 = 450 kg of Steel is needed.

450 kg x 98% = 450 x 0.98 = 441 kg of iron needed.

450 x 0.02 = 9 kg of carbon is needed for the steel.

50 kg of chromium is needed.

Chromium is 10% carbon, 50x 0.1 = 5 kg of carbon is needed for the chromium.

Total iron = 441 kg

Total carbon = 9 + 5 = 14 kg

Total chromium = 50 kg

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