The function W(t) = 40e^–0.35t models the healing of a wound after t hours, where W(t) represents the wound area in square millimeters. What relationship do W(t) and t have?
when t = 0, W(t) > 40
when t = 0, W(t) 0, W(t) > 40
when t > 0, W(t) < 40

ASAP I'm taking test

Answer(s): Reading your answers from top left, top right, bottom left, bottom right;

Circle A: 110, 70, 70, 110

Circle B: 127, 53, 53, 127

Step-by-step explanation:

Each circle will add up to 360 degrees.

Both acute and obtuse angles are congruent (the same or identical).

If you have an acute angle of 70 for circle 'A', your other acute angle is 70 as well since they are congruent.

Your other two angles will have to equal 220 because you already have 140 degrees and your circle needs to equal 360 degrees. Both of your unknown angles are identical, so divide 220 by 2 to get 110 for both your obtuse angles.

Do the same for your second circle.

Multiply 53 by two to get 106, then subtract 360 by 106 to get 254.

Divide 254 by 2 to get 127 for both of your obtuse angles.

I hope I managed to help. If not, DM me.

Answer:

a=20

Step-by-step explanation:

Answer:

Step-by-step explanation:

4a-2a+8-3=45

2a+5=45

2a+5-5=45-5

2a/2=40/2

a=20

The cost that should be included in the cost of land is C. cost to clear the land of old buildings.

The  cost of land can be described as the cost of all the items as well as the cost of the labor that is been used in making the land to be available for the erection of the building on it, it should be noted that this cost will include the cost that is required to clear the land as well as well as the cost of those that supervise the clearing activities.

In this case we can come into conclusion that  cost that should be included in the cost of land is C. cost to clear the land of old buildings.

Therefore, option C is correct.

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Answer:

71 /84

answer is not in imporper fraction.

Step-by-step explanation:

fractions need to be changed or converted to equivalent fractions inorder to solve them.

1.Total amount of cherries he bought and he already had in cupboard= 3/7 + 2/3

convert them to equivalent fractions inorder to add them by using LCM of the denominators.Which in this case is 21 (LCM of 7 and 3 is 21)

2. Now the common denominator is 21

change 3/7 to a fraction with 21 as denominator by multiplying the numerator to 3 and denominator also by 3 which will give you 3×3=9/ 7×3=21 or 9/21

note: you have to multiply both numerator and denominator by the same number which is used to convert the denominator to the number given by LCM.

3)Now change the second fractions denominator to 21 by multiplying the denominator 3 by 7 and numerator 2 to 7 :

2×7/3×7 = 14/21

4) Now the fractions have same denominator which means they can be added or subtracted.

5) Total amount of cherries he had= 9/21+14/21 = 23/21

6) The amount of cherries he ate = 1/4

7) Amount of cherries he has now with him after he ate 1/4 from 23/21 = 23/21 - 1/4

8) Again the fractions need to be changed to equivalent fractions inorder to subtract them.So,Take the LCM of the denominators (LCM 21 and 4 is 84).Now change the denominator of each fraction to 84.

9) 23/21 becomes 23× 4/21×4 = 92/84

1/4 becomes 1×21/4×21 = 21/84

now subtract them

92/84 - 21/84 = 71/84

71/84 cannot be properly divided so, 71/84 is the answer.

He has 71/84 pounds of cherries with him.

Answer:

315.0

Step-by-step explanation:

31.50x10 is just moving the digits up one place

Answer:

$76.50

Step-by-step explanation:

To find out how much he makes each hour, we do

31.5/7

resulting in 4.5

if he works for 17 hours

17 * 4.5

He would earn $76.50

Answer:-5.675

Step-by-step explanation:

Answer:

The answer is -227/40 or -5 27/40

Step-by-step explanation:

Easiest way to explain this is to first get the common denominator of the denominators of 5 and 8

This will equal 40 and we have to multiply the numerators as well so this will look like....

-35/40 - 4 32/40

Now we need to convert the whole number in -4 32/40 into a fraction

4 multiplied by 40 is 160 so we will need to add 160 and 32 making the equation now say -35/40 -192/40 which will equal -227/40

So this will make the answer -227/40 in fraction form and in a compound fraction it will be -5 27/40

For a function to have an inverse, it must be one-to-one_. To define the inverse sine function, we restrict the domain of the sine function to the interval [-pi, pi].

Two functions f(x) and g(x) are inverses if:

f(x) = y

g(y) = x

This means that the two functions need to be one-to-one, because if there are two values of x such that:

f(x₁) = y = f(x₂)

f(x) can't have an inverse because g(y) would give two different outputs, and then g(x) is not a function.

For the case of the sine (and all periodic functions) we restrict to the region where the function is one to one, which can be any interval of 2 pi radians (the common example is the interval [-pi, pi])

Then:

For a function to have an inverse, it must be one-to-one_. To define the inverse sine function, we restrict the domain of the sine function to the interval [-pi, pi].

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Answer:

There are 10 students

Step-by-step explanation:

69.55-(5.35*3)= 53.5

53.5/10=5.35 which is what each ticket costed

So the answer is 10 students

Substitute [tex]x=1-y[/tex] and [tex]dx=-dy[/tex].

[tex]\displaystyle \int_0^{1/2} \frac{\ln^2(1-x)}x \, dx = \int_{1/2}^1 \frac{\ln^2(y)}{1-y} \, dy[/tex]

Since [tex]|y|<1[/tex], we can expand into a power series and interchange the integral with the sum.

[tex]\displaystyle \int_{1/2}^1 \frac{\ln^2(y)}{1-y} \, dy = \int_{1/2}^1 \ln^2(y) \sum_{n=0}^\infty y^n \, dy \\\\ ~~~~~~~~~~~~~~~~~~~ = \sum_{n=0}^\infty \int_{1/2}^1 y^n \ln^2(y) \, dy[/tex]

Let

[tex]\displaystyle I_n = \int_{1/2}^1 y^n \ln^2(y) \, dy[/tex]

Integrate by parts with

[tex]u=\ln^2(y) \implies du = \dfrac{2\ln(y)}y \, dy[/tex]

[tex]dv = y^n\,dy \implies v = \dfrac{y^{n+1}}{n+1}[/tex]

[tex]\implies \displaystyle I_n = -\frac{\left(\frac12\right)^{n+1} \ln^2\left(\frac12\right)}{n+1} - \frac2{n+1} \int_{1/2}^1 y^n \ln(y) \, dy[/tex]

Integrate by parts again, now with

[tex]u = \ln(y) \implies du = \dfrac{dy}y[/tex]

[tex]dv = y^n \, dy \implies v = \dfrac{y^{n+1}}{n+1}[/tex]

[tex]\implies \displaystyle I_n = -\frac{\ln^2(2)}{2^{n+1}(n+1)} - \frac2{n+1} \left(-\frac{\left(\frac12\right)^{n+1}\ln\left(\frac12\right)}{n+1} - \frac1{n+1} \int_{1/2}^1 y^n \, dy\right) \\\\ ~~~~~~~~~~~ = \frac2{(n+1)^3} - \frac{\ln^2(2)}{2^{n+1}(n+1)} - \frac{\ln(2)}{2^n (n+1)^2} - \frac1{2^n (n+1)^3}[/tex]

Taking the sum over all [tex]n[/tex] gives

[tex]\displaystyle \int_0^{1/2} \frac{\ln^2(1-x)}x \, dx = \sum_{n=0}^\infty I_n \\\\ ~~~~~~~~ = \sum_{n=0}^\infty \left(\frac2{(n+1)^3} - \frac{\ln^2(2)}{2^{n+1}(n+1)} - \frac{\ln(2)}{2^n (n+1)^2} - \frac1{2^n (n+1)^3}\right) \\\\ ~~~~~~~~ = 2 \sum_{n=1}^\infty \frac1{n^3} - \ln^2(2) \sum_{n=1}^\infty \frac1{2^n n}-2\ln(2)\sum_{n=1}^\infty \frac1{2^n n^2}- 2 \sum_{n=1}^\infty \frac1{2^n n^3}[/tex]

Now recall the definition of the so-called polylogarithm function, given by

[tex]\displaystyle \mathrm{Li}_\nu(z) = \sum_{n=1}^\infty \frac{z^n}{n^\nu}[/tex]

which immediately gives us a "closed" form for the integral of

[tex]\displaystyle \int_0^{1/2} \frac{\ln^2(1-x)}x \, dx \\\\ ~~~~~~~~ = 2\,\mathrm{Li}_0(1) - \ln^2(2)\,\mathrm{Li}_1\left(\frac12\right) - 2\ln(2)\,\mathrm{Li}_2\left(\frac12\right) - 2\,\mathrm{Li}_3\left(\frac12\right)[/tex]

But we can do better. The first sum is [tex]2\zeta(3)[/tex] (by definition of Riemann zeta) and the second is [tex]\ln^2(2)\cdot\ln(2)=\ln^3(2)[/tex] (using the series expansion of [tex]\ln(1+x)[/tex]). The other two polylogs have exact values of

[tex]\displaystyle \mathrm{Li}_2\left(\frac12\right) = \frac{\pi^2}{12} - \frac12 \ln^2(2) \\\\ \mathrm{Li}_3\left(\frac12\right) = \frac{\ln^3(2)}6 - \frac{\pi^2}{12} \ln(2) + \frac78 \zeta(3)[/tex]

(according to what I found when searching "polylogarithm at half integers"). Putting all the results together, we end up with

[tex]\displaystyle \int_0^{1/2} \frac{\ln^2(1-x)}x \, dx = \boxed{\frac{\ln^3(2)}3 + \frac74 \zeta(3)}[/tex]

Mr. Arnett will pay $207 for all the trail mix bought by his children.

Here, we are given that Mr. Arnett allowed each of his children to fill their own bag as follows-

Child                 Ava   Grayson   Mason   Tyler

Amount of

Trail Mix (oz)      15        14            10            7

Further, cost of trail mix = $4.50 per pound

The total amount of trail mix collected by all 4 children will be-

15 + 14 + 10 + 7

= 46

Thus, in total the children put 46 pounds of trail mix in their bags.

Hence, the total cost will be-

46 × 4.5

= 207

Thus, Mr. Arnett will pay $207 for all the trail mix.

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Answer:

b

Step-by-step explanation:

P=160-70*cos(2π*(1/12)*t)

• Pressure in mathematics or physics is defined as force per unit area. The pressure exerted by a solid object which is resting on top of a solid surface is the weight divided by the area of the object . SI unit of force is Newton (N).

First, we find the amplitude by taking the difference between the peak values and dividing by two:

Amplitude=(230+90)/2=70

We can find the center value by either adding 70 to the minimum or subtracting 70 from the maximum:

90+70=160

230-70=160

This tells us that the Center Value=160

The frequency that we are operating at is given as:

f = 5/hour

so in minutes

f=5*(1/60)/minute=5/60=1/12 per minute

So, combining everything we get

P=160-70*cos(2π*(1/12)*t)

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The correct solution of Laurie's inequality expression is y ≥ 2x - 4

Laurie's inequality expression is given as

y > 2x - 4

The graph of the inequality expression that completes this question is added as an attachment

From the attached graph, we can see that the line of the inequality is a thick or closed line

Thick and closed line are represented by the inequality signs ≤ and ≥

Since the upper region is shaded, we make use of ≥ inequality sign

Hence, the correct solution of Laurie's inequality expression is y ≥ 2x - 4

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Answer:

The expected completion time of the project is:

10 days.

Step-by-step explanation:

Duration of Task A = 5 days

Task B and C depend on Task A

This implies that Task A must be completed before Task B and C can be started.

To complete Task B will take 5 days

To complete Task C will take 5 days (7 * 0.5) + (3 * 0.5)

Since Task A takes 5 days and Tasks B and C depend on Task A and Task B takes 5 days and Task C takes expected time of 5 days, it means that the project can be completed in 10 days (5 + 5) if tasks B and C are simultaneously carried out.

The expected completion time of the project is

(i)10 days if B&C are mutually independent

(ii)15 days if B &C are mutually dependent

Expected completion time of a task= p1x1 + p2x2

Where

p1 & p2 are probabilities.

x1 and x2 are samples.

p1=p2=0.5

x1=7

x2=3

Expected completion time of task C= 0.5*7+0.5*3 = 5 days

Task B and C will be due till task A is not accomplished.

Total time to accomplish task A = 5 days

Total time  to accomplish task B= 5 days

Expected time to accomplish task C = 5 days

If tasks B and C are mutually independent

expected time to complete the project = 5+5=10days

If task C depends on task B

Expected time to complete the project = 5+5+5 = 15 days.

Therefore

The expected completion time of the project is

(i)10 days if B&C are mutually independent

(ii)15 days if B and C are mutually dependent

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Answer:

3500

Step-by-step explanation:

I got it right

Rajesh own a plot of rectangular shape he has fenced it with a wire of length 750 ft . the length of the plot exceeds the breadth by 5ft.

Given that

To find

So, according to the question

We have,

Let's assume

He fenced this plot with a wire. So we can say this wire length is a perimeter of this plot of rectangular shape.

In mathematical form

           2 (length + breadth) = length of fenced wire

                               2 ( l + x) = W -------------------(1)

From question

                                          l = x +5 ------------------(2)

Now, putting the value of equation (2) and W in equation (1)

Then, we get

                               2 ( l + x) = W -------------------(1)

                      2 [( x + 5) + x] = 750

                        2 [ x + 5 + x] = 750/2

                               [ 2x + 5] = 375

                                        2x = 375-5

                                        2x = 370

                                          x = 370/2

                                          x = 185ft

Now, putting the value of x in equation (2)

Then, we get

                                          l = x +5 ------------------(2)

                                          l = 185 +5

                                          l = 190ft

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45+35=80

100-80=20

360×20/100

72 so the answer is this and the formula E=T×%/100

The Quotient and remainder of the polynomial is  x² + x -6 and 2 respectively

Synthetic division method is one of the method used to divide the polynomial equations.

The polynomial equation given here is

x³ + 3x² - 4x - 10

We need to divide this polynomial equation with x - 2

Thus by dividing the polynomial x³ + 3x² - 4x - 10 with x - 2, we get

the quotient as x² + x -6 and

     Remainder as 2

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Answer:

No

Step-by-step explanation:

I'm not 100% sure that this was the question but I hope so

2170+2570=$4740 per month

4740*12=$56880 per year

Food: 56880*0.5=$28440

Entertainment: 56880*0.3=$17064

Educational: 56880*0.15=$8532

28440+17064+8532=$54036

56880-54036=$2844

Or a quicker method: 1-0.5-0.3-0.15=0.05

0.05*56880=$2844

Answer:

Corresponding angles

Step-by-step explanation:

They have the same relative position to the parallel lines (in blue)

Answer:

6 apples.

How I solved it:

2/3+ 2/3+ 2/3+ 2/3+ 2/3+ 2/3+ 2/3+ 2/3+ 2/3=

18/3

18/3=6

3/3=1

6/1= 6 apples.

Answer:

648

Step-by-step explanation:

Answer:

1809.6 cubic feet

Step-by-step explanation:

Use the formula for the volume of a cylinder, V = [tex]\pi[/tex]r²h

Plug in the height and radius:

V = [tex]\pi[/tex]r²h

V = [tex]\pi[/tex](8²)(9)

V = 1809.6

So, the volume of the cylinder is 1809.6 cubic feet

Answer: 2/5 liters

Step-by-step explanation: This is because you need to add 1/10 and 3/10. The answer is 4/10, which can be simplified to 2/5.

Answer:

top is 13 gallons left

bottom is 7.8 gallons left

Step-by-step explanation:

30=1 gallon

90= 3 gallons

246/30= 8.2

8.2*1=8.2

16-8.2=7.8

Answer:

can you show us the table please.

Step-by-step explanation:

Answer: The third one Edg 2020

Step-by-step explanation: