A high-performance composite flywheel rotor can spin anywhere between 30,000 and 100,000 revolutions per minute. What
is the range of degrees through which the composite flywheel can travel in a minute? Write your answer in scientific
notation.

Answer:

a) C(2000)=1915

C(2014)=1915

b) [tex]C'(2000)=-\frac{275}{14}[/tex]

[tex]C'(2014)=-\frac{275}{14}[/tex]

c) [tex]C(t)=-\frac{275}{14}t+\frac{288405}{7}[/tex]

d) t=2021

e) too early

Step-by-step explanation:

a)

Since C(t) is the concentration of CFCs in ppt in year t, all we need to do to solve this part is determine what the concentration of CFCs is in years 2000 and 2014. Luckily for us, the problem already gives us those values, so:

C(2000)=1915    concentration in year 2000

C(2014)=1915      concentration in year 2014

b)

By definition, the derivative of a function at a given point is interpreted as the slope of the tangent line to the point of interest, so in order to find this answer, we need to find the slope of the line. Since the problem specifies that the behavior is linear, this means that the slope will always be the same no matter the year, so we get:

[tex]m=C'(t)=\frac{C'(t_{2})-C'(t_{1})}{t_2-t_1}[/tex]

so:

[tex]C'(t)=\frac{1640-1915}{2014-2000}=-\frac{275}{14}\approx -19.64[/tex]

therefore:

[tex]C'(2000)=-\frac{275}{14}[/tex]

[tex]C'(2014)=-\frac{275}{14}[/tex]

c)

Since the behavior is linear, we can calculate it with the point-slope form of the line which is:

[tex]y-y_{1}=m(x-x_{1})[/tex]

in this case:

[tex]C(t)-C(t_1)=C'(t)(t-t_{1})[/tex]

so we get:

[tex]C(t)-1915=-\frac{275}{14}(t-2000)[/tex]

and we can now solve for C(t) so we get:

[tex]C(t)=-\frac{275}{14}t+\frac{275000}{t}+1915[/tex]

for a final answer of:

[tex]C(t)=-\frac{275}{14}t+\frac{288405}{7}[/tex]

d)

So next we solve the equation for C(t)=1500 so we get:

[tex]1500=-\frac{275}{14}t+\frac{288405}{7}[/tex]

[tex]1500-\frac{288405}{7}=-\frac{275}{14}t[/tex]

[tex]-\frac{277905}{7}=-\frac{275}{14}t[/tex]

[tex]t=2021 \frac{7}{55}[/tex]

so we will reach that concentration level at the year 2021 approximately.

e)

Since the second derivative of the concentration function is greater than zero, this means that the original function might be a function in the form: .

This means that the decrease of the concentration levels is slower than that of a linear equation. So the projected date will be too early than the real date.

Answer:

If the answer is north why did you post it?

Answer:

the initial value is 15 and it represents the y-intersect in the context of this problem

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

2/3(2) + 1/2 = 5/6

If it's 2/3 * X then x is equal to 1/2.

Answer:

g = h/f - d/f

Step-by-step explanation:

Answer:

0.705

Step-by-step explanation:

Answer: the answer is .705

Step-by-step explanation:

the numbers 0.25 and 0.33 are technically 0.250 and 0.330

so just line them up and add. 0.250+0.125+0.330=0.705

Answer:

Correct mean = 32 grams

Correct Standard deviation = observed S.D = 2 grams

Step-by-step explanation:

We are told in the question above :

A scientist is weighing each of 30 fish. She obtains a mean of 30 g and a standard deviation of 2 g. After completing the weighing, she finds that the scale was misaligned and always under reported every weight by 2 g that is

The mean after correcting the error in the scale is :

= observed mean + 2g

= 30g + 2g = 32g

The standard deviation after correcting the error in the scale remains the same as the difference of 2g has no significant effect on the Standard deviation.

This standard deviation = 2g

Answer:

(30x2)x2

Step-by-step explanation:

Answer:

Step-by-step explanation:

O

Answer:

6 ounces per serving

Step-by-step explanation:

If you divide 15 ounces by 2.5 servings, you get 6 ounces per serving. I guess this is what you are trying to find, and hopefully it helps!

h = time in hours

20 + 4h = 546

4h = 526

h = 131.5

131.5 hours

Answer:

The Answer is D

Step-by-step explanation:

Do what answer D tells you to do. Obviously.

Answer:

25 and 18

Step-by-step explanation:

Answer:

Step-by-step explanation:

9. Alternative exterior

10. Alternate interior

11. Complementary

12. Corresponding

13. Corresponding

14. Alternate exterior

15. Vertical

16. Linear Pair

Answer:

X=8

Step-by-step explanation:

JK would equal 28, since it basically is double the side of that triangle. So now we have the equation, 2x+12=28. Now we solve using inverse operation. 28-12=16 and then 16 divided by 2 is 8, so x=8.

The required simplified value of x is 8, for the given triangle.

A midpoint is a point on the line whose distance from both ends of the line is equal.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

Here,
The property of a triangle states that the line joining the midpoints of the two adjacent sides is equal to half of the third side.
So,
JK = 2NO
2x + 12 = 24
x = 16 / 2
x  = 8

Thus, the required simplified value of x is 8, for the given triangle.

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Answer:

how many weeks are in a year?  52 so   2000 / 52 = ?

Step-by-step explanation:

the question asks how many  WEEKS to save 2000.... so just divide the weeks of one year into 2000 that you want to save for that year

my calculator says 2000/52=38.46  

so save $ 38.46 each week

Answer:

1.8 x 71 = 127.8, just 18 x 71 = 1278, then count the the decimal place from the right, i.e 127.8

same for 2.6 x 83 = 215.8

.......ok try 5.52 x 5

Answer:

27,579.24 OR 343.6

Step-by-step explanation:

I don't know if this is what you mean but 1.8x71x2.6x83=27,579.24

Also, (if that was not what you meant), 1.8x71=127.8, 2.6x83=215.8, 127.8+215.8=343.6

Answer:

.4625

Step-by-step explanation:

To find the mean, add up all the numbers, then divide by the number of terms

(0.2 +0.4+ 1+ 0.25) /4

1.85/4

.4625

Answer:

subtract from the maximum load the 1500 of the loading equipment and you have 6500 pounds of capacity for the containers you divide this by 300 which is what each of the containers weighs gives you 21,666 which tells us that the maximum of containers is 21

8000-1500 = 6500

6500/300 = 21.66

Step-by-step explanation:

Answer:

Survey data

Step-by-step explanation:

Survey data is defined as the resultant data that is collected from a sample of respondets that took a survey

The data obtained by conducting a survey is called as "survey data".

It is given that we are conducting a survey.

what will we call the data which is obtained through the survey.

What is a survey ?

Survey is a research method of gathering information or collecting the data.

Survey data is defined as the resultant data that is collected from a sample of respondents that took a survey.

The survey data is generally precise and enclosed within the topic of survey.

Thus, the data obtained by conducting the survey is called "survey data".

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Answer:

13

Step-by-step explanation:

Step 1:

EF + FG = EG        Equation

Step 2:

7 + 6 = EG        input values

AnsweR:

13 = EG            Add

Hope This Helps :)

Answer:

The answer is 23

Answer:

t = 23

Step-by-step explanation:

Answer: 65

Step 1: Multiply and add until you get 49.

11 x 4 = 44.

44 + 5 = 49.

Step 2: Multiply and add until you get 26, because 7:11 to 49 boys is 26,       26 : 49.

7 x 3 = 21.

21 + 5 = 26.

Step 3: Add 26 and 49.

26 + 49 = 65

Answer:

126 students

Step-by-step explanation:

Boys : Girls

7 : 11

How do you get from 7 to 49?

49 ÷ 7 = 7

Therefore, you should multiply the number of boys by 7.

Multiply:

7 : 11

7 × 7 = 49

49 : 11

Remember that whatever we do to the left, do to the right.

Multiply:

49 : 11

11 × 7 = 77

49 : 77

Now, let's add the number of boys and girls in the class to find the total number of students.

Add:

49 + 77 = 126

Therefore, there are 126 students in all.

Answer:

i think its C

Step-by-step explanation:

sorry if i get it wrong

Answer:

474$

Step-by-step explanation:

Answer:

0.32472

Step-by-step explanation:

Maple tree diameters in a forest area are normally distributed with mean 10 inches and standard deviation 2.2 inches. Find the proportion of trees having a diameter less than 9 inches.

The formula for calculating a z-score is z = (x-μ)/σ

where x is the raw score

μ is the population mean

σ is the population standard deviation

z = (9 - 10)/2.2

z = -1/2.2

= -0.45455

Probability value from Z-Table:

P(x ≤ 9) = P(x < 9)

= 0.32472

Therefore, the proportion of trees having a diameter less than 9 inches is

0.32472

The proportion of trees having a diameter less than 9 inches is 32.64%

z score is used to determine by how many standard deviations the raw score is above or below the mean.

It is given by:

[tex]z=\frac{x-\mu}{\sigma} \\\\where\ x\ is\ raw\ score.\mu\ is\ mean,\sigma\ is \ standard \ deviation[/tex]

Given that μ = 10, σ = 2.2, hence:

[tex]For\ x<9:\\\\z=\frac{9-10}{2.2} =-0.45[/tex]

From the normal distribution table, P(x < 9) = P(z < -0.45) = 0.3264 = 32.64%

The proportion of trees having a diameter less than 9 inches is 32.64%

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Answer:

4/16

Step-by-step explanation:

Answer:

a) C) The system has no solutions only when h=3 and k is any real number.

b) D) The system has a unique solution when [tex]h=(-\infty,3)U(3,\infty)[/tex] and k is any real number.

c) The system has may solutions when h=3 and k=15

Step-by-step explanation:

a) In order to determine when the system will have no solution, we can start by solving the equation by substitution. We can solve the first equation for x1:

[tex]x_{1}+hx_{2}=3[/tex]

so

[tex]x_{1}=3-hx_{2}[/tex]

Next we can substitute this into the second equation so we get:

[tex]5(3-hx_{2})+15x_{2}=k[/tex]

We distribute the 5 into the first parenthesis so we get:

[tex]15-5hx_{2}+15x_{2}=k[/tex]

and group like terms:

[tex]-5hx_{2}+15x_{2}=k-15[/tex]

we factor x2 so we get:

[tex]x_{2}(-5h+15)=k-15[/tex]

and solve for x2:

[tex]x_{2}=\frac{k-15}{-5h+15}[/tex]

this final answer is important because it tells us what value the system of equations is not valid for. That answer will not ve vallid if the denominator is zero, so we can set the denominator equal to zero and solve for h, so we get:

[tex]-5h+15= 0[/tex]

and solve for h:

[tex]-5h= -15[/tex]

[tex]h=\frac{-15}{-5}[/tex]

[tex]h= 3[/tex]

so it doesn't really matter what value k gets since all that matters is that the denominator of the answer isn't zero.

b)

For part b we need to know when the system of equations will have infinitely many answers. Generally, this will happen when both equations are basically the same, so we need to make sure to simplify the second equation so it looks like the first equation, compare them and determine the respective coefficients.

So we take the second equation and factor it:

[tex]5x_{1}+15x_{2}=k[/tex]

we start by factoring a 5 from the left side of the equation so we get:

[tex]5(x_{1}+3x_{2})=k[/tex]

Next, we divide both sides of the equation into 5 so we get:

[tex]x_{1}+3x_{2}=\frac{k}{5}[/tex]

we now compare it to the first equation:

[tex]x_{1}+hx_{2}=3[/tex]

[tex]x_{1}+3x_{2}=\frac{k}{5}[/tex]

In this case, every coefficient of the two equations must be the same for us to get infinitely many answers, so we can see that h=3 and [tex]\frac{k}{5}=3[/tex]

when taking the second condition and solving for k we get that:

[tex]k=3(5)[/tex]

so

k=15

Anything else than the specific combination h=3 and k=15 will give us unique solutions, so for b, the answer is:

D) The system has a unique solution when and k is any real number.

c)

We have already solved part c on the previous part of the problem, so the answer is:

The system has many solutions when h=3 and k=15