Water is flowing into a tank at a rate of 20 cm3/min. At the start, there is 250 cm3 of water in the tank.
(i) How much water will be in the tank after 30 minutes?
(ii) Find the time when there is 1210 cm3 of water in the tank.

Answers

Answer 1

Answer:

i) 410 cm³

ii) 48 min

Step-by-step explanation:

we start with 250 cm³.

and then we fill in 20 cm³ per minute.

i)

after 30 minutes we have

250 + 8×20 = 250 + 160 = 410 cm³

ii)

how long (how many minutes) does it take to reach 1210 cm³ in the tank ?

well, first we subtract the start amount (250).

and then we see how often 20 cm³ will "fit" into the remainder. and then we know how many minutes the water has to run.

1210 - 250 = 960 cm³

so, the incoming water needs to reach 960 cm³ to have a total of 1210 cm³.

and

960 cm³ / (20 cm³ / min) = 960 cm³ min / 20 cm³ =

= 960 min / 20 = 48 min


Related Questions

Log6^(4x-5)=Log6^(2x+1)

Answers

Answer:

[tex]x = 3[/tex]

Step-by-step explanation:

Given

[tex]\log6^{(4x-5)} =\log6^{(2x+1)}[/tex]

Required

Solve for x

We have:

[tex]\log6^{(4x-5)} =\log6^{(2x+1)}[/tex]

Remove log6 from both sides

[tex](4x-5) = (2x+1)[/tex]

Collect like terms

[tex]4x - 2x = 5 + 1[/tex]

[tex]2x = 6[/tex]

Divide by 2

[tex]x = 3[/tex]

Translate the triangle. Then enter the new coordinates. A(-3, 4) A'([?], [?]) B'([ ], [ ] C([],[]) B(0, 1) C(-4,1)

or

Answers

Answer:

The new coordinates are [tex]A'(x,y) = (3, 0)[/tex], [tex]B'(x,y) = (6, -3)[/tex] and [tex]C'(x,y) = (2, -3)[/tex].

Step-by-step explanation:

Vectorially speaking, the translation of a point can be defined by the following expression:

[tex]V'(x,y) = V(x,y) + T(x,y)[/tex] (1)

Where:

[tex]V(x,y)[/tex] - Original point.

[tex]V'(x,y)[/tex] - Translated point.

[tex]T(x,y)[/tex] - Translation vector.

If we know that [tex]A(x,y) = (-3,4)[/tex], [tex]B(x,y) = (0,1)[/tex], [tex]C(x,y) = (-4,1)[/tex] and [tex]T(x,y) = (6, -4)[/tex], then the resulting points are:

[tex]A'(x,y) = (-3, 4) + (6, -4)[/tex]

[tex]A'(x,y) = (3, 0)[/tex]

[tex]B'(x,y) = (0,1) + (6, -4)[/tex]

[tex]B'(x,y) = (6, -3)[/tex]

[tex]C'(x,y) = (-4, 1) + (6, -4)[/tex]

[tex]C'(x,y) = (2, -3)[/tex]

The new coordinates are [tex]A'(x,y) = (3, 0)[/tex], [tex]B'(x,y) = (6, -3)[/tex] and [tex]C'(x,y) = (2, -3)[/tex].

Which answer choice correctly identifies the extraneous information in the problem?

Anna babysat 2 children on Saturday night. She charges $8 an hour to babysit. She wants to save the money she earns babysitting to buy a stereo system that cost $225. If Nina babysat for 5 hours, how much money did she earn?

Answers

Answer: $40 / $80

Step-by-step explanation: 40$ if it's $8 for BOTH per hour, or if it's $8 for ONE per hour it's $80

The electric cooperative needs to know the mean household usage of electricity by its non-commercial customers in kWh per day. They would like the estimate to have a maximum error of 0.09 kWh. A previous study found that for an average family the variance is 5.76 kWh and the mean is 16.6 kWh per day. If they are using a 98% level of confidence, how large of a sample is required to estimate the mean usage of electricity

Answers

Answer:

A sample of 3851 is required.

Step-by-step explanation:

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.98}{2} = 0.01[/tex]

Now, we have to find z in the Z-table as such z has a p-value of .

That is z with a pvalue of , so Z = 2.327.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

Variance is 5.76 kWh

This means that [tex]\sigma = \sqrt{5.76} = 2.4[/tex]

They would like the estimate to have a maximum error of 0.09 kWh. How large of a sample is required to estimate the mean usage of electricity?

This is n for which M = 0.09. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.09 = 2.327\frac{2.4}{\sqrt{n}}[/tex]

[tex]0.09\sqrt{n} = 2.327*2.4[/tex]

[tex]\sqrt{n} = \frac{2.327*2.4}{0.09}[/tex]

[tex](\sqrt{n})^2 = (\frac{2.327*2.4}{0.09})^2[/tex]

[tex]n = 3850.6[/tex]

Rounding up:

A sample of 3851 is required.

Verify that the indicated family of functions is a solution of the given differential equation. Assume an appropriate interval I of definition for each solution.

d^2y/ dx^2 − 6 dy/dx + 9y = 0; y = c1e3x + c2xe3x When y = c1e3x + c2xe3x,

Answers

y'' - 6y' + 9y = 0

If y = C₁ exp(3x) + C₂ x exp(3x), then

y' = 3C₁ exp(3x) + C₂ (exp(3x) + 3x exp(3x))

y'' = 9C₁ exp(3x) + C₂ (6 exp(3x) + 9x exp(3x))

Substituting these into the DE gives

(9C₁ exp(3x) + C₂ (6 exp(3x) + 9x exp(3x)))

… … … - 6 (3C₁ exp(3x) + C₂ (exp(3x) + 3x exp(3x)))

… … … + 9 (C₁ exp(3x) + C₂ x exp(3x))

= 9C₁ exp(3x) + 6C₂ exp(3x) + 9C₂ x exp(3x))

… … … - 18C₁ exp(3x) - 6C₂ (exp(3x) - 18x exp(3x))

… … … + 9C₁ exp(3x) + 9C₂ x exp(3x)

= 0

so the provided solution does satisfy the DE.

Solve the following equation for
a
a. Be sure to take into account whether a letter is capitalized or not.

Answers

Answer:

6/5 n = a

Step-by-step explanation:

n = 5/6a

Multiply each side by 6/5

6/5 n = 6/5 * 5/6a

6/5 n = a

Identify the domain of the function shown in the graph.

A. -5 B. x> 0
C. 0 D. x is all real numbers.

Answers

I believe it could be D. X is al, real numbers but correct me if I’m wrong please.

Determine la razón de la siguiente progresión geométrica: 81,27,9,3,1,....

Answers

Answer:

BẠN BỊ ĐIÊN À

Step-by-step explanation:

CÚT

according to the fundemental theorem of algebra, how many roots exist for the polynomial function? f(x) = (x^3-3x+1)^2

Answers

Answer:

6

Step-by-step explanation:

First, we can expand the function to get its expanded form and to figure out what degree it is. For a polynomial function with one variable, the degree is the largest exponent value (once fully expanded/simplified) of the entire function that is connected to a variable. For example, x²+1 has a degree of 2, as 2 is the largest exponent value connected to a variable. Similarly, x³+2^5 has a degree of 2 as 5 is not an exponent value connected to a variable.

Expanding, we get

(x³-3x+1)²  = (x³-3x+1)(x³-3x+1)

= x^6 - 3x^4 +x³ - 3x^4 +9x²-3x + x³-3x+1

= x^6 - 6x^4 + 2x³ +9x²-6x + 1

In this function, the largest exponential value connected to the variable, x, is 6. Therefore, this is to the 6th degree. The fundamental theorem of algebra states that a polynomial of degree n has n roots, and as this is of degree 6, this has 6 roots

Given f(x) = 3sqrt(2x-1).
6(2x-1)^2-3

What is lim f(x)?

Answers

Answer:

[tex]\displaystyle 51[/tex]

General Formulas and Concepts:

Algebra I

Terms/CoefficientsFactoringFunctionsFunction Notation

Algebra II

Piecewise functions

Calculus

Limits

Right-Side Limit:                                                                                             [tex]\displaystyle \lim_{x \to c^+} f(x)[/tex]

Limit Rule [Variable Direct Substitution]:                                                             [tex]\displaystyle \lim_{x \to c} x = c[/tex]

Limit Property [Addition/Subtraction]:                                                                   [tex]\displaystyle \lim_{x \to c} [f(x) \pm g(x)] = \lim_{x \to c} f(x) \pm \lim_{x \to c} g(x)[/tex]

Limit Property [Multiplied Constant]:                                                                     [tex]\displaystyle \lim_{x \to c} bf(x) = b \lim_{x \to c} f(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle f(x) = \left \{ {{3\sqrt{2x - 1}, \ x \leq 2} \atop {6(2x - 1)^2 - 3, \ x > 2}} \right.[/tex]

Step 2: Solve

Substitute in function [Limit]:                                                                         [tex]\displaystyle \lim_{x \to 2^+} 6(2x - 1)^2 - 3[/tex]Factor:                                                                                                           [tex]\displaystyle \lim_{x \to 2^+} 3[2(2x - 1)^2 - 1][/tex]Rewrite [Limit Property - Multiplied Constant]:                                           [tex]\displaystyle 3\lim_{x \to 2^+} 2(2x - 1)^2 - 1[/tex]Evaluate [Limit Property - Variable Direct Substitution]:                             [tex]\displaystyle 3[2(2 \cdot 2 - 1)^2 - 1][/tex]Simplify:                                                                                                         [tex]\displaystyle 51[/tex]

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

Book: College Calculus 10e

which of the following statements must br true about this diagram exterior and interior angles

Answers

Answer:

C: w > y

D: w > x

E: x + y = w

X = The set of months in a year?

Answers

there are 12 set of months in a year

Find the area of the shaded regions: the green is the shaded area

PLS HELP ME!!!! I NEED THE ANSWER BY THIS EVENING CUZ I HAVE RSM TOMORROW. PLS HELP!!!!!

Answers

Answer:

the green area stands for the safe operation space

Step-by-step explanation:

u say b×h meaning say 80degrees ×9cm which is 720..

The combined value of the ages of Mary, Kate and Tom is 26 years. What will be their age in total after 2 years?

Answers

Answer:

32

Step-by-step explanation:

they will each age two years, 3x2 is 6, add 6 to 26

Answer:

32

Step-by-step explanation:

they will each age two years, 3x2 is 6, add 6 to 26

A cable that weighs 6 lb/ft is used to lift 600 lb of coal up a mine shaft 500 ft deep. Find the work done. Show how to approximate the required work by a Riemann sum. (Let x be the distance in feet below the top of the shaft. Enter xi* as xi.)

Answers

Answer:

A cable that weighs 6 lb/ft is used to lift 600 lb of coal up a mine shaft 500 ft deep. Find the work done. Show how to approximate the required work by a Riemann sum.

Step-by-step explanation:

Find the tangent line equations for the given functions at the given point(s): f(x) = tan x + 9 sin x at (π, 0)

Answers

Answer:

[tex]{ \bf{f(x) = \tan x + 9 \sin x }}[/tex]

For gradient, differentiate f(x):

[tex]{ \tt{ \frac{dy}{dx} = { \sec }^{2}x + 9 \cos x }}[/tex]

Substitute for x as π:

[tex]{ \tt{gradient = { \sec }^{2} \pi + 9 \cos(\pi ) }} \\ { \tt{gradient = - 8 }}[/tex]

Gradient of tangent = -8

[tex]{ \bf{y =mx + b }} \\ { \tt{0 = ( - 8\pi) + b}} \\ { \tt{b = 8\pi}} \\ y - intercept = 8\pi[/tex]

Equation of tangent:

[tex]{ \boxed{ \bf{y = - 8x + 8\pi}}}[/tex]

Rachel and Hugo sorted 236 crayons into boxes for a local arts project. Each box had 10 crayons. How many crayons were left over?

Help please lol

Answers

Answer:

6

Step-by-step explanation:

236/10 = 23 remainder 6, so 6 crayons is the answer

Evaluate −3w − 6p for w=2 and p = −7

Answers

-3w-6p when w=2 and p=-7

-3(2)-6(-7)

= -6 + 42

= 36

Answer:

48

Step-by-step explanation:

-3w-6p when w=2 and p--7

you want to plug in the numbers to their letters

-3(2)-6(-7)

then you want to times the numbers.

-6-42

=48

Student Engineers Council at an Indiana college has one student representative from each of the five engineering majors (civil, electrical, industrial, materials, and mechanical). Compute how many ways a president, a vice president, and a secretary can be selected.

Answers

Answer:

A president, a vice president, and a secretary can be selected in 60 ways.

Step-by-step explanation:

The order in which the people are chosen is important(first president, second vice president and third secretary), which means that the permutations formula is used to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this question:

3 students from a set of 5, so:

[tex]P_{(5,3)} = \frac{5!}{2!} = 5*4*3 = 60[/tex]

A president, a vice president, and a secretary can be selected in 60 ways.

What is the percent increase from 250 to 900?

1. Write the percent change formula for an increase.

Percent Increase =
Amount of Increase
Original Amount

2. Substitute the known quantities for the amount of the increase and the original amount.

Percent Increase =
900 − 250
250

3. Subtract.

Percent Increase =
650
250

Answers

Answer:

260% is the correct answer

Step-by-step explanation:

i hope i helped

The radius of a sphere is increasing at a rate of 3 mm/s. How fast is the volume increasing when the diameter is 60 mm

Answers

Answer:

The volume is increasing at a rate of 33929.3 cubic millimeters per second.

Step-by-step explanation:

Volume of a sphere:

The volume of a sphere of radius r is given by:

[tex]V = \frac{4\pi r^3}{3}[/tex]

In this question:

We have to derivate V and r implicitly in function of time, so:

[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]

The radius of a sphere is increasing at a rate of 3 mm/s.

This means that [tex]\frac{dr}{dt} = 3[/tex]

How fast is the volume increasing when the diameter is 60 mm?

Radius is half the diameter, so [tex]r = 30[/tex]. We have to find [tex]\frac{dV}{dt}[/tex]. So

[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]

[tex]\frac{dV}{dt} = 4\pi (30)^2(3) = 33929.3[/tex]

The volume is increasing at a rate of 33929.3 cubic millimeters per second.

help me please pls this ur really hard help

Answers

c done it on the test

Marquise has 200200200 meters of fencing to build a rectangular garden.
The garden's area (in square meters) as a function of the garden's width xxx (in meters) is modeled by:
A(x)=-x^2+100xA(x)=−x
2
+100xA, left parenthesis, x, right parenthesis, equals, minus, x, squared, plus, 100, x
WHAT IS THE MAXIMUM AREA POSSIBLE SQUARE METERS

Answers

Hence the maximum possible area is 2500 square meters

Given the area of the rectangular garden expressed as;

[tex]A(x)=-x^2+100x\\[/tex]

The maximum area occurs when dA(x)/dx = 0

[tex]\frac{dA(x)}{dx} = -2x + 100\\0= -2x + 100\\ 2x = 100\\x = \frac{100}{2}\\x = 50[/tex]

Next is to get the maximum area possible. Substitute x = 50 into the original function as shown;

[tex]A(50)= -50^2 + 100(50)\\A(50) = -2500+5000\\A(50) = 2500[/tex]

Hence the maximum possible area is 2500 square meters

Learn more here: https://brainly.com/question/17134596

2500 square meters

This question was on Khan Academy and I got it correct

I need help ASAP is anyone available

Answers

Answer:

C

Step-by-step explanation:

The graph has asymptotes at x = 2 and x = -1 corresponding to the denominator of option C.

Given: F = {(0, 1), (2, 4), (4, 6), (6, 8)} and G = {(2, 5), (4, 7), (5, 8), (6, 9), (7, 5)}

(F + G) (2) =

4
5
9

Answers

9514 1404 393

Answer:

  9

Step-by-step explanation:

The ordered pair (2, 4) in the relation for function F tells you F(2) = 4.

The ordered pair (2, 5) in the relation for function G tells you G(2) = 5.

Then the sum is ...

  (F+G)(2) = F(2) +G(2) = 4 +5

  (F+G)(2) = 9

HELP ME WITH THIS MATHS QUESTION
PICTURE IS ATTACHED

Answers

Answer:

In picture.

Step-by-step explanation:

To do this answer, you need to count the boxes up to the mirror line. This will give us the exact place to draw the triangle.

The picture below is the answer.

Which of the following statements are correct? Select ALL that apply!
Select one or more:
O a. -1.430 = -1.43
O b. 2.36 < 2.362
O c.-1.142 < -1.241
O d.-2.33 > -2.29
O e. 2.575 < 2.59
O f. -2.25 -2.46

Answers

I believe the answer is d.

Two workers finished a job in 12 days. How long would it take each worker to do the job by himself if one of the workers needs 10 more days to finish the job than the other worker

Answers

Two workers finished a job in 7.5 days.

How long would it take each worker to do the job by himself if one of the workers needs 8 more days to finish the job than the other worker?

let t = time required by one worker to complete the job alone

then

(t+8) = time required by the other worker (shirker)

let the completed job = 1

A typical shared work equation

7.5%2Ft + 7.5%2F%28%28t%2B8%29%29 = 1

multiply by t(t+8), cancel the denominators, and you have

7.5(t+8) + 7.5t = t(t+8)

7.5t + 60 + 7.5t = t^2 + 8t

15t + 60 = t^2 + 8t

form a quadratic equation on the right

0 = t^2 + 8t - 15t - 60

t^2 - 7t - 60 = 0

Factor easily to

(t-12) (t+5) = 0

the positive solution is all we want here

t = 12 days, the first guy working alone

then

the shirker would struggle thru the job in 20 days.

Answer:7 + 17 = 24÷2 (since there are 2 workers) =12. Also, ½(7) + ½17 = 3.5 + 8.5 = 12. So, we know that the faster worker will take 7 days and the slower worker will take 17 days. Hope this helps! jul15

Step-by-step explanation:

Use what you know about decomposing fractions to write 11/10 as a mixed number.

Help please :(

Answers

Answer:

11/10 is 1 1/10

Step-by-step explanation:

1 1/10

This is because is we divide 11 by 10 we get 1 1/10, the answer to this question.

Hope this helps! Please make me the brainliest, it’s not necessary but appreciated, I put a lot of effort and research into my answers. Have a good day, stay safe and stay healthy.

PLEASE HELP please I need this done now


The total cost of a truck rental, y, for x days, can be modeled by y = 35x + 25.
What is the rate of change for this function?

Answers
A- 35$
B-25$
C-60$
D-10$

Answers

Answer:

35

Step-by-step explanation:

y = 35x+23 is in the form

y = mx+b  where m is the slope and b is the y intercept

The slope can also be called the rate of change

35 is the slope

The answer to the question is A which is 35$
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Select the correct answer.Which of the following is a feature of the IdeaStorm website launched by Dell?A. tracks a competitor's marketing campaignB. promotes newly launched productsC. suggests new products for developmentD. informs investors about the company's goals in the process of rotation of the earth the longitude and the keep of changing able to write Kt lun s thch ng tm l ca sinh vin nm nht Which of the following statements is most accurate about human brain modularity? System 1 uses heuristics, while system 2 is more calculating; most decisions are made by system 1. System 1 uses heuristics, while system 2 is more calculating; system 2 regularly overcomes system 1's heuristics to make decisions. Both systems regularly use both heuristics and conscious calculations; both are equally important in decision making. System 1 uses heuristics, while system 2 is more calculating; both are equally important in decision making. The mass of a container is determined to be 1.2 g. A sample of a compound is transferred to this container, and the mass of the compound plus the container is determined to be 3.06 g. The mass of the compound should be reported as:__. What is the volume of this rectangular prism?Is it 3/2 x 1/4 x 5/3?? 1. A researcher is investigating the effects of exercise on weight. What are the independent and dependent variables in this experiment?A)The dependent variable is the amount of exercise; the independent variable is the number of calories consumed.B)The dependent variable is weight; the independent variable is exercise.C)The independent variable is weight; the dependent variable is the number of calories consumed.D)The independent variable is the number of calories consumed; the dependent variable is diet. How many square inches of sheet metal are used to make the vent transition shown? (The ends are open.) Over the past five hundred years, how many species are known to have gone extinct?Group of answer choicesa, 500 speciesb. 750 speciesc. 900 speciesd. an unknown number of species The domain for all variables in the expressions below is the set of real numbers. Determine whether each statement is true or false.(i)x y(x+y0) Last year, Mary opened an investment account with $5400. At the end of the year, the amount in the accounthad decreased by 6%. here is another question i need help At which values of x does the function Fx) have a vertical asymptote? Checkall that apply.F(x) =2/3x(x - 1)(x + 5)I A. -1B. 2C. 1D. -5E. 0F. 3 Pearl Harbor was caused by all of the following events EXCEPT:AJapan taking over China (Manchuria).BJapan's alliance with Germany.The U.S. cutting off oil and scrap metal.DJapan's alliance with Russia Writing equations in standard form:(1,-6) and (-7,2)How would I write this in standard form? I already tried but I keep getting x+y=7 and it says its wrong so could someone help? Argue whether we can infer anything about a candidates ability to work in a professional environment based on his or her resumes formatting.Compare how you would address a resume with wacky fonts to how you would respond to grammatical errors in a resume. Find the missing length the triangles are similar. Plz help me out with this ;) great love and great achievement involve great risk The population of a large U.S. city is 2,707,210. Which of the following best expresses this population? A 2.7 106 C 2.707 106 B 2.7 107 D 27.07 106