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
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?
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
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.
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.
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
Answer:
6
Step-by-step explanation:
236/10 = 23 remainder 6, so 6 crayons is the answer
Given f(x) = 3sqrt(2x-1).
6(2x-1)^2-3
What is lim f(x)?
Answer:
[tex]\displaystyle 51[/tex]
General Formulas and Concepts:
Algebra I
Terms/CoefficientsFactoringFunctionsFunction NotationAlgebra II
Piecewise functionsCalculus
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
according to the fundemental theorem of algebra, how many roots exist for the polynomial function? f(x) = (x^3-3x+1)^2
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
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!!!!!
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..
HELP ME WITH THIS MATHS QUESTION
PICTURE IS ATTACHED
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.
X = The set of months in a year?
there are 12 set of months in a year
Use what you know about decomposing fractions to write 11/10 as a mixed number.
Help please :(
Answer:
11/10 is 1 1/10
Step-by-step explanation:
The combined value of the ages of Mary, Kate and Tom is 26 years. What will be their age in total after 2 years?
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
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
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.
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
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
Determine la razón de la siguiente progresión geométrica: 81,27,9,3,1,....
Answer:
BẠN BỊ ĐIÊN À
Step-by-step explanation:
CÚT
help me please pls this ur really hard help
Translate the triangle. Then enter the new coordinates. A(-3, 4) A'([?], [?]) B'([ ], [ ] C([],[]) B(0, 1) C(-4,1)
or
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].
Log6^(4x-5)=Log6^(2x+1)
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]
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
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
Solve the following equation for
a
a. Be sure to take into account whether a letter is capitalized or not.
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
I need help ASAP is anyone available
Answer:
C
Step-by-step explanation:
The graph has asymptotes at x = 2 and x = -1 corresponding to the denominator of option C.
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
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:
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$
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
which of the following statements must br true about this diagram exterior and interior angles
Answer:
C: w > y
D: w > x
E: x + y = w
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
Answer:
260% is the correct answer
Step-by-step explanation:
i hope i helped
Evaluate −3w − 6p for w=2 and p = −7
-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
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
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
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.
Find the tangent line equations for the given functions at the given point(s): f(x) = tan x + 9 sin x at (π, 0)
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]
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.)
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:
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,
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.
Identify the domain of the function shown in the graph.
A. -5
B. x> 0
C. 0
D. x is all real numbers.