Answer:
Suppose there are 10 tables. Putting 4 chairs at each table requires 4*10 = 40 chairs. Since this is 6 more chairs than he has, he must have 40 - 6 = 34 chairs.
Now suppose we put pairs of table together ("double tables"), so that 6 chairs can fit around each pair. With 10 tables, there will be 5 pairs, and with 6 chairs around each of these, we need 5*6 = 30 chairs. So 4 of the 34 chairs are left over. That's exactly what the problem said, so this is the answer.
Now, you may find that this check provides you with a model for the second equation you need to write! At least, I hope it clarifies what the problem means by "double tables".
Step-by-step explanation:
this is just my interpritation, please tell me if wrong!!!
Solve 28,490-478.29
A large tank is filled to capacity with 300 gallons of pure water. Brine containing 5 pounds of salt per gallon is pumped into the tank at a rate of 3 gal/min. The well-mixed solution is pumped out at a rate of 6 gals/min. Find the number A(t) of pounds of salt in the tank at time t. A(t) = 1500(1−e−0.02t) lb How long (in minutes) will it take for the tank to be empty after this process has started? min
Answer:
(a) [tex]A = 1500(1 - e^{-0.01t})[/tex]
(b) [tex]t = 0[/tex]
Step-by-step explanation:
Given
[tex]V= 300gal[/tex] --- Volume of tank
[tex]B = 5lb/gal[/tex] --- Brine solution
[tex]R_1 = 3gal/min[/tex] --- Rate in, in gallon/min
[tex]R_2 = 6gal/min[/tex] --- Rate out, in gallon/min
Required
Determine A(t)
First, calculate the rate in (R in) and (R out) in lb/min
[tex]R_{in} = B * R_1[/tex]
[tex]R_{in} = 5lb/gal * 3gal/min[/tex]
[tex]R_{in} = 15lb/min[/tex]
R(out) is calculated by multiply the rate at which brine leaves the tank (lb/gal) * R2
So, we have:
[tex]R_{out} = \frac{A(t)}{300} lb/gal * 3gal/min[/tex]
[tex]R_{out} = \frac{3*A(t)}{300} lb/min[/tex]
[tex]R_{out} = \frac{A(t)}{100} lb/min[/tex]
The change in the amount of brin e in the tank at time t is given as:
[tex]A'(t) = R_{in} - R_{out}[/tex]
[tex]A'(t) = 15 - \frac{A(t)}{100}[/tex]
Rewrite:
[tex]\frac{dA}{dt} = 15 - \frac{A}{100}[/tex]
Multiply through by dt
[tex]dA = [15 - \frac{A}{100}]* dt[/tex]
Make dt stand alone
[tex]\frac{dA}{15 - \frac{A}{100}} = dt[/tex]
[tex]ln|15 - \frac{A}{100}| = -0.01t + ln\ c[/tex]
Express as exponents
[tex]15 - \frac{A}{100} = ce^{-\frac{t}{100}}[/tex]
Multiply through by 100
[tex]1500 - A = 100ce^{-\frac{t}{100}}[/tex]
[tex]A = 1500 - 100ce^{-\frac{t}{100}}[/tex]
[tex]A = 1500 - 100ce^{-0.01t}[/tex]
Apply initial conditions
[tex]A(0) = 0[/tex]
Substitute 0 for t in: [tex]A = 1500 - 100ce^{-0.01t}[/tex]
[tex]0 = 1500 - 100ce^{-0.01*0}[/tex]
[tex]0 = 1500 - 100ce^{0}[/tex]
[tex]0 = 1500 - 100c[/tex]
[tex]100c = 1500[/tex]
[tex]c = 15[/tex]
Substitute 15 for c in [tex]A = 1500 - 100ce^{-0.01t}[/tex]
[tex]A = 1500 - 100*15e^{-0.01t}[/tex]
[tex]A = 1500 - 1500e^{-0.01t}[/tex]
Factorize:
[tex]A = 1500(1 - e^{-0.01t})[/tex]
How long to empty the tank
Set A to 0
[tex]1500(1 - e^{-0.01t}) = 0[/tex]
Divide through by 1500
[tex]1 - e^{-0.01t} = 0[/tex]
Collect Like Terms
[tex]e^{-0.01t} = 1[/tex]
Take ln of both sides
[tex]ln\ (e^{-0.01t}) = ln\ 1[/tex]
[tex]-0.0t = 0[/tex]
[tex]t = 0[/tex]
You have to lend Rs. 75000 for two years for a purpose. If a
finance company A lends money at 10% per annum
compounded annually and finance company B lends money
at 8% per annum compounded semi-annuallly. From which
finance company will you take the loan and why? Give your
reason with calculation.
Answer:
The amount to be returned at Finance company B is less than that of Finance company A so it is profitable to take the loan from Finance company B.
Step-by-step explanation:
★ Finance company A :
A = 75,000 (1 + 0.1)²
A = 75,000 × 1.21
A = 90,750
★ Finance company B :
A = 75,000 (1 + 0.04)⁴
A = 75,000 × 1.16986
A = 87,739.5
The length of the coast to coast cycle challenge is 225 km. The scale on the map is 1 cm : 9 km. What is the length of the cycle route on the map?
9 km — 1 cm
225 km — 225 : 9 = 25 cm
The time it takes to charge the battery of a cell phone is directly proportional to the charge of the battery.
The equation, y = 0.21x, is used to approximate the time it takes to charge the battery of a cell phone.
Cell Phone Battery Charge
100
70
60
Bettery Charge (%)
SON
40
BO
20
NON
Time (AM)
Approximate how long it will take the battery to charge to 100%.
4 hours
7 hours
6 hours
5 hours
Please help me
Answer:
4 i believe
Step-by-step explanation:
Im so sorry if this is wrong and for being late
The time taken by the cell phone battery to charge 100% is 5 hours.
What is a linear equation?A linear equation is defined as a equation that has either one or two variables without exponents. A linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.
For the given situation,
The equation is y = 0.21x.
The time taken by the cell phone battery to charge to 100%,
⇒ [tex]100\% = 0.21x[/tex]
⇒ [tex]100\%=1[/tex]
Thus, [tex]1=0.21x[/tex]
⇒ [tex]x=\frac{1}{0.21}[/tex]
⇒ [tex]x=4.76[/tex] ≈ [tex]5[/tex]
Hence we can conclude that the time taken by the cell phone battery to charge 100% is 5 hours.
Learn more about linear equations here
https://brainly.com/question/10439298
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For a math assignment, Jane has to roll a set of six standard dice and record the results of each
trial. She wonders how many different outcomes are possible after rolling all six dice.
What is the total number of possible outcomes for each trial?
46,656
0 36
0216
0 7,776
SAVE AND CONTINUE
Answer:36
Step-by-step explanation: 6 sided dice = 6 possible outcomes
6×6=36
The required number of outcomes is 36 after rolling all six dice. Option B is correct.
Jane has to roll a set of six standard dice and record the results of each
trial. She wonders how many different outcomes are possible after rolling all six dice. the total number of possible outcomes for each trial to be determined.
Probability can be defined as the ratio of favorable outcomes to the total number of events for a system of the certain events.
For 1 dice, sample space = { 1 2 3 4 5 6}
total possible outcome = 6
Now 6 dice roll at once and the total outcome = 6 * 6
= 36
Meanwhile, Jane has a total of 36 outcomes.
Thus, the required number of outcomes is 36 after rolling all six dice. Option B is correct.
Learn more about probability here:
brainly.com/question/14290572
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help i can’t find this answer
Answer:
(-3,-17)
Step-by-step explanation:
is 1/10, 1/4, and 1/8 more or less than 1/2
Answer:
They are less than 1/2
Step-by-step explanation:
3x-14 when x equals 5 please help
Answer:
1
Step-by-step explanation:
15-14=1
Hope this helped!!
Step-by-step explanation:
3x-14 when x equals 5
3 (5) -14
15-14
x=1
What equation is equivalent to 6x + 13 - (3x - 7)
Answer:
6x + 12 - (3x - 7)
6x + 12 - 3x + 7
3x + 19
Step-by-step explanation:
Simplifying
6x + 13 + -3x + -7 = 0
Reorder the terms:
13 + -7 + 6x + -3x = 0
Combine like terms: 13 + -7 = 6
6 + 6x + -3x = 0
Combine like terms: 6x + -3x = 3x
6 + 3x = 0
Solving
6 + 3x = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-6' to each side of the equation.
6 + -6 + 3x = 0 + -6
Combine like terms: 6 + -6 = 0
0 + 3x = 0 + -6
3x = 0 + -6
Combine like terms: 0 + -6 = -6
3x = -6
Divide each side by '3'.
x = -2
Simplifying
x = -2
If 15×5 equals what what times five equals what
Answer:
15 x 5 = 75 x 5 = 375
Step-by-step explanation:
Not sure what you were saying but its just some spelling errors but i think i did what you said. You multiply the product of it to 5.
Pls answer correctly I’ll give you brainliest
Answer:
1=2(4)+b
Step-by-step explanation:
slope intercept looks like this y=mx(or y=#x+#
if the slope is 2 the equation will be y=2x+b
to find b so x=4 and y=1 we can plug those numbers into the equation to find b
If the length of AC equals 50, what is the length of the midsegment DE?
A)20
B)25
C)30
D)40
Answer:
25
Step-by-step explanation:
The mid-segment of the triangle is always parallel to the base and is half the length of the base
Simplify y^2-6y-7/2y^2-17y+21
Which is the graph of f(x)= 1 4 (4)^ x ?
Answer:
it is the last graph/D
Step-by-step explanation:
Can anyone plz help me
Answer:
a. 12(Nm)
b. anticlockwise
Step-by-step explanation:
Moment = force applied * distance
What are rexx sample?
Answer:
Following are the Arithmetic Operators available in Rexx. Operator, Description, Example. +, Addition of two operands, 1 + 2 will give 3
Step-by-step explanation:
So far this quarter, Samantha's quiz grades in her math class are as
follows: 68, 86, 94, 95, 82, 100, 95, and 84. If she gets an 89 on her next
quiz, which statement is true?
Find the area of the square in inches2 and enter your answer below. Do not include units in your answer.
Answer:
11.56
Step-by-step explanation:
The area formula is just Length * Height. Since this shape is a square, both the length and height are equivalent to the same thing, 3.4. So, all we have to do is multiply 3.4 * 3.4, or we can do 3.4^2.
2a-1-7b+4a-b+13? Simplyfying
2a - 1 - 7b + 4a - b + 13 =
= 2a + 4a - 7b - b - 1 + 13 =
= 6a - 8b + 12
Step-by-step explanation:
2a+4a-7b-b-1+13
6a-8b+12
A horseback rider travels 2 miles in 12 minutes. At this speed, how long does it take to travel 5 miles? Use the equation d=rt, where d is distance, r is rate, and t is time.
Answer:
30 minutes
Step-by-step explanation:
rate = 2/12 = 1 mile/6minutes
d = rt
5 = 1/6t
t= 5/(1/6)
t = 30 minutes
Find the measure of 48
00
48
[?]
Answer:
99°
Step-by-step explanation:
<8 = 99° [Since, corresponding angles of parallel lines]
Answer:
solution given:
<8=99° [corresponding angle]
Pls help! Write an equation of the line that passes through the points (1, 2) and (4, 8)
Answer (assuming it can be in slope-intercept form):
[tex]y =2x[/tex]
Step-by-step explanation:
1) First, find the slope of the line. Use the slope formula, [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]. Substitute the x and y values of the given points into the formula and solve:
[tex]m = \frac{(8)-(2)}{(4)-(1)} \\m = \frac{8-2}{4-1} \\m = \frac{6}{3} \\m = 2[/tex]
So, the slope is 2.
2) Now, use the point-slope formula [tex]y-y_1 = m (x-x_1)[/tex] to write the equation of the line in point-slope form. Substitute real values for [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex].
Since [tex]m[/tex] represents the slope, substitute 2 in its place. Since [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of a point the line intersects, choose one of the given points (it doesn't matter which one, the results will equal the same thing) and substitute its x and y values into the formula as well. (I chose (1,2), as seen below.) Then, isolate y to put the equation in slope-intercept form ([tex]y = mx + b[/tex] format) and find the following answer:
[tex]y-(2) = 2 (x-(1))\\y-2 = 2(x-1)\\y -2 = 2x-2\\y = 2x+0\\y = 2x[/tex]
Simplify: (8 2/3) ^ 4
Answer:
the answer is 558175
may it help you
Factorise the expressions.
Answer:
7 ([tex]y^{2}[/tex] + 6[tex]Z^{2}[/tex])
3a (x - 2y) - 4b(2y - x)
pq(p - 1) - [tex]r^{2}[/tex]( p - 1)
Step-by-step explanation:
(ii) 7y^2+35Z^2
=7(y^2+5Z^2)
(v) 3ax-6ay-8by+4bx
=x(3a+4b)-2y(3a+4b)
=(3a+4b)(x-2y)
viii)p^2q-pr^2-pq+r^2
=pq(p-1)-r^2(p-1)
=(p-1)(pq-r^2)
Yes or no
Just pick one
Answer:
Yes
Step-by-step explanation:
find the area and circumference of a circle which is 5cm
because it was the park of u the first thing I was going through and it is a lot
How many seconds are in 5 minutes? (1 minute= 60 seconds)
Answer: 300 seconds
Step-by-step explanation:
Answer:
300, I don't know if you need the work for it
What is the exponential form of the expanded form below?
4.4.4.4.4.4
a line has a slope of -3 and a y-intercept of 5. write the equation of the line in slope-intercept form and explain how you would use the slope and y-intercept to graph the equation?
Answer:
y = -3x + 5
Step-by-step explanation:
Since the y-intercept occurs at the point (0,5), you can use that and the point slope equation to find the equation.
This looks like y - 5 = -3 (x - 0);
Solving for y, you get y = -3x + 5;
To graph this equation you would put one point at (0,5), then use the slope to count down three and to the left one to find other points, or you could just plug in numbers for x to find their corresponding y values and plot it like that.
Hopefully this helps- let me know if you have any questions!