Step-by-step explanation:
combination
is answer of this question
Help please:))
2. When shipping ice cream, melting is understandably a big concern. You will notice that ice cream is not generally packaged in a cube-shaped container. A standard container of ice cream contains 1 L, or 1000 cm3 of ice cream,
a. What would be the optimal dimensions (radius and height) to minimize surface area?
b. What would the surface area be?
C. Suggest at least two reasons why this is different from the ice cream packaging that you see in the stores.
Answer:
a) Because this asks about the radius and height, I assume that we are talking about a cylinder shape.
Remember that for a cylinder of radius R and height H the volume is:
V = pi*R^2*H
And the surface will be:
S = 2*pi*R*H + pi*R^2
where pi = 3.14
Here we know that the volume is 1000cm^3, then:
1000cm^3 = pi*R^2*H
We can rewrite this as:
(1000cm^3)/pi = R^2*H
Now we can isolate H to get:
H = (1000cm^3)/(pi*R^2)
Replacing that in the surface equation, we get:
S = 2*pi*R*H + pi*R^2
S = 2*pi*R*(1000cm^3)/(pi*R^2) + pi*R^2
S = 2*(1000cm^3)/R + pi*R^2
So we want to minimize this.
Then we need to find the zeros of S'
S' = dS/dR = -(2000cm^3)/R^2 + 2*pi*R = 0
So we want to find R such that:
2*pi*R = (2000cm^3)/R^2
2*pi*R^3 = 2000cm^3
R^3 = (2000cm^3/2*3.14)
R = ∛(2000cm^3/2*3.14) = 6.83 cm
The radius that minimizes the surface is R = 6.83 cm
With the equation:
H = (1000cm^3)/(pi*R^2)
We can find the height:
H = (1000cm^3)/(3.14*(6.83 cm)^2) = 6.83 cm
(so the height is equal to the radius)
b) The surface equation is:
S = 2*pi*R*H + pi*R^2
replacing the values of H and R we get:
S = 2*3.14*(6.83 cm)*(6.83 cm) + 3.14*(6.83 cm)^2 = 439.43 cm^2
c) Because if we pack cylinders, there is a lot of space between the cylinders, so when you store it, there will be a lot of space that is not used and that can't be used for other things.
Similarly for transport problems, for that dead space, you would need more trucks to transport your ice cream packages.
al calls every 3 days, lee every 4 days, and pat every 6 day. Once every ? days, all three will call on the same day
Answer:
12
Step-by-step explanation:
Find the LCM (Least Common Multiple) of the three numbers.
We could multiply 3 x 4 x 6 to get 72, but there is a smaller multiple, 12.
6 x 2 = 12
4 x 3 = 12
3 x 4 = 12
Hope this helps!
Find x on this triangle
Answer:
3 sqrt(3) =x
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adj / hyp
cos 30 = x/6
6 cos 30 = x
6 ( sqrt(3)/2) = x
3 sqrt(3) =x
WILL MAKE BRAINLIEST
Answer:
x=3
Step-by-step explanation:
The ratios need to be the same
AB CB
---------- = ----------
AD ED
3 x
----- = ---------
3+9 12
3 x
----- = ---------
12 12
X must equal 3
What is the value of the expression 10(6 + 5)² when b = 3?
10(3+5)^2
10(8)^2
10(64)
=640
Given the exchange rate as K1: HK$1.353, calculate Hong Kong dollar equivalent of K70
Answer:
The Hong Kong dollar equivalent of K70 is HK $ 94.71.
Step-by-step explanation:
Given the exchange rate as K1: HK $ 1,353, to calculate Hong Kong dollar equivalent of K70 the following calculation must be performed:
1,353 x 70 = X
94.71 = X
Therefore, the Hong Kong dollar equivalent of K70 is HK $ 94.71.
Answer this please~!!!!
Answer:
12
Step-by-step explanation:
113.04=3.14 x 3^2 x h/3
Write an expression (or equation) that represents the number of square feet
of wallpaper you will need if the height of the family room is x feet, with a
length and width that are each 3 times the height of the room. The family
room has 1 door, which is 3 feet wide and 7 feet tall.
Answer: Given
room height is x feet
room length is 3x feet
room width is 3x feet
a door 3 ft wide by 7 ft tall
Find
The net area of the wall, excluding the door
Solution
The area of the wall, including the door, is the room perimeter multiplied by the height of the room. The room perimeter is the sum of the lengths of the four walls.
... gross wall area = (3x +3x +3x +3x)·x = 12x²
The area of the door is the product of its height and width.
... door area = (7 t)×(3 ft) = 21 ft²
Then the net wall area, exclusive of the door is ...
... net wall area = gross wall area - door area
... net wall area = 12x² -21 . . . . square feet
A solid oblique pyramid has a square base with edges measuring x cm. The height of the pyramid is (x + 2) cm.
A solid oblique pyramid has a square base with edges measuring x centimeters. The height is (x + 2) centimeters.
Which expression represents the volume of the pyramid?
StartFraction x cubed + 2 x squared Over 3 EndFraction cm3
StartFraction x squared + 2 x squared Over 2 EndFraction cm3
StartFraction x cubed Over 3 EndFraction cm3
StartFraction x cubed + 2 x squared Over 2 EndFraction cm3
Answer:
Hello,
Answer A StartFraction x cubed + 2 x squared Over 3 EndFraction cm3
Step-by-step explanation:
[tex]V=x^2*\dfrac{x+2}{3} \\\\\boxed{V=\dfrac{x^3+2x^2}{3} }\\[/tex]
the third of the sum of the cube of x and double of the square of x ( cm³)
The Volume of pyramid with a square base of side x cm and height of (x + 2) cm is (x³ + 2x²) / 3
What is volume?
Volume is the amount of space occupied by a three dimensional shape or object.
Area of the square base = x * x = x² cm²
Volume of pyramid = (1/3) * area of base * height = (1/3) * x² * (x + 2)
Volume of pyramid = (x³ + 2x²) / 3
The Volume of pyramid with a square base of side x cm and height of (x + 2) cm is (x³ + 2x²) / 3
Find out more on volume at: https://brainly.com/question/12410983
please help me with this on the image
Answer: For flour it is 360g
3 eggs
900ml of milk
Step-by-step explanation:
Answer:
First, find the amount of ingredient for one pancake:
240 ÷ 8 = 30g of plain flour per pancake2 ÷ 8 = 0.25 eggs per pancake600 ÷ 8 = 75 ml of milk per pancakeMultiply that amount by 12 to find the amount needed for 12 pancakes:
30 x 12 = 360g of plain flour0.25 x 12 = 3 eggs75 x 12 = 900 ml of milkFind the exact length of the curve. x=et+e−t, y=5−2t, 0≤t≤2 For a curve given by parametric equations x=f(t) and y=g(t), arc length is given by
The length of a curve C parameterized by a vector function r(t) = x(t) i + y(t) j over an interval a ≤ t ≤ b is
[tex]\displaystyle\int_C\mathrm ds = \int_a^b \sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2} \,\mathrm dt[/tex]
In this case, we have
x(t) = exp(t ) + exp(-t ) ==> dx/dt = exp(t ) - exp(-t )
y(t) = 5 - 2t ==> dy/dt = -2
and [a, b] = [0, 2]. The length of the curve is then
[tex]\displaystyle\int_0^2 \sqrt{\left(e^t-e^{-t}\right)^2+(-2)^2} \,\mathrm dt = \int_0^2 \sqrt{e^{2t}-2+e^{-2t}+4}\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^2 \sqrt{e^{2t}+2+e^{-2t}} \,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^2\sqrt{\left(e^t+e^{-t}\right)^2} \,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^2\left(e^t+e^{-t}\right)\,\mathrm dt[/tex]
[tex]=\left(e^t-e^{-t}\right)\bigg|_0^2 = \left(e^2-e^{-2}\right)-\left(e^0-e^{-0}\right) = \boxed{e^2-\frac1{e^2}}[/tex]
The exact length of the curve when the parametric equations are x = f(t) and y = g(t) is given below.
[tex]e^2 -\dfrac{1}{e^2 }[/tex]
What is integration?It is the reverse of differentiation.
The parametric equations are given below.
[tex]\rm x=e^t+e^{-t}, \ \ 0\leq t\leq 2\\\\y=5-2t, \ \ \ \ \ 0\leq t\leq 2[/tex]
Then the arc length of the curve will be given as
[tex]\int _0^2 \sqrt{(\dfrac{dx}{dt})^2+(\dfrac{dy}{dx})^2}[/tex]
Then we have
[tex]\rm \dfrac{dx}{dt} = e^t-e^{-t}\\\\ \dfrac{dy}{dt} = -2[/tex]
Then
[tex]\rightarrow \int _0^2 \sqrt{(\dfrac{dx}{dt})^2+(\dfrac{dy}{dx})^2}\ \ dt\\\\\rightarrow \int _0^2 \sqrt{(e^t-e^{-t})^2 + (-2)^2} \ dt\\\\\rightarrow \int _0^2 \sqrt{(e^t+e^{-t})^2} \ dt\\\\\rightarrow \int _0^2 (e^t+e^{-t}) \ dt\\\\\rightarrow (e^2-e^{-2}) \\\\\rightarrow e^2 - \dfrac{1}{e^2}[/tex]
More about the integration link is given below.
https://brainly.com/question/18651211
wrote the terms below.
–8, –4, 0, 4, 8, 12
What do these terms represent?
an arithmetic series
an arithmetic sequence
a geometric series
a geometric sequence
Answer:
an arithmetic sequence
Step-by-step explanation:
an arithmetic series is wrong also heres an example i found of an arithmetic sequence
The terms in the given sequence represents an arithmetic sequence.
What is Arithmetic Sequence?Arithmetic sequence is a sequence of numbers where the numbers are arranged ion a definite order such that the difference of two consecutive numbers is a constant. This constant of difference is called common difference which is commonly denoted by the letter 'd'.
Given sequence of numbers is,
-8, -4, 0, 4, 8, 12, ......
We have to find which sequence does it represent.
This is not a series since they are not represented as the sum.
If the sequence is a geometric sequence, then the ratio of consecutive numbers will be same.
If it is arithmetic sequence, then the difference of consecutive numbers will be same.
Here, ratio is not same.
Difference are same.
-4 - -8 = 4, 0 - -4 = 4, 4 - 0 = 4, 8 - 4 = 4, ........
Common difference is 4.
Hence it is an arithmetic sequence.
Learn more about arithmetic Sequence here :
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#SPJ3
HELP PLZ<3
An international company has 28,300 employees in one country. If this represents 34.1% of the company's employees, how many employees does it have in
total?
Round your answer to the nearest whole number.
Answer:
82991 employees
Step-by-step explanation:
One way to solve this would be to solve for 1% of the company's employees and use that value to solve for 100% (100%=the whole part, or the total). We know that
28300 = 34.1%
If we divide a number by itself, it turns into 1. Dividing both sides by 34.1, we get
829.912 = 1%
Then, we know that anything multiplied by 1 is equal to itself. We want to figure out 100%, or the whole part, so we can multiply both sides by 100 to get
100% = 82991
Ophelia is making homemade spaghetti sauce by combining 48 oz of tomato paste with 6 cups of water.how many ounces of tomatoes paste are needed for every cup of water show your work.
Answer:
8 ounces of tomato paste for each cup of water.
Step-by-step explanation:
Just divide 48 / 6 to get 8 oz of tomato paste per cup of water.
Hope this helps!
Work Shown:
48 oz of tomato paste = 6 cups of water
48/6 oz of tomato paste = 6/6 cups of water
8 oz of tomato paste = 1 cup of water
In short, we divide both values by 6 so that the "6 cups" becomes "1 cup". We can say the unit rate is 8 oz of tomato paste per cup of water.
Subtract.
8 over 9 minus 1 over 3
Answer:
5 over 9
Step-by-step explanation:
multiplayer both sides of the second fraction by 3, then you have 3 over 9. So the problem becomes 8-3=5
Assume that in the absence of immigration and emigration, the growth of a country's population P(t) satisfies dP/dt = kP for some constant k > 0.
a. Determine a differential equation governing the growing population P(t) of the country when individuals are allowed to immigrate into the country at a constant rate r > 0.
b. What is the differential equation for the population P(t) of the country when individuals are allowed to emigrate at a constant rate r > 0?
Answer:
[tex](a)\ \frac{dP}{dt} = kP + r[/tex]
[tex](b)\ \frac{dP}{dt} = kP - r[/tex]
Step-by-step explanation:
Given
[tex]\frac{dP}{dt} = kP[/tex]
Solving (a): Differential equation for immigration where [tex]r > 0[/tex]
We have:
[tex]\frac{dP}{dt} = kP[/tex]
Make dP the subject
[tex]dP =kP \cdot dt[/tex]
From the question, we understand that: [tex]r > 0[/tex]. This means that
[tex]dP =kP \cdot dt + r \cdot dt[/tex] --- i.e. the population will increase with time
Divide both sides by dt
[tex]\frac{dP}{dt} = kP + r[/tex]
Solving (b): Differential equation for emigration where [tex]r > 0[/tex]
We have:
[tex]\frac{dP}{dt} = kP[/tex]
Make dP the subject
[tex]dP =kP \cdot dt[/tex]
From the question, we understand that: [tex]r > 0[/tex]. This means that
[tex]dP =kP \cdot dt - r \cdot dt[/tex] --- i.e. the population will decrease with time
Divide both sides by dt
[tex]\frac{dP}{dt} = kP - r[/tex]
If there is a 65% chance you will make a free throw, what percent of the
time you will miss? *
Given:
There is a 65% chance you will make a free throw.
To find:
The percent of the time you will miss.
Solution:
If p is the percent of success and q is the percent of failure, then
[tex]p+q=100\%[/tex]
[tex]q=100\%-p[/tex] ...(i)
It is given that there is a 65% chance you will make a free throw. It means the percent of success is 65%. We need to find the percent of the time you will miss. It means we have to find the percent of failure.
Substituting p=65% in (i), we get
[tex]q=100\%-65\%[/tex]
[tex]q=35\%[/tex]
Therefore, there is a 35% chance you will miss the free throw.
In the picture the exponent says 5/3
Answer:
the answer is B
Step-by-step explanation:
[tex] {{ (- 2)}^{3}}^{5 \div 3} = { ( - 2)}^{5} = - 32[/tex]
write -8 form of 2 on up and complete other steps
Rubin grew 9 tomatoes with 6 seed packs. How many seed packs does Rubin need to have a total of 21 tomatoes in his garden?
Answer: 14 seed packs
Step-by-step explanation:
You'd divide the 9 tomatoes by the 6 seed packs that were necessary to grow them, resulting in 1.5 tomatoes per seed pack. Divide 21 by this 1.5 to find the number of seed packs needed to grow 21 tomatoes, which would be 14.
What is the common difference in this sequence: 3, 11, 19, 27,35?
1
ОА.1/8
O B. 3
O C. 8
O D. 12
Answer:
8
Step-by-step explanation:
To determine the common difference, take the second term and subtract the first term
11-3 = 8
Check with the other terms in the sequence
19-11= 8
27-19 = 8
35-27=8
The common difference is 8
Answer:
C. 8
Step-by-step explanation:
There is a common difference between them and that’s 8.
3 + 8 = 11
11 + 8 = 19
19 + 8 = 27
27 + 8 = 35
f(x) = 2x2 + 4x - 5
g(x) = 6x3 – 2x2 + 3
Find (f + g)(x).
Answer:
4x-5=4x-5
(f+g) (x)=6x³+3Step-by-step explanation:
Which of the following is equivalent to the expression below?
8^11•8^x
A. 8^x-11
B. 8^11x
C. 8^11+x
D. 8^11-x
Answer:
C
Step-by-step explanation:
[tex] \sf {a}^{c} \times {a}^{b} = {a}^{b + c} \\ \sf = {8}^{11} \times {8}^{x} \\ \sf = {8}^{11 + x} (c)[/tex]
According to The Wedding Report, Inc., the mean cost for a wedding in the United States is $28732 (as of November 2008). Suppose the cost for a wedding is normally distributed with a standard deviation of $1500, and that a wedding is selected at random. Use the appropriate Excel function to calculate each of the following. (Note - Part (e) can be done by hand.)
(a) Find the probability that the wedding costs less than $22000.
(b) Find the probability that the wedding costs more than $32000.
(c) Find the probability that the wedding costs between $25000 and $30000.
(d) Find Q1 (the 25th percentile) and Q3 (the 75th percentile).
(e) Find the IQR for the wedding costs.
(f) The top 10% of weddings cost more than how much?
Answer:
Following are the solution to the given points:
Step-by-step explanation:
[tex]X = \text{cost of wedding}\sim \text{Normal}\ (\mu = 28732, \sigma= 1500)\\\\[/tex]
For point a:
[tex]Probability\ = 0.00000359\\\\ \text{(Using Excel function:} =NORMDIST(22000,28732,1500,1)).[/tex]
For point b:
[tex]Probability \ = 0.014678\\\\\text{(Using Excel function:} =1-NORMDIST(32000,28732,1500,1))\\\\[/tex]
For point c:
[tex]Probability\ = 0.794614436 \\\\[/tex]
[tex]\text{(Using Excel function:} \\=NORMDIST (30000,28732,1500,1)-NORMDIST(25000,28732,1500,1))\\\\[/tex]
For point d:
[tex]Q_1 = 27720.26537 \\\\\text{(Using Excel function:} =NORMINV(0.25,28732,1500)) \\\\Q_3 = 29743.73463 \\\\\text{(Using Excel function:} =NORMINV(0.75,28732,1500)).[/tex]
For point e:
[tex]IQR = Q_3 - Q_1 = 29743.73463 - 27720.26537 = 2023.469251.[/tex]
For point f:
[tex]Top\ 10\% = 30654.32735 \\\\\text{(Using Excel function:} =NORMINV(0.9,28732,1500)).[/tex]
For a standard normal distribution, find:
P(z > -1.6)
Express the probability as a decimal rounded to 4 decimal places.
Answer:
P(z > -1.76) = 1 - P(z < -1.76) = 1 - 0.0392 = 0.960
Rudy Banks has won $5000 to attend university. If he invests the money in an
account at 12% per annum, compounded monthly, how much can he draw monthly
for the next 3 years?
Answer:
$7153.84
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Compounded Interest Rate Formula: [tex]\displaystyle A = P(1 + \frac{r}{n})^{nt}[/tex]
P is principle amountr is raten is compound ratet is timeStep-by-step explanation:
Step 1: Define
Identify variables
P = 5000
r = 12% = 0.12
n = 12
t = 3
Step 2: Find Interest
Substitute in variables [Compounded Interest Rate Formula]: [tex]\displaystyle A = 5000(1 + \frac{0.12}{12})^{12(3)}[/tex][Exponents] Multiply: [tex]\displaystyle A = 5000(1 + \frac{0.12}{12})^{36}[/tex](Parenthesis) Add: [tex]\displaystyle A = 5000(1.01)^{36}[/tex]Evaluate exponents: [tex]\displaystyle A = 5000(1.43077)[/tex]Multiply: [tex]\displaystyle A = 7153.84[/tex]15
Simplify
a
25
O A. a3
O B. a10
O c. a-10
O D. a-3
Answer:
B is the correct answer of your question.
I HOPE I HELP YOU....
Not sure how to do this
Is 1 2/6 a rational number?
Answer:
Yes, it is rational number.
Step-by-step explanation:
A rational number is any integer, fraction, terminating decimal, or repeating decimal.
Hope it is helpful.....can someone help me out with this question???
Answer:
a
Step-by-step explanation:
a soft drink vendor at a popular beach analyzes his sales recods and finds that if he sells x cans of soda pop in one day, his profit (in dollars) is given by
Complete Question:
A soft-drink vendor at a popular beach analyzes his sales records, and finds that if he sells x cans of soda pop in one day, his profit (in dollars) is given by P(x) = -0.001x² + 3x - 1800.
a. What is his maximum profit per day?
b. How many cans must be sold in order to obtain the maximum profit?
Answer:
a. $450
b. 1500 cans
Step-by-step explanation:
Given the following quadratic function;
P(x) = -0.001x² + 3x - 1800 ......equation 1
a. To find his maximum profit per day;
Since P(x) is a quadratic equation, P(x) would be maximum when [tex] x = \frac {-b}{2a} [/tex]
Note : the standard form of a quadratic equation is ax² + bx + c = 0 ......equation 2
Comparing eqn 1 and eqn 2, we have;
a = -0.001, b = 3 and c = -1800
Now, we determine the maximum profit;
[tex] x = \frac {-b}{2a} [/tex]
Substituting the values, we have;
[tex] x = \frac {-3}{2*(-0.001)} [/tex]
Cancelling out the negative signs, we have;
[tex] x = \frac {3}{2*0.001} [/tex]
[tex] x = \frac {3}{0.002} [/tex]
x at maximum = 1500
Substituting the value of "x" into equation 1;
P(1500) = -0.001 * 1500² + 3(1500) - 1800
P(1500) = -0.001 * 2250000 + 4500 - 1800
P(1500) = -2250 + 2700
P(1500) = $450
b. Therefore, the soft-drink vendor must sell 1500 cans in order to obtain the maximum profit.
