Answer:
3 berries
Explanation:
Opportunity costs for the Orange group:
Opportunity cost of pumping 1 gallon of water = 3/1 = 3 berries
Opportunity cost of picking 1 berry = 1/3 = 0.333 gallons of water
Opportunity costs for the Yellow group:
Opportunity cost of pumping 1 gallon of water = 8/2 = 4 berries
Opportunity cost of picking 1 berry = 2/8 = 0.25 gallons of water
Opportunity cost for both groups combined:
Opportunity cost of pumping 1 gallon of water = 3 berries (Orange group should pump water since opportunity cost is lower)
Opportunity cost of picking 1 berry = 0.25 gallons of water (Yellow group should pick berries since opportunity cost is lower)
Opportunity costs are the extra costs or benefits lost resulting from choosing one investment or activity over another alternative. In this case, people can either pump water or pick berries, but they cannot do both at the same time. When they are pumping water, the opportunity cost is the amount of berries that they will not be able to collect, and vice versa.
Find the zeros of each function. Part 3. Please show work.
1. f(x)= x^4 - x^3 - x^2 - x - 2
2. f(x)= x^3 - 8x^2 + 19x - 12
9514 1404 393
Answer:
real: -1, 2; complex: +i, -i1, 3, 4Step-by-step explanation:
1. The graph (red) shows the only real zeros to be -1 and 2. When the corresponding factors are divided from the function, the remaining factor is the quadratic (x^2 +1), which has only complex roots. The quadratic is graphed in green.
The linear factorization is ...
f(x) = (x +1)(x -2)(x -i)(x +i)
The roots are -1, 2, -i, +i.
__
2. The graph (blue) shows the zeros are 1, 3, 4.
You observe that the sum of coefficients is zero, so x=1 is a root. Factoring that out gives the quadratic (x^2 -7x +12), which you recognize factors as
(x -3)(x -4) . . . zeros of 3 and 4
__
I have attached a spreadsheet that does synthetic division. There are web sites that will do this, too. The tables shown correspond to f1(x)/(x-2) and f2(x)/(x-1). When you fill in the zero and coefficients, the built-in formulas do the rest.
9514 1404 393
Answer:
real: -1, 2; complex: +i, -i
1, 3, 4
Step-by-step explanation:
1. The graph (red) shows the only real zeros to be -1 and 2. When the corresponding factors are divided from the function, the remaining factor is the quadratic (x^2 +1), which has only complex roots. The quadratic is graphed in green.
The linear factorization is ...
f(x) = (x +1)(x -2)(x -i)(x +i)
The roots are -1, 2, -i, +i.
__
2. The graph (blue) shows the zeros are 1, 3, 4.
You observe that the sum of coefficients is zero, so x=1 is a root. Factoring that out gives the quadratic (x^2 -7x +12), which you recognize factors as
(x -3)(x -4) . . . zeros of 3 and 4
__ The tables shown correspond to f1(x)/(x-2) and f2(x)/(x-1).
Which of the following is a description of the data with a correlation coefficient of 0.1?
8 The fourth grade had 363 students. Over winter break, 94 students moved away, but
26 new students moved in.
а
How
many students are now in fourth grade Show your work.
There are now
students in fourth grade
Answer:
the answer is 295 students
Answer:
363-94+26 = 295 students
Convert 52 centimetres to millimeters.
Answer:
Step-by-step explanation:
1 cm = 10mm
52cm = 52 x 10 = 520mm
Use synthetic division to solve (x3 + 1) = (x - 1). What is the quotient?
x² + x + 1 + 1 2 3
x2-x+1
x2+x+1+2
x3 - x2 + x
Synthetic division yields
1 | 1 0 0 1
. | 1 1 1
= = = = = = = = = =
. | 1 1 1 2
which translates to
(x³ + 1) / (x - 1) = x² + x + 1 + 2/(x - 1)
where the quotient is x² + x + 1.
You are traveling in a car. Your speed is 50 miles per hour. What is your speed in feet per minute?
Answer:
4399.98 ft per min
Step-by-step explanation:
Divide 50 mi by 60 min = 0.83333Multiply this by 5280 = 4399.9824 ft per minHow many terms are in the expression, 4x + 5y + 15?
Answer:
There are 3 terms.
Which problem has a sum or difference of 7/12 ? Mark all that apply.
A. 3/4 + 1/6
B. 3/4 - 1/6
C. 1/3 + 1/4
D. 1/4 + 1/6 + 1/12
E. 2/3 - 1/12
F. 2/3 + 1/6
will mark you brainliest
Answer:
a and b
Step-by-step explanation:
the arithmetic mean of a data set is the measure of center ______. (PHOTO INCLUDED)
Answer:
Option A is correct option.
Step-by-step explanation:
We need to fill in the blank:
the arithmetic mean of a data set is the measure of center ______
Arithmetic mean is calculating average of data i.e adding all the value divided by total number of values.
So, Option A is correct option.
Assume that there are two pairs of congruent triangles in the diagram
AROB = APTA
O True
O False
what is the 8th term of the following sequence?
3/25, 3/5, 3, 5
Answer:
The 8th term of the following sequence is 9375.
Step-by-step explanation:
Given the sequence
3/25, 3/5, 3, 15
As we know that a geometric sequence has a constant ratio and is defined by:
[tex]\:a_n=a_0\cdot r^{n-1}[/tex]
so
[tex]\frac{3}{25},\:\frac{3}{5},\:3,\:15[/tex]
[tex]\frac{\frac{3}{5}}{\frac{3}{25}}=5,\:\quad \frac{3}{\frac{3}{5}}=5,\:\quad \frac{15}{3}=5[/tex]
As the ratio 'r' is the same.
so
[tex]r=5[/tex]
As the first element of the sequence is
[tex]a_1=\frac{3}{25}[/tex]
Therefore, the nth term is computed by
[tex]\:a_n=a_0\cdot r^{n-1}[/tex]
[tex]a_n=\frac{3}{25}\cdot \:5^{n-1}[/tex]
Putting n = 8 to determine the 8th term.
[tex]a_8=5^7\cdot \frac{3}{25}[/tex]
[tex]a_8=\frac{3\cdot \:5^7}{25}[/tex]
[tex]=\frac{5^7\cdot \:3}{5^2}[/tex]
[tex]=5^5\cdot \:3[/tex]
[tex]=9375[/tex]
Therefore, the 8th term of the following sequence is 9375.
what is the area of a rectangular garden that is 60 feet by 20 feet
andy is scuba diving he starts at sea level and then descends 10 feet in 2 1/2 minutes. how would you represent andy’s descent as a unit rate? express your answer as an integer
Answer:
4 feet/minute
explanation:
The rate of descent = (10 feet)/(2.5 mn) = 4 ft/min
Help now fast please
Answer:
3/4 or .75
Step-by-step explanation:
slope = dy/dx
dy = 1 - -2 = 3
dx = 2 - -2 = 4
slope = 3/4
Step-by-step explanation:
(1+2)/(2+2)= 3/4 is the slope
PLEASE HELP (ASSIGNMENT DUE IN 20 MINUTES)
Answer:
11 widgets
Step-by-step explanation:
544.50/4.5 = 121
square root 121 = 11
What is the ratio of the number of days in the week that do not begin with the letter "T" to the number of days in the week that do begin with the letter "T"? (1 point)
Answer:
5:7
Step-by-step explanation:
The days in the week whose names don't begin with 'T' are Sunday, Monday, Wednesday, Friday, and Saturday. I counted them, and found that there are five (5) of them. Then I counted the number of days in a full week, no matter how they're spelled. I counted seven (7) that time. The ratio of 5 to 7 is. 5:7 or 5/7.
True or false that integers can be negative numbers
Answer:
true
Step-by-step explanation:
Using the frequency table below, what is the
probability of selecting a boy and a person who
bought 10 up to 20 lunches?
Answer:
[tex]\frac{1}{6}[/tex]
Step-by-step explanation:
P(Boy and 10-20 lunches)
[tex]=\frac{20}{10+20+30+5+25+30}\\=\frac{20}{120}\\=\frac{1}{6}[/tex]
The answer to this problem is 1/6.
1) Greaters sold 30 milkshakes last week. 20%. of the milkshakes had whipped cream on them. How many shakes had whipped cream? Answer: I
Answer:
6
plz vote me brainliest
Step-by-step explanation:
PLZ HELP ME WITH THIS ITS DUE SOON AND IDK HOW TO DO IT :(
Answer:
Is it everything or which ones particularly?
help???
anyone?
thank you
Answer:
$285.12
Step-by-step explanation:
Start by finding the discount price
$480 * 0.45 = 216
Now subtract
$480 - 216 = 264
Then you will need to find the sales tax
264 * 0.08 = 21.12
now add
21.12 + 264 = 285.12
$264.00
45% off means that the new price of the desk will be 55% of the original price.
$480.00(100-45) = $480.00(55)
Converting the percent to a decimal gives:
$480.00(0.55)
Your Answer:
$264
Find the exact area of the surface obtained by rotating the curve about the x-axis. x = 1 3 (y2 + 2)3/2, 3 ≤ y ≤ 4
Answer:
21π/2
Step-by-step explanation:
94.55π is the area of the required surface.
What is the exact area of a surface obtained by rotating the curve y=f(x), [tex]x_1\leq x\leq x_2[/tex] about the x-axis?[tex]S=\int\limits^{x_1}_{x_2} {2\pi f(x)\sqrt{1+f'(x)^2} \, dx[/tex]
is the exact area of a surface obtained by rotating the curve y=f(x), [tex]x_1\leq x\leq x_2[/tex] about the x-axis
How to solve the problem?Given,
[tex]x=\frac{1}{3}(y^2+2)^{\frac{3}{2}}[/tex]
[tex]\implies (3x)^\frac{2}{3}=y^2+2\\\implies y^2=(3x)^\frac{2}{3}-2[/tex]
[tex]\implies y=\sqrt{(3x)^\frac{2}{3}-2}[/tex]
Let
[tex]y=\sqrt{(3x)^\frac{2}{3}-2}=f(x)[/tex]
Now, the range of y is given 3≤y≤4
hence, the range of x is [tex](\frac{1}{3}(3^2+2)^{\frac{3}{2}}[/tex],[tex]\frac{1}{3}(4^2+2)^{\frac{3}{2}})[/tex]=(12.16,25.46).
So, [tex]S=\int\limits^{25.46}_{12.16} {2\pi f(x)\sqrt{1+f'(x)^2} dx\\\\=[\frac{\pi}{2}(3x)^{\frac{4}{3}}-\pi (3x)^{\frac{2}{3}}]^{25.46}_{12.16}\\=101.63\pi - 6.99 \pi \\= 94.55 \pi[/tex]
is the area of the required surface.
Hence, 94.55π is the area of the required surface.
Learn more about the area of surface- brainly.com/question/24126051
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2,4000,000 in standard form
Answer:
24 million
Step-by-step explanation:
24,000,000 if you put it porperly
The units are, Unit, Tens, Hundreds, Thousand, Ten-Thousand, Hundred-Thousand, Million, Ten million, Hundred million Billion and so on
Arden has 15 cards and 3 of those cards are red. What percent of her cards are red? *
Answer: 20%
Step-by-step explanation: 3/15 = 1/5 = .20 = 20%
PLEAS HELP ME I WILL GIVE YOU FREE ROBUX PLEASE HELP ME ON THIS ANSWER
Question:Name each polygon by its number of sides and then classify it as CONVEX or CONCAVE and REGULAR or IRREGULAR
Answer:
1.Nonagon-convex, regular
2.Quadrilateral-convex, irregular
3.Hexagon-concave, irregular
Answer:
1.-Nonagon-convex, regular
2.-Quadrilateral-convex, irregular
3.-Hexagon-concave, irregular
what is the value of x in the proportion 2 1/4/x = 1 1/2/3 3/5?
(A) 2 2/5
(B) 5 2/5
(C) 8 1/10
(D) 12 3/20
Answer:
its d bc it is so yeah suck a toe hehehehehehehhehehehehehehehehhehehehehehehehehhehehehehhehehehehhehehehehehehehehehhehhehehehhhehehehehhehhehehehe
Answer: I’m pretty sure ur answer would be B) 5 2/5
Step-by-step explanation: good luck ! <3
3) g(x) = 4x
h(x) = -3x^2 + 4
Find (g + h)(x)
Answer:
The answer is the last line below.
Step-by-step explanation:
g(x) = 4x
h(x) = -3x^2 + 4
(g + h)(x) = 4x - 3x^2 + 4
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Solve for x in angle bisector please
Answer:
x = 15
Step-by-step explanation:
Since, BX is the bisector of [tex] \angle BAC[/tex]
[tex]\therefore m\angle ABX = \frac {1}{2} m\angle ABC\\\\
\therefore 24= \frac {1}{2}\times (4x - 12)\\\\
\therefore 24= \frac {1}{2}\times 2(2x - 6)\\\\
\therefore 24= (2x - 6)\\\\
\therefore 24 = 2x - 6 \\ \\
\therefore 24 +6 = 2x\\\\
\therefore 30 = 2x \\\\
\therefore x = \frac{30}{2} \\\\
\therefore x = 15
[/tex]
Need help ASAP ! Determine whether the following polygons are similar.
Answer:
they are not similar because you can't multiply both sides given by the same number to get the second polygon
Answer:
NO THEY arent
Step-by-step explanation:
if you were to multiply both, you wouldnt get the same answer also the scale factor isnt the same.