Answer:c
Step-by-step explanation:
Profit maximization happens with marginal revenue is equal to marginal cost, so if Grant's assumption was right before selling the extra unit, when he actually sells the extra unit, this will increase his revenue
That's why the answer is c
Marginal revenue will exceed marginal cost
Shawn bought fruit last week, consisting of 2.26 pounds of bananas, 1.5 pounds of grapes, and a watermelon that weighed 6.78 pounds. What is the total weight, in pounds, of the fruit that Shawn bought last week?
Answer:
10.54 pounds is right answer
Step-by-step explanation:
bananas 2.26 pounds
Grapes 1.5 pounds
water melon 6.78 pounds
total weight = 10.54 pounds
Answer:
10.54 pounds
Step-by-step explanation:
What is the value of h for the parallelogram?
Answer:
9.6 units
Step-by-step explanation:
The area of the parallelogram is the product of the base length and distance between parallel sides, either way you figure it.
16 × 6 = area = 10 × h
96 = 10h
h = 96/10 = 9.6 . . . . units
Mikayla is a waitress who makes a guaranteed $50 per day in addition to tips of 20% of all her weekly customer receipts, t. She works 6 days per week. Which of the following functions best represents the amount of money that Mikayla makes in one week?
A) f(t) = 50 + 20t
B) f(t) = 300 + 20t
C) f(t) = 50 + 0.2t
D) f(t) = 300 + 0.2t
Answer:
D. [tex]f(t)=300+0.20t[/tex]
Step-by-step explanation:
We have been given that Mikayla is a waitress who makes a guaranteed $50 per day.
Since Miklaya works 6 days per week, so the guaranteed income for one week would be [tex]\$50\times 6=\$300[/tex]
We are also told that she gets tips of 20% of all her weekly customer receipts, t. So amount earned from tips would be 20% of t, that is [tex]\frac{20}{100}t=0.20t[/tex].
Total amount earned in one week would be guaranteed income for 1 week plus 20% of t:
[tex]300+0.20t[/tex]
Therefore, our required function is [tex]f(t)=300+0.20t[/tex] and option D is the correct choice.
This Venn diagram shows the pizza topping preferences for 9 students. Let event A = The student likes pepperoni. Let event B = The student likes olives. What is P(A or B)?
Answer:
[tex]P(A\ or\ B)=\frac{7}{9}[/tex]
Step-by-step explanation:
We need to use the formula to calculate the probability of (A or B) where
A=Probability a student likes pepperoni
B=Probability a student likes olive
A and B =Probability a student likes both toppings in a pizza
A or B =Probability a student likes pepperoni or olive (and maybe both), a non-exclusive or
The formula is
[tex]P(A\ or\ B)=P(A)+P(B)-P(A\ and\ B)[/tex]
Since 6 students like pepperoni out of 9:
[tex]P(A) = \frac{6}{9}[/tex]
Since 4 students like olive out of 9:
[tex]P(B) = \frac{4}{9}[/tex]
Since 3 students like both toppings out of 9
[tex]P(A\ and\ B) = \frac{3}{9}[/tex]
Then we have
[tex]P(A\ or\ B)=\frac{6}{9}+\frac{4}{9}-\frac{3}{9}[/tex]
[tex]P(A\ or\ B)=\frac{7}{9}[/tex]
In a game of poker a hand of five cards is dealt to each player from a deck of 52 cards. find the probablility of a hand containing a spade flush.
Answer:
0.00597
Step-by-step explanation:
Given,
Total number of cards = 52,
In which flush cards = 20,
Also, the number of spade flush cards = 5,
Since,
[tex]\text{Probability}=\frac{\text{Favourable outcomes}}{\text{Total outcomes}}[/tex]
Thus, the probability of a hand containing a spade flush, if each player has 5 cards
[tex]=\frac{\text{Ways of selecting a spade flush card}}{\text{Total ways of selecting five cards}}[/tex]
[tex]=\frac{^{20}C_5}{^{52}C_5}[/tex]
[tex]=\frac{\frac{20!}{5!15!}}{\frac{52!}{5!47!}}[/tex]
[tex]=\frac{15504}{2598960}[/tex]
= 0.00597
A government's congress has 376 members, of which 44 are women. An alien lands near the congress building and treats the members of congress as as a random sample of the human race. He reports to his superiors that a 95% confidence interval for the proportion of the human race that is female has a lower bound of 0.085 and an upper bound of 0.149. What is wrong with the alien's approach to estimating the proportion of the human race that is female?
Answer:
Alien does not take the sample because alien choose the data of a Government's congress and congress contain less women.
On the other hand general population contain women greater than congress
So as compared to general population confidence interval is not representative.
Answer: The sample is not a simple random sample
Step-by-step explanation:
Complete the sentence below The _____ _____, denoted Modifying Above p with caret, is given by the formula Modifying Above p with caret equals_____, where x is the number of individuals with a specified characteristic in a sample of n individuals. The _____ _____ mean proportion error variance deviation , denoted Modifying Above p with caret, ________is given by the formula Modifying Above p with caretequals Start Fraction n Over x End Fraction xn Start Fraction x Over n End Fraction , where x is the number of individuals with a specified characteristic in a sample of n individuals.
Answer:down t
Step-by-step explanation: j this is world. Theo t sit with this
Find the values of x and y using trig
Answer:
Step-by-step explanation:
The triangle is a right angle triangle. This is because one of its angles is 90 degrees.
Let us determine x
Taking 47 degrees as the reference angle,
x = adjacent side
11 = hypotenuse
Applying trigonometric ratio,
Cos # = adjacent side / hypotenuse
# = 47 degrees
Cos 47 = x/11
x = 11cos47
x = 11 × 0.6820
x = 7.502
Let us determine y
Taking 47 degrees as the reference angle,
y = opposite side
11 = hypotenuse
Applying trigonometric ratio,
Sin # = opposite side / hypotenuse
# = 47 degrees
Sin 47 = y/11
x = 11Sin47
x = 11 × 0.7314
x = 8.0454
A jogger runs around a circular track of radius 55 ft. Let (x,y) be her coordinates, where the origin is the center of the track. When the jogger's coordinates are (33, 44), her x-coordinate is changing at a rate of 15 ft/s. Find dy/dt.
Using related rates and the Pythagorean theorem, we can find that dy/dt, the rate of change of the y-coordinate, is 0 ft/s.
Explanation:To find dy/dt, we need to determine the rate of change of the y-coordinate of the jogger. Since the jogger is running on a circular track, we can use the concept of related rates to solve this problem.
Let's assume that the jogger completes a full lap around the track in a time interval of Δt. During this time interval, the x-coordinate of the jogger changes by Δx, the y-coordinate changes by Δy, and the distance traveled along the track is Δs.
Since the jogger is running at a constant speed, the distance Δs is equal to the distance traveled in a straight line, which is the hypotenuse of a right triangle with legs Δx and Δy. Using the Pythagorean theorem, we have:
Δs^2 = Δx^2 + Δy^2
Taking the derivative with respect to time, we have:
2Δs(dΔs/dt) = 2Δx(dΔx/dt) + 2Δy(dΔy/dt)
Substituting the given values, Δx is 15 ft/s, Δy is 0 (since the y-coordinate is not changing), and Δs is the distance around the circular track, which is equal to the circumference of the circle:
2π(55ft) = 2(15ft)(dΔx/dt) + 2(0)(dΔy/dt)
Simplifying, we have:
dΔx/dt = π(55ft)/15s = 11π/3 ft/s
Therefore, dy/dt = dΔy/dt = 0 ft/s, since the y-coordinate is not changing.
A submarine was stationed 700 feet below sea level. It ascends 259 feet every hour. If the submarine continues to ascend at the same rate when will the submarine be at the surface?
Answer: it will take 2.7 hours to get to the surface
Step-by-step explanation:
A submarine was stationed 700 feet below sea level. It means that the height of the submarine from the surface is 700 feet.
It ascends 259 feet every hour.
If the submarine continues to ascend at the same rate, the time it will take for it to get to the surface will be the distance from the surface divided by its constant speed.
Time taken to get to the surface
700/259 = 2.7 hours
In a swim-and-run biathlon, An Athlete must get to a point on the other side of a 50 meter wide river, 100 meters downstream from her starting point. Ann can swim 2 m/sec and run 5 m/sec. What path should Ann take in order to minimize her total time?
Answer:
running distance = 78,18 m
swimmingdistance = 92m
Step-by-step explanation:
Ann has to run a distance 100 - x and swim √ (50)² + x²
at speed of 5 m/sec and 2 m/sec
As distance = v*t t = d/v
Then running she will spend time doing d = ( 100-x)/5
and √[(50)² + x² ] / 2 swimming
Therefore total time of biathlon
t(x) = ( 100 - x )/5 + √[(50)² + x² ] / 2
Taking derivatives both sides of the equation we get
t´(x) = - 1/5 + [1/2 ( 2x)*2] / 4√[(50)² + x²]
t´(x) = - 1/5 + 2x / 4√[(50)² + x²] t´(x) = - 1/5 + x/2√(50)² + x²
t´(x) = 0 - 1/5 + x/2√(50)² + x² = 0
- 2√[(50)²+ x²] + 5x = 0
- 2√(50)²+ x² ) = -5x
√(50)²+ x² = 5/2 *x
squared
(50)² + x² = 25/4 x²
2500 - 21/4 x² = 0
x² = 2500*4/21
x = 21,8 m
Therefore she has to run 100 - 21,82 = 78,18 m
And swim √(50)² + (78,18)² = 92m
The question pertains to Physics and involves calculating the optimal path in a swim-and-run biathlon to minimize total time, which would typically involve physics and calculus. However, the scenario is incomplete and lacks necessary information for a precise solution.
Explanation:The subject of this question is Physics, as it involves concepts of speed, velocity, and optimization of travel paths in a biathlon, which includes both swimming and running. To answer the question on the optimal path Ann should take in the swim-and-run biathlon, we would use principles of physics and calculus to find the path that minimizes the total time. The calculation would involve deriving the functional relationship between swimming and running speeds, and the distances covered in each stage, then determining the point at which Ann should exit the water to reach the end point in the shortest total time. However, since the problem in the question is incomplete and requires additional information, such as the current of the river or whether Ann swims at a constant speed relative to the water, we cannot solve it without making assumptions that may be incorrect.
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A 3 by 3 matrix Bis known to have eigenvalues 0, 1, 2. This information is enough to find three of these (give the answers where possible) : (a) the rank of B (b) thedeterminantofBTB (c) theeigenvaluesofBTB (d) the eigenvalues of (B2 + J)-1.
Answer with Step-by-step explanation:
We are given that a matrix B .
The eigenvalues of matrix are 0, 1 and 2.
a.We know that
Rank of matrix B=Number of different eigenvalues
We have three different eigenvalues
Therefore, rank of matrix B=3
b.
We know that
Determinant of matrix= Product of eigenvalues
Product of eigenvalues=[tex]0\times 1\times 2=0[/tex]
After transpose , the value of determinant remain same.
[tex]\mid B^TB\mid=\mid B^T\mid \mid B\mid =0\times 0=0[/tex]
c.Let
B=[tex]\left[\begin{array}{ccc}0&-&-\\-&1&-\\-&-&2\end{array}\right][/tex]
Transpose of matrix:Rows change into columns or columns change into rows.
After transpose of matrix B
[tex]B^T=\left[\begin{array}{ccc}0&-&-\\-&1&-\\-&-&2\end{array}\right][/tex]
[tex]B^TB=\left[\begin{array}{ccc}0^2&-&-\\-&1^2&-\\-&-&2^2\end{array}\right][/tex]
[tex]B^TB=\left[\begin{array}{ccc}0&-&-\\-&1&-\\-&-&4\end{array}\right][/tex]
Hence, the eigenvalues of [tex]B^TB[/tex] are 0, 1 and 4.
d.Eigenvalue of Identity matrix are 1, 1 and 1.
Eigenvalues of [tex]B^2+I=(0+1),(1+1),(2^2+1)=1,2,5[/tex]
We know that if eigenvalue of A is [tex]\lambda[/tex]
Then , the eigenvalue of [tex]A^{-1}[/tex] is [tex]\frac{1}{\lambda}[/tex]
Therefore, the eigenvalues of [tex](B^2+I)^{-1}[/tex] are
[tex]\frac{1}{1},\frac{1}{2},\frac{1}{5}[/tex]
The eigenvalues of [tex](B^2+I)^{-1}[/tex] are 1,[tex]\frac{1}{2}[/tex] and [tex]\frac{1}{5}[/tex]
Please answer quick guys! 3. Given LJ ≅ MK, and LK ≅ MJ, prove ∠L ≅ ∠M (Picture is below)
Answer:
The Proof is given below.
Step-by-step explanation:
Given:
LJ ≅ MK
LK ≅ MJ
To Prove:
∠ L ≅ ∠ M
Proof:
In Δ LKJ and Δ MJK
LK ≅ MJ ……….{Given}
KJ ≅ KJ ………..{Reflexive Property}
LJ ≅ MJ ……….{Given}
Δ LKJ ≅ Δ MJK ....….{Side-Side-Side test}
∴∠ KLJ ≅ ∠ JMK .....{corresponding angles of congruent triangles (c.p.ct)}
i.e ∠ L ≅ ∠ M ............Proved.
Find the positive number such that the sum of 8 times this number and 7 times its reciprocal is as small as possible.
Answer:
√56/8
Step-by-step explanation:
Let the number be x
f(x) = 8x + 7(1/x)
f(x) = 8x + 7/x
Differentiate f(x) with respect to x
f'(x) = 8x - 7/x = 0
8 - 7/x^2 = 0
(8x^2 - 7)/2 = 0
8x^2 - 7 = 0
8x^2 = 7
x^2 = 7/8
x = √7/8
x = √7 /√8
x = (√7/√8)(√8/√8)
x = (√7*√8) / √8*√8)
x = √56/8
Look at the graph of this system of equations: y = - x2 + 1 and y = x2. At which approximate points are the two equations equal? There more than one answer.
A.(-0.7, 0.5)
B.(0.5, 0.7)
C.(0.7, 0.5)
D.(-0.5, 0.7)
Answer:
option A and C, (-0.7, 0.5) and (0.7, 0.5)
Step-by-step explanation:
The two equations are equal means, the points at which the two graphs meet.
In that case the x and y coordinates satisfy both the graphs.
let the coordinates at the intersection point be (a,b).
Inserting in first equation,
[tex]b = -a^{2} + 1[/tex]
Inserting in second equation,
[tex]b = a^{2}[/tex]
Inserting value of b from second to first equation, we get
[tex]b = -b + 1[/tex]
[tex]b = \frac{1}{2} = 0.5[/tex]
Now inserting the value of b second equation, we get
[tex]\frac{1}{2} = x^{2}[/tex]
[tex]x = \sqrt{\frac{1}{2} } = +\frac{1}{1.414} or -\frac{1}{1.414} = +0.7 or -0.7[/tex]
Thus points are, (-0.7, 0.5) and (0.7, 0.5)
The bill is $330. We want to split it but a friend gave us $50 for it. Therefore we each owe $140 after the $50. Since I have the $50 in my possession I wok give him $165 since were splitting the $50. Correct?
I don't think that's correct
Step-by-step explanation:
Why are you splitting the $50? you'd end up paying more than the bill and he'd be getting back more money than he put in. Sounds like a rip off. If he had given you each $50 than maybe you'd each owe $140. I assume there is 3 friends, the original bill price would have been $110 for each of you. But then one friend gave $50 to help pay the bill, if you had split the $50 you'd still not be paying back that much. Also why are YOU paying so much more? Everyone else is paying $140 and you're paying $165? You would not be giving him that much, all of you would not be paying an extra $30 either. you'd be splitting it to where it equals $50 all around, so instead it'd be around $93.00. Not $140 or $165. $16.7 multipled by 3 = $50.1
But at the end of the day, just tell him to take his money back. He really didn't help pay the bill that much with his $50, he still owes you $60 if he too had participated in whatever you guys were doing. So instead of going through the trouble, just tell him to take back his money.
The average hourly wage of workers at a fast food restaurant is $6.75 with a standard deviation of $0.25. If the distribution is normal, what is the probability that a worker selected at random earns more than $7.00 an hour?
Answer:
25% would be the answer
Step-by-step explanation:
How many terms are in this equation?
Answer:
2
Step-by-step explanation:
Terms are products separated by +'s and −'s. Here, there are 2 terms:
2 tan(1/t) / (1/t)
sec²(1/t)
Please find the center of dialation given the information in the link. Real answers only.
Answer:
(-4, 0)
Step-by-step explanation:
The scale factor of 1/2 means each "dilated" point is 1/2 the distance from the center of dilation that the original point is. That is, the dilated point is the midpoint between the original and the dilation center.
If O is the origin of the dilation, then ...
(O + X)/2 = P . . . . . P is the dilation of point X
O +X = 2P
O = 2P -X = 2(0, 2) -(4, 4)
O = (-4, 0)
The center of dilation is (-4, 0).
_____
Another way to find the center of dilation is to realize that dilation moves points along a radial line from the center. Hence the place where those radial lines converge will be the center of dilation. See the attachment for a solution that way.
Based on the Polynomial Remainder Theorem what is the value of the function below when x = 3.
Answer:
Remainder = 64
Step-by-step explanation:
Given equation,
[tex]x^4+3x^3-6x^2-12x-8[/tex]
Remainder theorem says a polynomial can be reset in terms of its divisor (a) by evaluating the polynomial at x=a
Plug x=3,
[tex]=3^4+3(3)^3-6(3)^2-12(3)-8\\=81+81-54-36-8\\=162-54-36-8\\=64[/tex]
Thus the remainder is 64 at x=3 ,using polynomial remainder theorem.
A boat leaves the entrance to a harbor and travels 150 miles on a bearing of Upper N 56 degrees Upper E. How many miles north and how many miles east from the harbor has the boat traveled?
Answer:
83.9 miles north124.4 miles eastStep-by-step explanation:
It can be helpful to draw a diagram. In the attached diagram, point H represents the harbor, point B represents the position of the boat, and point N represents a point directly north of the harbor and west of the boat.
The bearing N56E means the direction of travel is along a path that is 56° clockwise (toward the east) from north.
__
The mnemonic SOH CAH TOA reminds you of the relationships between the sides of a right triangle. Here, we are given the length of the hypotenuse, and we want to know the lengths of the sides opposite and adjacent to the angle. One of the useful relations is ...
Sin = Opposite/Hypotenuse
In our diagram, this would be ...
sin(56°) = BN/BH
We want to find length BN, so we can multiply by BH to get ...
BN = BH·sin(56°) = 150·0.829038 = 124.4 . . . . miles (east)
__
For the adjacent side, we use the relation ...
Cos = Adjacent/Hypotenuse
cos(56°) = HN/HB
HN = HB·cos(56°) = 150·0.559193 = 83.9 . . . . miles (north)
The boat has traveled 124.4 miles north and 83.9 miles east of the harbor entrance.
There are 24 basketball teams competing in a tournament. After each round half the teams are eliminated. This situation can be modeled by the function
Answer:
b(x)=24(1/2)x
Step-by-step explanation:
The situation can be modeled by the exponential function will be y = 24 (0.5)ˣ.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The exponent is given as
y = a(b)ˣ
There are 24 ball groups contending in a competition. After each round around 50% of the groups is dispensed with.
Then the value of the b will be 1/2 and the value of the variable 'a' will be 24. Then the exponential equation is given as,
y = 24 (1/2)ˣ
y = 24 (0.5)ˣ
The situation can be modeled by the exponential function will be y = 24 (0.5)ˣ.
More about the exponent link is given below.
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Twenty-four blue socks and twenty-four red socks are lying in a drawer in a dark room. What is the minimum number of socks you need to pull out of the drawer so that you are sure to have at least two blue socks
Answer:
26 socks
Step-by-step explanation:
There are a total of 48 socks here. Let us assume you pulled out 24 socks at a go and all are red. Now, you would have exhausted the number of red socks here. You would be left with only blue socks which you can pull one after the other to give a total of 26 socks pulled out to have 2 blue socks at least.
Asha invests rs 8000 at a certain rate for three yrs compounded annually . She finds at the end of the first year it amounts to rs 9200. Calculate(1) R%(2)interest acquired in second year (3)amount at the end of the third year
Answer:
= 12169 rs
Step-by-step explanation:
Asha invest total=rs 8000
Total years = 3
Amount after 1 year= 9200 rs
Interest on first year =9200-8000= 1200 rs
So for second and third years
A= P (1 + R/100)ⁿ
9200= 8000( 1+ R/100)¹
9200= 8000( 100+ R/100)
115= 100 +R
R = 15
So amount after second year
A= 8000 (1 +15/100)²
A= 10580
Interest on second is = 10580 –P-interest on ist
=10580-8000-1200
= 1380 rs
So total amount at the end
A = 8000 ( 1 +15/100) ³
=12169 rs
the volume of a cylindrical can is 500cm^3. The materail used to make the top and bottom costs 0.012 cent/cm^2 the material used for the sides costs 0.01 cent?cm^2, and the seam joining the top and bottom to the sides costs .015 cent/cm. what size can would cost the least to produce?
Answer:
radius: 3.671 cmheight: 11.810 cmStep-by-step explanation:
The total cost of producing a cylindrical can with radius r and height h will be ...
cost = (lateral area)×(side cost) +(end area)×(end cost) +(seam length)×(seam cost)
__
The lateral area (LA) is ...
LA = 2πrh
Since the volume of the can is fixed, we can write the height in terms of the radius using the volume formula.
V = πr²h
h = V/(πr²)
Then the lateral area is ...
LA = 2πr(V/(πr²)) = 2V/r = 2·500/r = 1000/r
__
The end area (EA) is twice the area of a circle of radius r:
EA = 2×(πr²) = 2πr²
__
The seam length (SL) is twice the circumference of the end:
SL = 2×(2πr) = 4πr
__
So, the total cost in cents of producing the can, in terms of its radius, is ...
cost = (1000/r)(0.01) +(2πr²)(.012) +(4πr)(0.015)
We can find the minimum by setting the derivative to zero.
d(cost)/dr = -10/r² +0.048πr +.06π = 0
Multiplying by r² gives the cubic ...
0.048πr³ +0.06πr² -10 = 0
r³ +1.25r² -(625/(3π)) = 0 . . . . . . divide by .048π
This can be solved graphically, or using a spreadsheet to find the value of r to be about 3.671 cm. The corresponding value of h is ...
h = 500/(π·3.671²) ≈ 11.810 . . . cm
The minimum-cost can will have a radius of about 3.671 cm and a height of about 11.810 cm.
_____
A graphing calculator can find the minimum of the cost function without having to take derivatives and solve a cubic.
A farmer is using a barn as one side of a fence to enclose his cattle. If the barn is 80 feet long what is the width of the rectangular enclosure if the farmer has 260 ft. Of fencing to complete the project?
Answer:
90 feet
Step-by-step explanation:
The perimeter is the sum of the side lengths of the enclosure. The length is given as 80 ft, but only one side that long counts as part of the 260 ft of fence. So, we have ...
260 ft = 2×W + L = 2×W + 80 ft . . . . . length of fence for 3 sides
180 ft = 2×W . . . . . . subtract 80
90 ft = W . . . . . . . . . divide by 2
The width of the enclosure is 90 feet.
Final answer:
To find the width of the farmer's rectangular enclosure, we subtract the length of the barn (80 ft) from the total amount of fencing available (260 ft) to get the length available for the other three sides. Dividing this by two (because there are two widths), we find that the width of the enclosure will be 90 feet.
Explanation:
The question asks about creating a rectangular enclosure using a fixed length of fencing and a barn as one of the sides. With 260 feet of fencing available and the barn covering one side of 80 feet, the farmer must use the remaining fencing for the other three sides of the rectangle.
To find the width of the rectangular enclosure, we need to subtract the length of the barn side from the total amount of fencing available, and then divide by two (because there are two widths in a rectangle), as follows:
260 ft - 80 ft = 180 ft for both widths, so each width will be
180 ft / 2 = 90 ft.
Therefore, the width of the rectangular enclosure will be 90 feet.
In a typical start for his baseball team, Rick throws 120 total pitches with a ratio of 3 fastballs thrown for every 2 curveballs. If Rick makes a relief appearance of 30 pitches using the same ratio, how many fastballs will he throw in the relief appearance?
Answer:
18 fastballs
Step-by-step explanation:
Let x represent each throw
fastball : curve ball = 3:2
For fastball we have 3x while for curve ball we have 2x
If Rick makes a relief appearance of 30 pitches with the same ratio,
3x + 2x = 30
5x = 30
x = 30/5
x = 6
fastball, 3x= 3*6
= 18
curveball = 2x = 2*6
= 12
Rick will throw 18 fast balls
A jar contains 800 red and green jelly beans. Of those, 320 are red and the rest are green. What is the ratio of red and green jelly beans?
Answer:
The ratio is 2 to 3.
Step-by-step explanation:
The jar is comprised of only red and green jelly beans. We are given the number of total beans and the number of red beans. We calculate the number of green beans by doing 800-320 = 480.
The problem is asking for the ratio of red to green jelly beans, which is 320 to 480, or 320/480. Simplified, this is 2/3.
The ratio of red to green jellybeans will be 1/3.
What are ratios and proportion?Ratio is a quantitative relation between two amounts showing the number of times one value contains or is contained within the other. A statement expressing the equality of two ratios A:B and C:D is called a proportion. We can express proportion as -
A : B ∷ C : D
AND
A x D = B x C
Product of extremes equal to product of means
We have a jar that contains 800 red and green jelly beans. Of those, 320 are red and the rest are green.
Number of red beans = 320
Number of green jelly beans = 800 - 320 = 480
Ratio of red to green jellybeans = 320/480 = 1/3
Therefore, the ratio of red to green jellybeans will be 1/3.
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A bakery decided to expand since business was going so well. Originally, the width was five times the length. Now they are adding 5 feet to the length. If the length was originally 15 feet, what will be the area of the new bakery?
Step-by-step explanation:
We need to find new area of bakery.
Old length = 15 feet
Old width = New width = 5 x Old length = 5 x 15 = 75 feet
New length = Old length + 5 feet = 15 + 5 = 20 feet
New area = New length x New width
New area = 75 x 20 = 1500 square feet.
New area of bakery = 1500 square feet.
Given: dp/dt = k(M- P)
where P(t) measures the performance of someone learning a skill after a training time t, M is the maximum level of performance, and k is a positive constant. Solve this differential equation to find an expression for P(t). (Use P for P(t). Assume that P(0) = 0.)
Answer:
[tex]P=M(1-e^{-kt})[/tex]
Step-by-step explanation:
The relation between the variables is given by
[tex]\frac{dP}{dt} = k(M- P)[/tex]
This is a separable differential equation. Rearranging terms:
[tex]\frac{dP}{(M- P)} = kdt[/tex]
Multiplying by -1
[tex]\frac{dP}{(P- M)} = -kdt[/tex]
Integrating
[tex]ln(P-M)=-kt+D[/tex]
Where D is a constant. Applying expoentials
[tex]P-M=e^{-kt+D}=Ce^{-kt}[/tex]
Where [tex]C=e^{D}[/tex], another constant
Solving for P
[tex]P=M+Ce^{-kt}[/tex]
With the initial condition P=0 when t=0
[tex]0=M+Ce^{-k(0)}[/tex]
We get C=-M. The final expression for P is
[tex]P=M-Me^{-kt}[/tex]
[tex]P=M(1-e^{-kt})[/tex]
Keywords: performance , learning , skill , training , differential equation
The differential equation dp/dt = k(M - P) can be solved via separating variables, integrating and applying the initial condition. Result provides the equation for performance over time: P(t) = M(1 - e-kt).
Explanation:The subject of the question is around a differential equation. Firstly, you will rewrite the given equation dp/dt = k(M - P) in the form necessary for separation of variables: dp/(M - P) = k dt. Then, integrate both sides: ∫dp/(M - P) = ∫k dt. The left-hand side integral results in -ln|M - P|, and the right side is k*t + C, where C is the constant of integration. Finally, solve for P(t) by taking the exponential of both sides, and rearranging. The procedure results in the performance level equation.
P(t) = M - Ce-kt
Since we're given P(0) = 0, we can determine that C = M. Hence, we finally have the solution:
P(t) = M(1 - e-kt)
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