Answer:
(a) 100 fishes
(b) t = 10: 483 fishes
t = 20: 999 fishes
t = 30: 1168 fishes
(c)
[tex]P(\infty) = 1200[/tex]
Step-by-step explanation:
Given
[tex]P(t) =\frac{d}{1+ke^-{ct}}[/tex]
[tex]d = 1200\\k = 11\\c=0.2[/tex]
Solving (a): Fishes at t = 0
This gives:
[tex]P(0) =\frac{1200}{1+11*e^-{0.2*0}}[/tex]
[tex]P(0) =\frac{1200}{1+11*e^-{0}}[/tex]
[tex]P(0) =\frac{1200}{1+11*1}[/tex]
[tex]P(0) =\frac{1200}{1+11}[/tex]
[tex]P(0) =\frac{1200}{12}[/tex]
[tex]P(0) = 100[/tex]
Solving (a): Fishes at t = 10, 20, 30
[tex]t = 10[/tex]
[tex]P(10) =\frac{1200}{1+11*e^-{0.2*10}} =\frac{1200}{1+11*e^-{2}}\\\\P(10) =\frac{1200}{1+11*0.135}=\frac{1200}{2.485}\\\\P(10) =483[/tex]
[tex]t = 20[/tex]
[tex]P(20) =\frac{1200}{1+11*e^-{0.2*20}} =\frac{1200}{1+11*e^-{4}}\\\\P(20) =\frac{1200}{1+11*0.0183}=\frac{1200}{1.2013}\\\\P(20) =999[/tex]
[tex]t = 30[/tex]
[tex]P(30) =\frac{1200}{1+11*e^-{0.2*30}} =\frac{1200}{1+11*e^-{6}}\\\\P(30) =\frac{1200}{1+11*0.00247}=\frac{1200}{1.0273}\\\\P(30) =1168[/tex]
Solving (c): [tex]\lim_{t \to \infty} P(t)[/tex]
In (b) above.
Notice that as t increases from 10 to 20 to 30, the values of [tex]e^{-ct}[/tex] decreases
This implies that:
[tex]{t \to \infty} = {e^{-ct} \to 0}[/tex]
So:
The value of P(t) for large values is:
[tex]P(\infty) = \frac{1200}{1 + 11 * 0}[/tex]
[tex]P(\infty) = \frac{1200}{1 + 0}[/tex]
[tex]P(\infty) = \frac{1200}{1}[/tex]
[tex]P(\infty) = 1200[/tex]
5. Alexis has $95. She has 2 more five-dollar bills, 5 more one-dollar bills, and 2 more
ten-dollar bills than Kasai. How much money does Kasai have?
Answer:
60
Step-by-step explanation:
:)) tht should b right
These two polygons are similar.
4
2
16
15
w
w = [?
]
Enter
Answer:
w = 12
Step-by-step explanation:
Answer:
W=9
Step-by-step explanation:
[tex] \frac{2}{6 } = \frac{4}{12} = \frac{3}{9} [/tex]
so W= 9
Subjects with pre-existing cardiovascular symptoms who were receiving subitramine, an appetite suppressant, were found to be at increased risk of cardiovascular events while taking the drug. The study included 9804 overweight or obese subjects with pre-existing cardiovascular disease and/or type 2 diabetes. The subjects were randomly assigned to subitramine (4905 subjects) or a placebo (4899 subjects) in a double-blind fashion. The primary outcome measured was the occurrence of any of the following events: nonfatal myocardial infarction or stroke, resuscitation after cardiac arrest, or cardiovascular death. The primary outcome was observed in 561 subjects in the subitramine group and 495 subjects in the placebo group. Do the data give good reason to think that there is a difference between the proportions of treatment and placebo subjects who experienced the primary outcome
HELP ASAP I WILL MARK BRAINLEY
The diagram below shows Cameron's budgeted expenses for a trip he is planning. O $46.08 O 580 O $1,200 O $4,608 CLEAR ALL Cameron has budgeted $240 for meals during his full trip. What is the total budget for the trip?
A $46.08
B $80
C $1,200
D $4,608
Answer:
C $1,200
Step-by-step explanation:
The computation of the total budget fro the trip is as follows:
Since it is given that the budgeted amount for meals is $240 i.e. equivalent to 20%
By this information we can easily compute other budgeted expenses
For Lodging
= $240 × 0.32 ÷ 0.20
= $384
For transportation
= $240 × 0.36 ÷ 0.20
= $432
For Gifts
= $240 × 0.12 ÷ 0.20
= $144
Now the total budget for the trip is
= $384 + $240 + $432 + $144
= $1,200
In a right triangle, the 58-cm hypotenuse makes a 51-degree angle with one of the legs. To the nearest
tenth of a cm, how long is that leg?
Answer:
36.5 cm
Step-by-step explanation:
The Adjacent leg is 36.5 cm
What are trigonometric functions?"The trigonometric functions (also called circular functions, angle functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths."
What is hypotenuse, opposite and adjacent side of a right angled triangle?"In a right angled triangle, the hypotenuse is the longest side, an opposite side is the one across from a given angle, and an adjacent side is next to a given angle."
We have
Hypotenuse (AB) = 58 cm
Angle θ = 51 degree
From the figure, by using trigonometric functions
Cos θ = [tex]\frac{BC}{AB}[/tex]
we have to find BC
Cos [tex]51^{0}[/tex] = [tex]\frac{BC}{AB}[/tex]
We have, AB = 58 cm
BC = AB cos [tex]51^{0}[/tex]
⇒BC = 58 . cos [tex]51^{0}[/tex]
⇒BC = 36.50 cm
⇒BC = 36.5 cm
Hence, Adjacent leg is 36.5 cm
Learn more about trigonometric functions here
https://brainly.in/question/1013629
#SPJ2
Find the equation of the circle with center at (3, -2) and radius of 3.
Formula to help you get the answer:
(x - h)² + (y - k)² = r²
hope this helps!
Ten field hockey teams are competing in a tournament. Only the top three teams will be recognized as the first place, second place and third place winners. In how many ways could the ranking of the top three teams occur?
Answer:
The ranking of the top three teams could occur in 720 ways.
Step-by-step explanation:
The order in which the teams are ranked is important, that is, for example, Oilers, Flames and Canucks is a different outcome of Oilers, Canucks and Flames. This 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 how many ways could the ranking of the top three teams occur?
Three teams from a set of 10. So
[tex]T = P_{(10,3)} = \frac{10!}{7!} = 720[/tex]
The ranking of the top three teams could occur in 720 ways.
Help please I will give Brainliest to whoever answeres.
Answer:
area = 220.5 ft²
Step-by-step explanation:
2(Length) + 2(10.5) = 63 feet
2L + 21 = 63
subtract 21 from each side of the equation:
2L = 42
divide both sides by 2:
L = 21 feet
area = L x W = 21 x 10.5 = 220.5 ft²
Answer:
A = 220.5 ft
Step-by-step explanation:
[tex]2(Length) + 2(10.5) = 63 feet\\[/tex]
[tex]2L + 21 = 63\\[/tex]
[tex]63 - 21[/tex]
[tex]2L = 42[/tex]
[tex]42/2[/tex]
L = 21 feet
[tex]A=l * w[/tex]
[tex]21 x 10.5 = 220.5 ft^{2}[/tex]
Hope this helps
The North American feather-winged beetle is one of the world's smallest beetles.
It is less than 0.0005 meters in length. What is the length of scientific notation?
A. 5.0 x 10-4
B. 5.0 x 10
C.5.0 x 102
D. 5.0 x 104
(PLEASE ANSWER FAST)
Some friends are eating crackers. The number of crackers, y, that each person gets is inversely proportional to the number of people, x, who are sharing the crackers. When 4 people share the crackers, each person gets 12 crackers. What is an inverse proportion equation that represents this situation? How many crackers will each person get if 8 people are sharing the crackers?
(PLEASE ANSWER FAST)
Answer: yx (4)(12) / 8
Step-by-step explanation:
Answer:
1. What is an inverse proportion equation that represents this situation?
y=48/k
2. How many crackers will each person get if 8 people are sharing the crackers?
6 crackers
Step-by-step explanation:
1. What is an inverse proportion equation that represents this situation?
The number of crackers, y, is inversely proportional to the number of people, x. In mathematical terms, this is y=k/x, where k is some number.
When there are 4 people, each person gets 12 crackers:
y=k/x
12=k/4
48=k
Therefore, our equation is y=48/x
2. How many crackers will each person get if 8 people are sharing the crackers?
y=48/x, where y is the number of cracker and x is the number of people.
y=48/8
y=6
Determine if 0.875 is rational or irrational and give a reason for your answer.
what is 32 + 7898 - 400 + 12 divided by 667
Answer:
(Short answer) 11.3073
(Long Answer) 11.3073463268
Step-by-step explanation:
32 + 7898 - 400 + 12 = 7542
7542 / 667 = (Short answer) 11.3073
(Long Answer) 11.3073463268
4. Vivian uses a debit card to pay for a purchase, but she spends more than she has in her bank account. What will happen next?
Answer:
Vivian will have to get a loan, and pay back the money she spent with her debit card. If she cannot pay back this loan in time, the interest will grow higher and higher. Using a debit card is NOT good because if you don't have the money for something and you buy it anyway, you'll have to pay back double the money if you miss the deadline for the loan.
What are the mean, median, mode, and range of the data set given the altitude of lakes in feet
-11, -28, -17,-25, -28, -39, 6, and -46?
mean = -25, median=-26.5, mode=-28; range = 40
mean=-25, median=-40, mode=-26.5, range=28
mean = -26.5, median =-25; mode=-28, range = 28
O mean = -26.5, median = -28, mode =-25; range = 40
Answer:
Mean (Average) = -23.5
Median = -26.5
Mode = -28
Range = 52
Step-by-step explanation:
Mean is found when adding all numbers and dividing the outcome by the number of numbers, so -
-11 + -28 + -17 + -25 + -28 + -39 + 6 + -46 = -188
-188 ÷ 8 = -23.5
Median is found in the center, and can be found ordered from least to greatest -
-46, -39, -28, -28, -25, -17, -11, 6
last 2 remaining number would be -28 and -25, add those and divide by 2 which gives you -26.5.
The Median would be -26.5
Mode is the number that has repeated itself the most.
-28 repeated itself the most.
The Range is found when the least number is subtracted by the greatest number so -
6 - (-46) = 52
A bike store sells scooters at a 54% markup. If the store bought each scooter for $29.25, what is the resale price to the nearest dollar? Show your work
9514 1404 393
Answer:
$45
Step-by-step explanation:
The relation is ...
resale price = cost + markup
= cost + 0.54×cost
= 1.54×cost
Then the resale price is ...
resale price = 1.54×29.25 = 45.045 ≈ 45.00
The resale price is $45.00.
Anyone who know the answer please answer????
The circumference of a circle is 23 pi M what is the area in square meters express your answer in terms of pie
Answer:132.25π m²
Step-by-step explanation:The circumference of a circle is 23π
On the other hand, The circumference of a circle = 2×π×r ; where r is the radius. Then by equating the last two expressions we get: 23π = 2πr then r = 23/2 then the area = π × r² = (23/2)²×π = (132.25)×π
I need it please I will give 20
Given: cos θ = -4/5 , sin x = -12/13, θ is in the third quadrant, and x is in the fourth quadrant; evaluate tan x.
-12/5
-13/5
-5/12
Answer:
Step-by-step explanation:
Given: cos θ = -4/5 , sin x = -12/13, θ is in the third quadrant, and x is in the fourth quadrant; evaluate tan x.
-12/5
-13/5
-5/12
Find the sector area.
Answer:
D
Step-by-step explanation:
A new robotic toy was selling for $24 before it become very popular. The store raised the price by 25%. What was the cost of the toy after the markup?
Answer:
$30
Step-by-step explanation:
So we know that the toy cost 24 dollars. We also know that the cost is increased by 25%.
What is 25% of 100%? Thats 1/4. So, what is 1/4 of 24? That will be 6.
Since we are increasing the cost by 25%, we are increasing 24 dollars by 6. 24 plus 6 equals 30.
So the answer:
$30
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You sell 500 shares of Coldwater Creek stock (CWTR). You purchased the stock at $2.98 per share and sold it at $0.88
per share. What was the percent decrease in the stock? Round to the nearest whole percent.
Answer:
70%
Step-by-step explanation:
Given that,
Cost price of the stock = $2.98 per share
Sold price of the stock = $0.88 per share
We need to find the percent decrease in the stock. It can be done as follows :
[tex]\%=\dfrac{2.98-0.88}{2.98}\times 100\\\\=70.46\%[/tex]
or
= 70%
So, the decrease in the stock is equal to 70 %.
Please help mee (don't send a link)
Answer:
a
Step-by-step explanation:
the sign flips when you divide or multiply one
Answer:
B.
Step-by-step explanation:
4x-8>(with a line underneath)12
-8 -8
4x>(with a line underneath)12
/4 /4
x>(with a line underneath)3
It stays the same because you aren't dividing or multiplying by a negative. Only a negative will cause you to flip the inequality sign.
Two triangles have bases with lengths 5in and 8in.
a. Find the ratio of the areas of the triangles
b. If the area of the smaller triangle is 15in², what is the area of the larger triangle?
Show work
Answer:
i. The ratio of the areas of the two triangles is 5:8.
ii. The area of the larger triangle is 24 in².
Step-by-step explanation:
Let the area of the smaller triangle be represented by [tex]A_{1}[/tex], and that of the larger triangle by [tex]A_{2}[/tex].
Area of a triangle = [tex]\frac{1}{2}[/tex] x b x h
Where; b is its base and h the height.
Thus,
a. The ratio of the area of the two triangles is:
[tex]\frac{area of the smaller triangle}{area of the larger triangle}[/tex]
Area of smaller triangle = [tex]\frac{1}{2}[/tex] x b x h
= [tex]\frac{1}{2}[/tex] x 5 x h
= [tex]\frac{5}{2}[/tex]h
Area of the lager triangle = [tex]\frac{1}{2}[/tex] x b x h
= [tex]\frac{1}{2}[/tex] x 8 x h
= 4h
So that;
Ratio = [tex]\frac{\frac{5}{2}h }{4h}[/tex]
= [tex]\frac{5}{8}[/tex]
The ratio of the areas of the two triangles is 5:8.
b. If the area of the smaller triangle is 15 in², then the area of the larger triangle can be determined as;
[tex]\frac{area of the smaller triangle}{area of the larger triangle}[/tex] = [tex]\frac{5}{8}[/tex]
[tex]\frac{15}{A_{2} }[/tex] = [tex]\frac{5}{8}[/tex]
5 [tex]A_{2}[/tex] = 15 x 8
= 120
[tex]A_{2}[/tex] = [tex]\frac{120}{5}[/tex]
= 24
The area of the larger triangle is 24 in².
Irene is making bags of trail mix for hiking club. She will use 22 ounces of walnuts, 11.2 ounces of
almonds, and 12.3 ounces of cashews. This amount makes 25 bags of trail mix. How many
ounces are in each bag?
Please help :/ if i dont finish theses questions i will go to summer school & i dont wanna go there
Answer:
In each bag there will be 1.82 ounces of mixture.
Step-by-step explanation:
Since Irene is making bags of trail mix for hiking club, and she will use 22 ounces of walnuts, 11.2 ounces of almonds, and 12.3 ounces of cashews to make 25 bags of trail mix, to determine how many ounces are in each bag you must perform the following calculation:
(22 + 11.2 + 12.3) / 25 = X
45.5 / 25 = X
1.82 = X
Thus, in each bag there will be 1.82 ounces of mixture.
What is the area, in square feet, of the deck?
Answer:
42 square feet.
Step-by-step explanation:
A heavy piece of equipment has wheels on one side and legs on the other as shown in the diagram below.
Two people are trying to move the equipment. Each person grabs a handle and begins to lift. The first person imparts an upward force of 300 N and the second person imparts an upward force of 290 N. This is enough to lift the side of the equipment, but they also need to get it moving.
While maintaining the upward forces, the first person imparts a horizontal force of 185 N and the second person a horizontal force of 205 N. They maintain these forces while the equipment begins to move.
What is the total force in the horizontal direction?
____ N
What is the total force in the upward direction?
____ N
Determine the magnitude and direction of this resultant vector (the resultant vector from combining the forces of the two people).
Magnitude: ____ N
Direction: _____ °
9514 1404 393
Answer:
horizontal: 390 Nvertical: 590 N707.2∠56.5° NStep-by-step explanation:
The problem statement tells you the two horizontal forces are 185 N and 205 N. The total horizontal force is (185 +205) N = 390 N.
The vertical forces are said to be 300 N and 290 N. The total vertical force is (300 +290) N = 590 N.
The magnitude of the resultant is the root of the sum of the squares:
√(390² +590²) = √(152100 +348100) = √500200 ≈ 707.248
The angle of the resultant (relative to the horizontal) is ...
α = arctan(vertical/horizontal) = arctan(590/390) ≈56.53°
The resultant force is about 707.2 N at an angle of 56.5° above the horizontal.
What is the volume of this
pyramid?
Answer:
There is not pictutre.
Step-by-step explanation:
Of segments CDF and CED, which of the segments has a greater area based on the given information? Justify with your work.(Do not use sin)
Circle A has radius 10m and m angle CAD=90 degrees
Circle B has radius 12m and m angle CBD=60degrees
Answer:
Segment CED has greater areaStep-by-step explanation:
Circle AArea of ΔCAD, right triangle:
A = 1/2*10*10 = 50 m²Area of the sector CAD:
A = 1/4*π*10² = 78.54 m²Area of segment CED:
A = 78.54 - 50 = 28.54 m²Circle BArea of ΔCBD, equilateral triangle:
A = √3/4*12² = 62.36 m²Area of sector CBD:
A = 1/6*π*12² = 75.40 m²Area of segment CFD:
A = 75.40 - 62.36 = 13.04 m²Compare the areas of the segments:
CED = 28.54 > CFD = 13.04Answer:
for 1 st
area of segment CAD=90/360×π×10²=78.54m²
for second
area of segmentBCD=60/360×π×12²=75.4m²
so
CAD has greater area
Help! find the area of the parallelogram
28.2
Step-by-step explanation
A=bh=6·4.7≈28.2
