Answer:
The population that gives the maximum sustainable yield is 45000 swordfishes.
The maximum sustainable yield is 202500 swordfishes.
Step-by-step explanation:
Let be [tex]f(p) = -0.01\cdot p^{2}+9\cdot p[/tex], the maximum sustainable yield can be found by using first and second derivatives of the given function: (First and Second Derivative Tests)
First Derivative Test
[tex]f'(p) = -0.02\cdot p +9[/tex]
Let equalize the resulting expression to zero and solve afterwards:
[tex]-0.02\cdot p + 9 = 0[/tex]
[tex]p = 450[/tex]
Second Derivative Test
[tex]f''(p) = -0.02[/tex]
This means that result on previous part leads to an absolute maximum.
The population that gives the maximum sustainable yield is 45000 swordfishes.
The maximum sustainable yield is:
[tex]f(450) = -0.01\cdot (450)^{2}+9\cdot (450)[/tex]
[tex]f(450) =2025[/tex]
The maximum sustainable yield is 202500 swordfishes.
A clothing store is having a sale on shirts and jeans. Four shirts and two pairs of jeans cost $78. Three shirts and five pairs of jeans cost $111. The system of equations
4s + 2j = 78
3s + 5j = 111
models this situation, where s is the cost of a shirt and j is the cost of a pair of jeans. How much does one shirt and one pair of jeans cost?
Answer:
One shirt is $12 and one pair of jeans is $15
Step-by-step explanation:
Solve by elimination by multiplying the top equation by 3 and the bottom equation by -4:
12s + 6j = 234
-12s - 20j = -444
Add these together, and solve for j:
-14j = -210
j = 15
So, a pair of jeans is $15. Plug in 15 as j into one of the equations and solve for s:
3s + 5j = 111
3s + 5(15) = 111
3s + 75 = 111
3s = 36
s = 12
One shirt is $12 and one pair of jeans is $15.
Evaluate the following expression
Graph the function f(x)=x^2+2x-8
what are x intercepts
what are y intercepts
what is maximum or minimum value
Answer:
The x intercepts are 2, -4
The y intercept is -8
The minimum is -9
Step-by-step explanation:
f(x)=x^2+2x-8
To find the x intercepts, set equal to zero and factor
0 =x^2+2x-8
0 = (x+4)(x-2)
Using the zero product property
0 = x+4 0 = x-2
x = -4 x = 2
The x intercepts are 2, -4
To find the y intercepts, set x =0 and solve for y
y = 0^2 +2(0) -8
y = -8
The y intercept is -8
Since the coefficient of the x^2 is positive, the parabola opens up so we have a minimum.
The vertex is halfway between the x intercepts
(-4+2)/2 = -2/2 = -1
To find the minimum substitute x= -1 into the equation
f(x)=x^2+2x-8
f(-1) = (-1)^2 +2(-1)-8 = 1-2-8 = -9
The minimum is -9
Graph attached
y=x²+2x-8y=x²+4x-2x-8y=x(x+4)-2(x+4)y=(x+4)(x-2)x intercepts (-4,0) and (2,0)
Y intercept :-
Put x=0
y=-8(0,-8)
Vertex is the minimum
(-1,-9)
The right triangle on the right is a scaled copy of the right triangle on the left. Identify
the scale factor. Express your answer as a whole number or fraction in simplest form.
3
15/4
Answer
Submit Answer
9514 1404 393
Answer:
5/4
Step-by-step explanation:
The ratio of long sides is ...
right/left = 5/4
The scale factor is 5/4.
A grass seed company conducts a study to determine the relationship between the density of seeds planted (in pounds per 500 sq ft) and the quality of the resulting lawn. Eight similar plots of land are selected and each is planted with a particular density of seed. One month later the quality of each lawn is rated on a scale of 0 to 100. The sample data are given below where x denotes seed density, and y denotes lawn quality.x 1 1 2 3 3 3 4 5y 30 40 40 40 50 65 50 50The sample linear correlation coefficient is r=0.600. At the 1% significance level, do the data provide sufficient evidence to conclude that seed density and lawn quality are positively linearly correlated?
Answer:
I think it -1.50 to 10.58
Step-by-step explanation:
Please help me understand this question!
Answer:
C
Step-by-step explanation:
The first sentence basically sets up the equation which is given, so we can read it for knowledge but it is not crucial to solve the problem.
We start here:
we are given: $120 - 0.2($120)
= 120 - (0.2)(120) (factoring out 120)
= 120 (1 - 0.2)
= 120 (0.8)
= 0.8 (120) (answer c)
donald is a taxi driver. for each ride in the taxi, the cost, c, is given by c = 500+130d, where c is in cents and d is the distance of the ride, in miles. what is the meaning of the value 500 in this equation? a) donald charges 500 cents per mile b) donald drives 500 customers per day c) donald charges at least 500 cents per taxi ride d) donald charges at most 500 cents per taxi ride
can u go to my page real quick and answer my question pls
Which of the following relations is a function? A. (1, 4), (-4, 2), (8, 1), (-8, 2) B. (1, 4), (-4, 6), (1, 3), (-8, 2) C. (1, 0), (-4, 3), (8, 1), (-4, 5) D. (8, 1), (-4, 4), (1, 1), (8, 2)
Answer:
A. (1, 4), (-4, 2), (8, 1), (-8, 2)
Step-by-step explanation:
Each x goes to only 1 y to be a function
A. (1, 4), (-4, 2), (8, 1), (-8, 2)
function
B. (1, 4), (-4, 6), (1, 3), (-8, 2)
1 goes to 4 and 3 so not a function
C. (1, 0), (-4, 3), (8, 1), (-4, 5)
-4 goes to 3 and 5 so not a function
D. (8, 1), (-4, 4), (1, 1), (8, 2)
8 goes to 1 and 2 so not a function
Answer:
[tex]\Large \boxed{\mathrm{A. \ (1, 4), (-4, 2), (8, 1), (-8, 2)}}[/tex]
Step-by-step explanation:
[tex]\sf A \ function \ is \ a \ relation \ if \ each \ x \ value \ is \ for \ each \ y \ value.[/tex]
[tex](1, 4), (-4, 2), (8, 1), (-8, 2) \ \sf represents \ a \ function.[/tex]
[tex](1, 4), (-4, 6), (1, 3), (-8, 2) \ \sf does \ not \ represent \ a \ function.[/tex]
[tex](1, 0), (-4, 3), (8, 1), (-4, 5) \ \sf does \ not \ represent \ a \ function.[/tex]
[tex](8, 1), (-4, 4), (1, 1), (8, 2) \ \sf does \ not \ represent \ a \ function.[/tex]
-8 + (-15)
Evaluate this expression
Answer:
-23
Step-by-step explanation:
-8+(-15) means that you are subtracting 15 from -8. So you end up with -8-15=-23.
What is the value of the logarithm below? (Round your answer to two decimal
places.)
log4 12
Answer:
1.68
Step-by-step explanation:
log(4)12=log(48)
log(48)=1.6812... or rounded, 1.68
10 orange sodas, 15 cream sodas and 7 cherry sodas are in an ice chest. How many sodas must be removed from the chest to guarantee that on type of soda has been chosen?
PLEASE, GIVE A STEP BY STEP EXPLANATION
Answer:
25 sodas if the type of soda chosen is cherry sodas
I will name you Brainly hurryyyy What two integers are in between 0.7142
Answer:
0.71419 &0.71421 are the correct.
8. Write 3x3 – 21x2 + 36x in factored form.
3x(x - 4)(x - 3)
3x(x - 5)(x - 2)
3x(x + 6)(x + 2)
O
3x(x + 4)(x + 3)
Answer:
A
Step-by-step explanation:
3x^3 – 21x^2 + 36x=3x(x^2-7x+12)=3x(x - 4)(x - 3)
Which one is correct? in need of large help
Answer:
Option C. x + 12 ≤ 2(x – 3)
Step-by-step explanation:
From the question, we obtained the following information:
x + 12 ≤ 5 – y .......(1)
5 – y ≤ 2(x – 3) ....... (2)
To know which option is correct, do the following:
From equation 2,
5 – y ≤ 2(x – 3)
Thus, we can say
5 – y = 2(x – 3)
Now, we shall substitute the value of 5 – y into equation 1 as shown below:
x + 12 ≤ 5 – y
5 – y = 2(x – 3)
x + 12 ≤ 2(x – 3)
From the above illustration, we can see that if x + 12 ≤ 5 – y and 5 – y ≤ 2(x – 3), then x + 12 ≤ 2(x – 3) must be true.
Option C gives the correct answer.
what is (2y + 5)(y - 3) in simplified form using the distributive property
Answer:
[tex]\boxed{2y^{2} - y - 15}[/tex]
Step-by-step explanation:
Use the FOIL technique in order to distribute the terms properly. FOIL stands for First Terms, Outside Terms, Inside Terms, and Last Terms. In order to properly distribute, multiply the common terms based on the steps in the FOIL technique. So, in this case:
The first terms are 2y and y. The outside terms are 2y and -3. The inside terms are 5 and y.The last terms are 5 and -3.Therefore, multiply the terms:
2y and y to get 2y²2y and -3 to get -6y5 and y to get 5y5 and -3 to get -15Then, add or subtract based on the signs:
2y² - 6y + 5y - 15
Then, add like terms to finish simplifying the expression. This leaves you with 2y² - y - 15.
Answer:
2y2 – y – 15
Step-by-step explanation:
(2y + 5)(y – 3)
= 2y(y – 3) + 5(y – 3)
= 2y2 – 6y + 5y – 15
= 2y2 – y –15
generate a continuous and differentiable function f(x) with the following properties: f(x) is decreasing at x=−5 f(x) has a local minimum at x=−3 f(x) has a local maximum at x=3
Answer:
see details in graph and below
Step-by-step explanation:
There are many ways to generate the function.
We'll generate a function whose first derivative f'(x) satisfies the required conditions, say, a quadratic.
1. f(x) has a local minimum at x = -3, and
2. a local maximum at x = 3
Therefore f'(x) has to cross the x-axis at x = -3 and x=+3.
Furthermore, f'(x) must be increasing at x=-3 and decreasing at x=+3.
f'(x) = -x^2+9
will satisfy the above conditions.
Finally f(x) must be decreasing at x= -5, which implies that f'(-5) must be negative.
Check: f'(-5) = -(-5)^2+9 = -25+9 = -16 < 0 so ok.
f(x) can then be obtained by integrating f'(x) :
f(x) = integral of -x^2+9 = -x^3/3 + 9x = 9x - x^3/3
A graph of f(x) is attached, and is found to satisfy all three conditions.
A function is differentiable at [tex]x = a[/tex], if the function is continuous at [tex]x = a[/tex]. The function that satisfy the given properties is [tex]f(x) = 9x - \frac{x^3}{3} + 3[/tex]
Given that:
The function decreases at [tex]x = -5[/tex] means that: [tex]f(-5) < 0[/tex]
The local minimum at [tex]x = -3[/tex] and local maximum at [tex]x = 3[/tex] means that:
[tex]x = -3[/tex] or [tex]x = 3[/tex]
Equate both equations to 0
[tex]x + 3 = 0[/tex] or [tex]3 - x = 0[/tex]
Multiply both equations to give y'
[tex]y' = (3 - x) \times (x + 3)[/tex]
Open bracket
[tex]y' = 3x + 9 - x^2 - 3x[/tex]
Collect like terms
[tex]y' = 3x - 3x+ 9 - x^2[/tex]
[tex]y' = 9 - x^2[/tex]
Integrate y'
[tex]y = \frac{9x^{0+1}}{0+1} - \frac{x^{2+1}}{2+1} + c[/tex]
[tex]y = \frac{9x^1}{1} - \frac{x^3}{3} + c[/tex]
[tex]y = 9x - \frac{x^3}{3} + c[/tex]
Express as a function
[tex]f(x) = 9x - \frac{x^3}{3} + c[/tex]
[tex]f(-5) < 0[/tex] implies that:
[tex]9\times -5 - \frac{(-5)^3}{3} + c < 0[/tex]
[tex]-45 - \frac{-125}{3} + c < 0[/tex]
[tex]-45 + \frac{125}{3} + c < 0[/tex]
Take LCM
[tex]\frac{-135 + 125}{3} + c < 0[/tex]
[tex]-\frac{10}{3} + c < 0[/tex]
Collect like terms
[tex]c < \frac{10}{3}[/tex]
[tex]c <3.33[/tex]
We can then assume the value of c to be
[tex]c=3[/tex] or any other value less than 3.33
Substitute [tex]c=3[/tex] in [tex]f(x) = 9x - \frac{x^3}{3} + c[/tex]
[tex]f(x) = 9x - \frac{x^3}{3} + 3[/tex]
See attachment for the function of f(x)
Read more about continuous and differentiable function at:
https://brainly.com/question/19590547
After setting up the width of the compass using the original line segment, why is it important to keep the compass the same
width before drawing an arc? (1 point)
If the width of the compass changed, it would make the arc smaller or larger. This would then make the line segment to be drawn
smaller or larger, so it would not match the original.
of the width of the compass changed, it would make the arc smaller or larger. This would change the angle the new line segment is
drawn at, so it would not match the original.
O if the width of the compass changed, it would be possible for the arc to intersect the original line segment, which is not allowed.
The width of the compass does not matter. All that matters is that a straightedge is used to draw the line segment
Answer:
If the width of the compass changed, it would make the arc smaller or larger. This would then make the line segment to be drawn smaller or larger, so it would not match the original.
Step-by-step explanation:
We assume your construction is trying to copy the length of a line segment. That length is "measured" by the width of the compass. If it is changed, it no longer matches the length of the segment you're trying to copy, so you will not get the copy you want.
Solve for x -3x-3=-3(x+1)
Step-by-step explanation:
[tex] - 3x - 3 = - 3(x + 1) \\ - 3x - 3 = - 3x - 3 \\ - 3x + 3x = - 3 + 3 \\ 0 = 0[/tex]
Step 1: Use 3 to open the bracket
Step 2 : Collect like terms and simplify
Answer = 0
Monique makes $11 per hour delivering pizzas. Monique works Monday
through Friday, and on average she earns $20 a day in tips. If Monique
made no less than $450 for one week, find an inequality for the number
of hours she worked
Answer:
x > 39 hours
Step-by-step explanation:
Let x be the number of hours she worked.
11x - is how much she would get paid for working for x hours
11x + 20 > 450
11x > 430
x > 39 hours
Hope that helped!!! k
In the given diagram if AB || CD, ∠ABO = 118° ∠BOD = 152° then find the value of ∠ODC. please help !!!!!!
The chief business officer of a construction equipment company arranges a loan of $9,300, at 12 1 /8 % interest for 37.5 months. Find the amount of interest. (Round to the nearest cent)
a. $2,761.21
b. $3,583.83
c. $3,523.83
d. $3,722.47
Answer:
C). $3523.83
Step-by-step explanation:
loan of principles p= $9,300,
at rate R= 12 1 /8 % interest
Rate R = 12.125%
for duration year T = 37.5 months
T= 37.5/12 = 3.125 years
Interest I=PRT/100
Interest I =( 9300*12.125*3.125)/100
Interest I = (352382.8125)/100
Interest I = 3523.83
Interest I= $3523.83
Please help me with this
Answer:
Median; 60
Step-by-step explanation:
For a data plot as shown in the question above, one easier measure of center that can be used for the data set represented is the median.
From the dot plot, we can easily pinpoint the exact median, which can be used as a measure of center.
There are 11 data points represented on the dot plot by 11 dots. The median, that is the median value of the data set, would be the 6th value represented by the 6th dot on the dot plot.
Thus, the middle value is 60.
60 is the median of the data set.
3. CD is the diameter of a circle. The coordinates are C(-2, -3) and D(-12,-5). At what coordinate
is the center of the circle located?
A. (5,1)
B. (-5,-1)
C (-4,-7)
D. (-7,-4)
Answer:
D) (-7,-4)
Step-by-step explanation:
Halfway from -2 to -12 is -7
Halfway from -3 to -5 is -4
The sum of two positive number is 6 times their difference. what is the reciprocal of the ratio of the larger number to the smaller?
let the numbers be a and b, a>b
a+b=6(a-b)
we need to find reciprocal of ratio of larger to smaller , which will be same as ratio of smaller to larger or b/a, let's call it x
divide the equation by a.
1+x=6(1-x)
on solving, x=5/7
The MCAT is the admission exam that medical schools use as one of the criteria for accepting students. The exam is based on a scale of 0-45. The following data shows the MCAT scores for nine students.
32 36 29 31 30 35 34 26 30
The 35th percentile of this data set is:________
a. 31
b. 32
c. 31.5
d. 30
Answer:
d. 30
Step-by-step explanation:
The computation of the 35th percentile of this data set is shown below:
Before that first we have to series the number in ascending number
S. No Numbers
1 26
2 29
3 30
4 30
5 31
6 32
7 34
8 35
9 36
Now use the formula
Here n = 9
Percentile = 100
[tex]= \frac{35(9 + 1)}{100} \\\\[/tex]
= 3.5th
= 3th + 0.5 (4th - 3th)
= 3th + 0.5 (30 - 30)
= 3th + 0
= 30
What is the scale factor of this dilation?
Answer:
5/3
Step-by-step explanation:
on both sides we can see that the orginal length of 3 increased to five
therfore if we multiply 3 by 3/5 we get five which means the scale factor is 5/3
I need help in math please, if you can
Answer:
Step-by-step explanation:
400*e^(.09*3)
$523.97
answer is b
Answer: Option B
$523.97
Explanation:
= 400×e^(0.09×3)
= $523.97
Must click thanks and mark brainliest
Which expression is equal to 7 times the sum of a number and 4
Answer:
7(n + 4)
Step-by-step explanation:
Represent the number by n. Then the verbal expression becomes
7(n + 4).
If the sin of angle x is 4 over 5 and the triangle was dilated to be two times as big as the original, what would be the value of the sin of x for the dilated triangle? Hint—Use the slash symbol ( / ) to represent the fraction bar, and enter the fraction with no spaces. (4 points)
Answer:
Sin of x does not change
Step-by-step explanation:
Whenever a triangle is dilated, the angle remains the same as well as the ratio for sides of triangle. For smshapes with dimensions, when shapes are dilated the dimensions has increment with common factor.
From trigonometry,
Sin(x)=opposite/hypotenose
Where x=4/5
Sin(4/5)= opposite/hypotenose
But we were given the scale factor of 2 which means the dilation is to two times big.
Then we have
Sin(x)=(2×opposite)/(2×hypotenose)
Then,if we divide by 2 the numerator and denominator we still have
Sin(x)=opposite/hypotenose
Which means the two in numerator and denominator is cancelled out.
Then we still have the same sin of x. as sin(4/5)
Hence,Sin of x does not change
Answer:
Step-by-step explanation:
sin of angle x = [tex]\frac{4}{5}[/tex]
If the triangle is dilated 2 times - it becomes two time larger.
4 times 2 = 8 and 5 times 2 = 10
So the ratio would be [tex]\frac{8}{10}[/tex], which when reduced (divide numerator and denominator by 2) becomes [tex]\frac{4}{5}[/tex].
This is correct as dilation changes the size of an image - but not its angles or proportions, meaning ratios remain the same.
So the answer is 4/5.
PLzzzz answer quick will give good rate nd say thanks
What is the slope of the line? 5(y+2)=4(x-3)
A 2/3
B 4/5
C 5/4
D 3/2
Step-by-step explanation:
Here,
[tex]5y = 4x - 12 - 10[/tex]
[tex]y = \frac{4}{5} x - \frac{22}{5} [/tex]
slope is 4÷5
Answer:
The answer is option BStep-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
5(y+2)=4(x-3)
To find the slope first expand the terms in the equation
That's
5y + 10 = 4x - 12
Write the equation in the form y = mx+ c
That's
5y = 4x - 12 - 10
5y = 4x - 22
Divide both sides by 5 to make y stand alone
y = 4/5x - 22/5
Comparing with the general equation above the slope of the line is
4/5Hope this helps you