A fish population grew according to the following quadratic model, the number of fish a day is given by
P(t)=800t-t^2
What is the average growth rate between t=400 and t=600
Answers
Answer: -200
Step-by-step explanation:
P(t) = 800t - t²
P(600) = 800(600) - (600)²
= 480,000 - 360,000
= 120,000
P(400) = 800(400) - (400)²
= 320,000 - 160,000
= 160,000
\(\text{rate of change}=\dfrac{P(600)-P(400)}{600-400}=\dfrac{120,000-160,000}{200}=\dfrac{-40,000}{200}=-200\)
Related Questions
Fourteen is 6 less a number (n). Which equation shows this relationship?
Answers
Answer:
14 = n - 6
Step-by-step explanation:
"Is" indicates equal to. "Less" means subtract.
The equation that shows this relationship would be; 14 = n - 6.
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1.
The standard form of a linear equation is of the form Ax + B = 0.
We have been given a statement "Fourteen is 6 less a number (n)."
So here, "Is" indicates equal to sign. "Less" means subtract.
The equation form would be;
14 = n - 6
The equation that shows this relationship would be; 14 = n - 6.
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Find for x HELPPPP MEEEEEE
Answers
Answer:
3
Step-by-step explanation:
(x + 1) : (3x + 1) = 8 : 20
20(x + 1) = 8(3x + 1)
20x + 20 = 24x + 8
12 = 4x
x = 3
What will it look like
Answers
Answer:
-5, 5
Step-by-step explanation:
If x = 5, then which inequality is true
Answers
Answer:
G
Step-by-step explanation:
Plug X into the inequality.
(5) - 2 < 7 is true
Hope this helps! :)
Answer: G) x-2<7
Step-by-step explanation:
x=5
5-2<7
3<7
three is less than 7.
the spinner shown below has 12 congruent sections. the spinner spun 150 times. what is a reasonable prediction for the number of items the spinner will land on an even number. (pls help asap!!)
Answers
Answer:45
Step-by-step explanation:
There are 3 even numbers out of A total of 8 numbers.
Each spin would have a 3/8 chance of landing in an even number.
Multiply the chance of landing on even by number of spins:
120 x 3/8 = 360/8 = 45
The answer would be 45 times.
Find the value of x, 6,4, 3x, 4x+1
Answers
Answer:
If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.
6(3x) = 4(4x + 1)
18x = 16x + 4
2x = 4
x = 2
Evaluate x2 + 6, when x=8
Help.
Answers
8(2)+6=22
you plug in 8 for x then, multiply 8 and 2 to get 16 then, you add the 6 and get 22
Which set of side lengths can be used to construct a triangle?
А
55 inches, 110 inches, 45 inches
B
45 inches, 45 inches, 90 inches
C
100 inches, 45 inches, 35 inches
D
75 inches, 55 inches, 45 inches
Answers
9514 1404 393
Answer:
D 75 inches, 55 inches, 45 inches
Step-by-step explanation:
The sum of the two shortest sides must exceed the length of the longest side. This is only the case for choice D.
A. 45+55 < 110
B. 45+45 = 90 . . . . needs to be greater, not equal
C. 35+45 < 100
D. 45+55 > 75 . . . . will form an obtuse triangle
Xavier shoots a basketball in which the height, in feet, is modeled by the equation,h(t) = -4t2 + 10 + 18, where t is time, in
seconds. What is the maximum height of the basketball?
Answers
Answer:
The maximum height of the basketball is of 24.25 feet.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
\(f(x) = ax^{2} + bx + c\)
It's vertex is the point \((x_{v}, y_{v})\)
In which
\(x_{v} = -\frac{b}{2a}\)
\(y_{v} = -\frac{\Delta}{4a}\)
Where
\(\Delta = b^2-4ac\)
If a<0, the vertex is a maximum point, that is, the maximum value happens at \(x_{v}\), and it's value is \(y_{v}\).
Height of the basketball:
Given by the following function:
\(h(t) = -4t^2 + 10t + 18\)
Which is a quadratic function with \(a = -4, b = 10, c = 18\)
What is the maximum height of the basketball?
y(in this case h) of the vertex. So
\(\Delta = b^2-4ac = 10^2 - 4(-4)(18) = 388\)
\(y_{v} = -\frac{388}{4(-4)} = 24.25\)
The maximum height of the basketball is of 24.25 feet.
The rate constant for first-order degradation of a N2O2 in a solution (1.0 mg/ml) at 40°C
is 0.00351 hr-1, activation energy is 2000 cal/mol, and R = 1.987 cal/mol/degree.
Calculate
a. The rate constant for first-order degradation of N2O2 at room temperature (25°C).
Answers
The 0.0035 hr⁻¹ first-order degradation rate constant in the 40 °C, 1.0 mg/ml solution, where R = 1.987 cal/mol/degree and 2,000 cal/mol activation energy indicates;
a. The rate constant for first-order degradation of N₂O₂ at room temperature is approximately 4.12595 × 10⁻² hr⁻¹
What is a first-order reaction?A first order reaction is one that has a rate that varies linearly with the concentration of one reactant
The given parameters are;
Temperature of the solution = 40°C
T₁ = 40 °C + 273.15 = 313.15 K
The rate constant, K₁ = 0.00351 hr⁻¹
Concentration of the solution = 1.0 mg/ml
Activation energy, Eₐ = 2000 Cal/mol
R = 1.987 cal/mol/degree
The formula by which the rate constant can be found is presented as follows;
\(log\dfrac{k_2}{k_1} =\dfrac{E_a}{2.303\times R} \times \dfrac{T_2-T_1}{T_1\cdot T_2}\)
a. Room temperature = 25 °C
T₂ = 25 °C + 273.15 = 298.15 K
Therefore;
\(log\dfrac{k_2}{0.00351} =\dfrac{2000}{2.303\times 1.987} \times \dfrac{313.15-298.15}{313.15 \times 298.15}\)
\(k_2=0.00351 \times 10^{\left(\dfrac{2000}{2.303\times 1.987} \times \dfrac{313.15-298.15}{313.15 \times 298.15}\right)} \approx 4.12595\times 10^{-2}\)
The rate constant for first-order degradation of N₂O₂ at room temperature is k₂ ≈ 4.12595 × 10⁻² hr⁻¹Learn more about the rate constant for first-order degradation here:
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A pump discharges 278 gallons of water in 3.5 minutes. How long would it take to empty a container with 750 gallons? Round up to the nearest minute
Answers
PLS HELP THANK YOUUUUUUU
Answers
that factorises you make
y= (x+7)(x+3)
this has to be reversed
so a=-7
and b=-3
Determine if it is possible to form a triangle using the set of segments with the given measurements.
4.5 in., 5.6 in, 10 in.
a) No, adding all three sides does not add up to the correct measurements.
b) No, because two sides add up to less than the third one.
c) No, because two sides add up to more than the third one.
d) Yes, because two sides add up to less than the third one.
e) Yes, because two sides add up to more than the third one.
Answers
Answer:
e) Yes, because two sides add up to more than the third one.-------------------------
Apply the Triangle Inequality Theorem.
It states that:
For a triangle to exist, the sum of the lengths of any two sides must be greater than the length of the third side.We'll take the sum of two shortest sides and compare with the longest:
4.5 + 5.6 = 10.1 > 10It confirms the theorem, without testing the other two sides (which is obvious) so the answer is yes.
The matching answer choice is e).
A triangular arch is to be constructed over a busy street in order to place a sky bridge traversing one side of the triangle to the other. The base of the arch spans the width of the street, which is 20 feet. Each side of the triangular arch measures 30 feet in length. If the entrances of the sky bridge lie at the midpoints of each side of the triangular arch, and the bridge is to be parallel to the street below, how long will the sky bridge be?
Answers
Answer:
15
Step-by-step explanation:
William and his puppy Rover are out for a morning jog at a comfortable pace of 10 minutes per mile. If they keep up this pace for 2 hours, how many miles will they jog?
Answers
Answer:
12 miles
Step-by-step explanation:
60 min in 1 hr and 10 min = 1 mile..... so 6, 10 min intervals..... and so 6 time 2 is 12
center =
3. A diameter of a circle has endpoints P(-7,-4) and Q (3,2).
a. Find the center of the circle (hint use midpoint formula)
b. Find the radius. If your answer is not and integer, express in radical form. (hint use
distance formula)
c. Write an equation for the circle.
17
radius=
equation of the circle:
work:
< 2/3
I
>
Answers
a. The center of the circle is (-2, -1).
b. The radius of the circle is √136.
c. The equation of the circle is (x + 2)^2 + (y + 1)^2 = 136.
a. To find the center of the circle, we can use the midpoint formula, which states that the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is given by:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
In this case, the endpoints of the diameter are P(-7, -4) and Q(3, 2).Applying the midpoint formula:
Midpoint = ((-7 + 3)/2, (-4 + 2)/2)
= (-4/2, -2/2)
= (-2, -1)
Therefore, the center of the circle is at the coordinates (-2, -1).
b. To find the radius of the circle, we can use the distance formula, which calculates the distance between two points (x1, y1) and (x2, y2). The radius of the circle is half the length of the diameter, which is the distance between points P and Q.
Distance = √\([(x2 - x1)^2 + (y2 - y1)^2]\)
Using the distance formula:
Distance = √[(3 - (-7))^2 + (2 - (-4))^2]
= √\([(3 + 7)^2 + (2 + 4)^2]\)
= √\([10^2 + 6^2\)]
= √[100 + 36]
= √136
Therefore, the radius of the circle is √136.
c. The equation for a circle with center (h, k) and radius r is given by:
\((x - h)^2 + (y - k)^2 = r^2\)
In this case, the center of the circle is (-2, -1), and the radius is √136. Substituting these values into the equation:
\((x - (-2))^2 + (y - (-1))^2\) = (√\(136)^2\)
\((x + 2)^2 + (y + 1)^2 = 136\)
Therefore, the equation of the circle is (x + 2)^2 + (y + 1)^2 = 136.
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This figure was broken into a triangle and a rectangle as
shown.
Use the figures to complete the statements
The height of the triangle h is __ cm
The area of the triangle is __ cm
The area of the rectangle is __ cm
The area of the irregular figure is __ cm
Answers
Answer:
The height of the triangle is 8 centimeters.
The area of the rectangle is 48 square centimeters.
The area of the rectangle is 216 square centimeters.
The area of the irregular figure is 264 square centimeters.
Step-by-step explanation:
The height of the triangle is the total height of the figure minus the height of the rectangle, that is:
\(h = 26\,cm - 18\,cm\)
\(h = 8\,cm\)
The height of the triangle is 8 centimeters.
The area of the triangle (\(A\)), measured in square centimeters, is determined by the following formula:
\(A = \frac{1}{2}\cdot b\cdot h\) (1)
Where:
\(b\) - Base of the triangle, measured in centimeters.
\(h\) - Height of the triangle, measured in centimeters.
If we know that \(b = 12\,cm\) and \(h = 8\,cm\), then the area of the triangle is:
\(A = \frac{1}{2}\cdot (12\,cm)\cdot (8\,cm)\)
\(A = 48\,cm^{2}\)
The area of the rectangle is 48 square centimeters.
The area of the rectangle (\(A\)), measured in square centimeters, is determined by the following formula:
\(A = b\cdot H\) (2)
Where \(H\) is the height of the rectangle, measured in centimeters.
If we know that \(b = 12\,cm\) and \(H = 18\,cm\), then the area of the rectangle is:
\(A = (12\,cm)\cdot (18\,cm)\)
\(A = 216\,cm^{2}\)
The area of the rectangle is 216 square centimeters.
The area of the irregular figure is the sum of the areas of the rectangle and the triangle. Then, the area of the irregular figure is 264 square centimeters.
Answer:
This figure was broken into a triangle and a rectangle as shown.
A figure can be broken into a rectangle and triangle. The rectangle has a base of 12 centimeters and height of 18 centimeters. The triangle has a base of 12 centimeters and height of 8 centimeters.
Use the figures to complete the statements.
The height of the triangle h is
✔ 8
cm.
The area of the triangle is
✔ 48
cm2.
The area of the rectangle is
✔ 216
cm2.
The area of the irregular figure is
✔ 264
cm2.
Step-by-step explanation:
Melanie read 52 pages in 1 hours. If she continues reading at the same rate, how
many pages will she read in an hour?
Answers
If she read 52 pages in one hour, then she'll continue at a rate of 52 pages per hour.
Answer:
52 pages
Step-by-step explanation:
Since she reads 52 pages in 1 hour we multiply 52 by the amount of hours she reads.
52 pages times 1 hour equals 52 pages.
52 x 1 = 52
sin0= 5/13. find tan 0
Answers
Answer:
C. 5/12
Step-by-step explanation:
Finding the missing side :
Opposite side² + Adjacent side² = Hypotenuse²(5)² + Adjacent side² = (13)²Adjacent side² = 169 - 25Adjacent side² = 144Adjacent side = √144Adjacent side = 12Taking the tan ratio :
tanθ = opposite side / adjacent sidetanθ = 5/12who ever gives to correct answer I will mark the brainiest
Answers
Answer:
the answer is B
Step-by-step explanation:
on the Cartesian plane u have to think of the distance from both the positive and negative side
so 3 is 3 units from the origin and -6 is 6 units from the origin
Therefore the total length is 9 (3+6)
And B is the only answer which will give 9
Find all values of x that are NOT in the domain of f
Answers
Answer:
……….
Step-by-step explanation:
Given the function:
f(x) = 1/2 (3x+7)
What is the output of the function when the input is x = 9?
A 9
B 15
C 17
D 21
Answers
Answer: C
Step-by-step explanation:
It's easy! Don't worry!
f(x) = 1/2(3x+7)
f(9) = 1/2(3(9)+7)
f(9) = 1/2(27+7)
f(9) = 1/2(34)
f(9) = 17
Trust me when you finish algebra this stuff is cake not going to lie. I did it under a minute. ;)
Also, gl passing algebra!
C. A musician had 1.2 x 102
fans at his very first show
ever played. Six years later,
84,000 people were at his
show. How many times more
people were at his most recent
show compared to the very
first show he played?
Answers
Answer:
688 people
Step-by-step explanation:
A successful basketball player has a height of 6 feet 4 inches, or 193 cm. Based on statistics from a data set, his height converts to the z score of 2.66. How many standard deviations is his height above the mean?
Answers
Answer: 2.66 standard deviations above the mean
Explanation:
The z score directly determines how far we are from the mean. For positive z values, we are above the mean, while negative z values are below the mean.
The mean itself is z = 0
The absolute value of the z score is the distance from the score to 0. So having a z score of z = 2.66 means we are 2.66 standard deviations above the mean. Something like z = -2 means we are 2 standard deviations below the mean.
The lowest point in Death Valley is Badwater at 282 feet below sea level. The highest point in
the surrounding mountains is Telescope Peak at 11,043 feet above sea level. How many feet
higher is Telescope Peak than Badwater?
Answers
Answer:
Step-by-step explanation:
Given
\(Badwater = -282ft\)
\(Telescope\ Peak = 11043ft\)
The position of badwater is negated because it is below sea level
The interpretation of the question, is to calculate the distance between the two given points.
This is calculated as:
\(Difference = Telescope\ Peak - Badwater\)
\(Difference = 11043ft - (-282ft)\)
Open bracket
\(Difference = 11043ft+282ft\)
\(Difference = 11325ft\)
Hence, the distance between both is 11325ft
In certain deep parts of oceans, the pressure of sea water,P, in pounds per square foot, at a depth of d feet below the surface, is given by the following equation P=14+ 4d/9
If a scientific team uses special equipment to measure the pressure under water and find it to be 306 pounds per square foot, at what depth is the team making their measurements?
Answers
It is important to note that this equation assumes a constant density of seawater, which is not always the case in the deep ocean. In addition, the pressure at a given depth can vary depending on factors such as temperature and salinity. This equation should be used with caution and in conjunction with other measurements and data analysis techniques.
The given equation for pressure in pounds per square foot at a depth of d feet is P = 14 + 4d/9. We are given that the pressure measured by the scientific team is 306 pounds per square foot. To find the depth at which this pressure is measured, we need to solve the equation for d.
Substituting P = 306 in the equation, we get:
306 = 14 + 4d/9
Multiplying both sides by 9, we get:
2754 = 126 + 4d
Subtracting 126 from both sides, we get:
2628 = 4d
Dividing both sides by 4, we get:
d = 657 feet
The scientific team is measuring the pressure at a depth of 657 feet below the surface of the ocean.
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Based on the demand graph and the supply graph shown above, what is the price at the point of equilibrium?
A. 100
B. 70
C. 40
D. There is not enough information given to determine the point of equilibrium
Answers
B. 70
I took the test on Edge 2022
How many
1/4-foot cubes would fill the inside of the prism?
Write the answer in the box.
Answers
There are 4 cubes of size 1/4 foot would fill the inside of the prism.
We have to given that;
Height of cuboid = 3 feet
Length of cuboid = 3/4 feet
Width of cuboid = 1/2 feet
We know that;
Volume of cuboid = Length x width x height
Hence,
V = 3/4 x 3 x 1/2
V = 9/8
Thus, Number of 1/4-foot cubes which would fill the inside of the prism is,
= (9/8) ÷ (1/4)
= (9/8) x 4
= 9/2
= 4.5
Thus, There are 4 cubes of size 1/4 foot would fill the inside of the prism.
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on the graph, the horizontal red line is the mechanical energy of an object, and the blue line below it is the potential energy as a function of x. at which value of x is:
Answers
The kinetic energy will be maximum if the potential energy is minimum.
Given that,
On the graph, an object's mechanical energy is represented by the horizontal red line, and its potential energy as a function of x is shown by the blue line beneath it. at what x value is:
Value of x at which
1) potential energy at the largest
2kinetic energy at the largest
3)The force on the object in the negative direction.
4)The force on the object the largest magnitude.
More above the x-axis, greater the value of potential energy. Therefore, the point at which potential energy is large at x = 4
Mechanical energy is sum of potential energy and kinetic energy
So, kinetic energy will be maximum if the potential energy is minimum.
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Melissa is planning a rectangular vegetable garden with a square patch for tomatoes. She wants the length of the garden to exceed three times the length of the tomato patch by 2 feet. She also wants the garden’s width to exceed the width of the tomato patch by 5 feet.
Let x represent the length, in feet, of the square tomato patch.
Answers
Answer:
If x is the length of the square tomato patch, then the width of the tomato patch is also x, since it is a square.
According to the problem, the length of the rectangular vegetable garden must exceed three times the length of the tomato patch by 2 feet, so the length of the garden is:
3x + 2
The width of the rectangular vegetable garden must exceed the width of the tomato patch by 5 feet, so the width of the garden is:
x + 5
To find the area of the garden, we multiply its length by its width:
Area of garden = length x width
Area of garden = (3x + 2)(x + 5)
To find the area of the tomato patch, we note that it is a square with side length x, so its area is:
Area of tomato patch = x²
Therefore, the area of the vegetable garden that is not taken up by the tomato patch is:
(3x + 2)(x + 5) - x²
And the total area of the vegetable garden, including the tomato patch, is:
x² + (3x + 2)(x + 5)
Simplifying:
x² + (3x² + 17x + 10)
4x² + 17x + 10
So the total area of the garden is 4x² + 17x + 10 square feet.