The rate of change of length of the Clupea harengus (Atlantic herring) at t = 7 years is approximately 2.8 cm per year.
Explanation:To determine how fast the length of Clupea harengus (Atlantic herring) is changing at age t = 7 years, you need to calculate the derivative of the given function, l(t) = 32(1 − e−0.37t), with respect to time. The derivative measures the rate of change of a function, which in this case corresponds to the speed of growth of the herring.
The derivative of l(t) with respect to t is given by: l'(t) = 32 * 0.37e^(-0.37t).
Substitute t = 7 into this derivative function to get: l'(7) = 32 * 0.37e^(-0.37*7) ≈ 2.8 cm/year.
So, the length of the Atlantic herring is increasing at approximately 2.8 cm per year when the herring is 7 years old.
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To find the rate at which the length of the Atlantic herring is changing at age t = 7 years, we need to take the derivative of the length function and evaluate it at t = 7.
Explanation:To find the rate at which the length of the Atlantic herring is changing at age t = 7 years, we need to find the derivative of the length function with respect to time. The function l(t) = 32(1 − e−0.37t) represents the average length of the herring at age t. Taking the derivative of this function gives us:
l'(t) = 32 * (-0.37) * e−0.37t
Now, we can substitute t = 7 into the derivative to find the rate of change at that age:
l'(7) = 32 * (-0.37) * e−0.37(7)
This expression can be simplified further to find the exact value of the rate of change.
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DeShawn is 37 years old. How old is he in hours?
According to the question, we are to convert the given years to hours. The age of Deshawn in hours is 324120hrs
Conversion of years to hoursAccording to the question, we are to convert the given years to hours.
Using the conversion factor
1 year = 8760 hours
Convert 37 years
37years = 37(8760)hrs
37years = 324120hrs
Hence the age of Deshawn in hours is 324120hrs
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The positions of two divers from the water's surface after a dive are shown:
Kris: –17 feet
Graham: –22 feet
Which inequality explains why Graham is deeper in the water than Kris? (1 point)
Because –22 < –17, so –22 is closer to 0 than is –17
Because –22 > –17, so –22 is closer to 0 than is –17
Because –22 < –17, so –22 is farther from 0 than is –17
Because –22 > –17, so –22 is farther from 0 than is –17
which of the following is being constructed in the image?
In the shown image of construction, first a line constructed.
Then they draw an angle.
They make an arc to represent the angle on the constructed line in step 1.
They cut the arc by measuring the angle.
They kept open same width of the compass and they cut another arc above.
They joined the points to make equal corresponding angles.
After joining points, we got a parallel line we draw in first point.
Therefore, correct option is:
A parallel line to a given line through a point not on the line.Answer:
Option 1 is correct. The line created will be parallel to the given line and passing through a point not on the given line.
Step-by-step explanation:
In the given image, firstly a line is constructed.
After drawing the line, an intersecting line is drawn. Now, the measure of angle between these two lines is calculated.
After calculating the measure of angle, an angle of same measure is created at a point not on the first line.
Then, a line is drawn passing through that point with the same angle measure.
The created line will now be parallel to the first line because the corresponding angles are equal.
Therefore, option 1 is correct. The line created will be parallel to the given line and passing through a point not on the given line.
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At Danielle’s clothing boutique, if an item does not sell for eight weeks, she marks it down by 15%. If it remains unsold after that, she marks it down an additional 5% each week until she can no longer make a profit. Then she donates it to charity. Rafael wants to buy a coat originally priced $150, but he can’t afford more than $110. If Danielle paid $100 for the coat, during which week(s) could Rafael buy the coat within his budget? Justify your answer.
8 weeks the coat would cost 150 * (1-0.15+ = 127.50
9 week it would cost 127.50 *(1-0.05) = 121.13
10 week = 121.13 * (1-0.05) = 115.07
week 11 = 115.05 * (1-0.05) = 109.32
he can buy it in week 11, because it would be less than 110 and the sore would still make a profit, because it costs more than 100
7/8(−32−48x)+36=2/3(−33x−18)−10x
I am doing geometry and I don't know how to do this!
How do you find the hypotenuse of an obtuse triangle with only the angle and one leg given?
An obtuse triangle is a triangle in which one of the angles is an obtuse angle. (Obviously, only a single angle in a triangle can be obtuse or it wouldn't be a triangle.) A triangle must be either obtuse, acute, or right.
An obtuse triangle can be dissected into no fewer than seven acute triangles
I saw this in my brothers math book. Hope this helps
PLEASE HELP DUE TODAY!!!!
while browsing in an antique store, cameron found this page that came from an old book of riddles
Simultaneous equations can be solved if the number of unknown variables are equal to the number of equations. In the geometry question, the equations are given by the relationship between the lines and angles
Part A
m = 7°, p = 10°, t = 5°, a = 6, and s = 2°
Part B
Arranging the variables from least to greatest gives; stamp
A stamp sits at the corner of an envelope but travels around the world
Part A
From the diagram, we have;
H is a vertical angle to the 90° angle
(7·m + 3)° + 90° + (8·m - 18)° = 180° (linear angles)
∴ (7·m + 3)° + (8·m - 18)° = 180° - 90° = 90°
(15·m - 15)° = 90°
15·m = 90°+ 15° = 105°
m = 105°/15 = 7°
m = 7°
(7·m + 3)° = (5·p + 2)° (vertically opposite angle theorem)
∴ (5·p + 2)° = (7 × 7 + 3)° = 52°
p = (52° - 2°)/5 = 10°
p = 10°
(8·m - 18)° = (11·t - 17)° (vertically opposite angle theorem)
∴ (8 × 7 - 18)° = (11·t - 17)°
38° = (11·t - 17)°
11·t = 38° + 17° = 55°
t = 55°/11 = 5°
t = 5°
CD = 5·a + 12 and DE = 9·a - 12 are congruent segments
5·a + 12 = 9·a - 12 (Definition of congruent segments)
9·a - 5·a = 12 + 12 = 24
4·a = 24
a = 24/4 = 6
a = 6
(21·s + 6° and 48° are congruent congruent angles
21·s + 6° = 48° (Definition of congruent angles)
∴ s = (48° - 6°)/21 = 2°
s = 2°
Part B
Arranging the values of the variables from least to most gives;
s = 2°
t = 5°
a = 6
m = 7°
p = 10°
Which gives;
The answer to the riddle = s, t, a, m, p = Stamp
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A change in the dollar price of yen from $1 = 100 yen to $1 = 50 yen will:
Pablo's goal is to have 5000 after 4 years is this possible if he invest with a rate of return of 6%
To achieve a future value of $5000 after 4 years with a 6% rate of return, Pablo would need to invest an initial amount.
Explanation:To calculate the future value of an investment with a given rate of return, you can use the formula:
FV = PV * (1 + r)ⁿ
Where FV is the future value, PV is the present value, r is the rate of return expressed as a decimal, and n is the number of years.
In this case, Pablo wants to have $5000 after 4 years with a 6% rate of return. Assuming he doesn't invest any initial amount, we can substitute these values into the formula:
FV = $0 * (1 + 0.06)⁴
FV = $0 * 1.262476
FV = $0
Based on the calculation, it is not possible for Pablo to have $5000 after 4 years with a 6% rate of return if he doesn't invest any initial amount.
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What is the value of tanA
8/10
6/10
8/6
6/8
A clock gains 0.020 s/min. how many seconds will the clock gain in exactly six months, assuming 30 days are in each month
Final answer:
To calculate the total seconds a clock gains in six months, we multiply the number of minutes in six months by the gain per minute, resulting in a total of 5,184 seconds gained.
Explanation:
The question asks us to determine how many seconds a clock gains over a six-month period, assuming each month has 30 days. The clock gains 0.020 seconds per minute.
To find the total seconds gained, we need to calculate the number of minutes in six months and then multiply that by the gain per minute. There are 60 minutes in an hour, 24 hours in a day, and the problem assumes 30 days in a month. Over six months, this totals:
60 minutes/hour × 24 hours/day × 30 days/month × 6 months = 259,200 minutesNow, multiply the total minutes by the gain per minute:
259,200 minutes × 0.020 seconds/minute = 5,184 secondsTherefore, the clock will gain a total of 5,184 seconds over a six-month period assuming each month has 30 days.
Find the markup and the selling price of the following item. Round answers to the nearest cent.
A skateboard costing $39.00 marked up 40% on cost.
Markup = a. $97.50
b. $15.60
c. $40.00
Selling price = a. $1.00
b. $54.60
c. $79.00
Answer:
Mark up: $15.6 (option b)
Selling Price: $54.6 (option b)
Step-by-step explanation:
Hi, to answer this question we have to analyze the information given:
A skateboard costing $39.00 marked up 40% on cost.
To calculate the markup we have to multiply the skateboard cost (39) by the percentage in decimal form (40/100= 0.4)
39 x 0.4 =15.6
Mark up: $15.6 (option b)
For the selling price we have to sum the cost and the markup:
15.6 + 39 = 54.6
Selling Price: $54.6 (option b)
Feel free to ask for more if needed or if you did not understand something.
Someone draws a card at random out of a deck, replaces it, and then draws another card at random. What is the probability that the first card is the ace of clubs and the second card is a club (any club).
I don't need an explanation, just the answer
I need help and the answer to #9
perimeter of rectangle = 20+20 +15+15 = 70 yards = 70*3 = 210 feet
210/5 = 42 seconds
Courtney walks it in 42 seconds
the diagonal = 15^s + 20^2 = 225+400=625
sqrt(625) = 25 yards
Natalie walks 20 +15 +25 = 60 yards
60*3 = 180 feet
180 /5 =36 seconds
42 - 36 = 6 seconds faster
. Complete the missing steps in the paragraph proof of Theorem 3-8.
The scatter plot shows the number of milk cow operations in New Mexico from 1975 to 1995.
A box with a square base has sides of 5" and is 8" tall. What is its volume? Question 1 options: 40 320 200 150
Daniel is currently 26 years older than his son in 6 years he will be three times older than his son how old are both of them now
A certain store is advertising this deal: “Rent a TV for only $10.50 a week.” How much is this a year? (There are 52 weeks in a year.)
Answer:
Rent of a TV for one year would be $546.
Step-by-step explanation:
A certain store is advertising this deal :
"Rent a TV for only $10.50 a week."
We have to calculate the rent for a year.
As we know there are 52 weeks in a year.
∵ Rent of a TV for one week = $10.50
∴ Rent of a TV for one year = 10.50 × 52
= $546.00
Rent of a TV for one year would be $546.
100 POINTS Evaluate.
-|-7 + 3|
-4
4
-10
-7+3 = -4
but since it is an absolute value it becomes positive 4
there is a negative sign in front of the equation so the positive 4 now becomes -4
Answer is -4
The price of apples has dropped, but Nancy does not buy any more because she has enough. To what factor of demand does this refer?
Nancy does not have the resources to purchase more apples
Nancy has reached maximum utility for apples
Apples are no longer available at the price Nancy is willing to pay
Nancy would rather eat oranges than apples
Nancy heard that apples are unhealthy
Answer:
Nancy has reached maximum utility for apples
Step-by-step explanation:
Given that the price of apples has dropped, but Nancy does not buy any more because she has enough.
This is because she has reached maximum utility for apples. So she does not want any more apples
Option A is incorrect because Nancy has resources but does not buy because she has enough.
Option C is incorrect as apples are still available at lower prices
Option D is incorrect as per given information as about oranges nothing mentioned.
How can you use transformations to graph this function? y=3.7^{-x}+2 Explain your steps
Answer:
Steps are explained in the explanation part and graph is attached below.
Step-by-step explanation:
We have to graph the function [tex]y=3.7^{-x}+2[/tex] using the rule for transformation.
Let us suppose the parent function is [tex]y=3.7^x[/tex]. Below, is the graph of the parent function (fig 1)
When we add some constant 'c' in the function then the graph of the parent function shifts upward by 'c' units.
Hence, when we add 2 then the parent function will get shifted upward by 2 units. The graph of [tex]y=3.7^{x}+2[/tex] is attached below (fig 2)
Finally, x is replaced by -x hence the graph is reflected about y axis.
In figure 3 the graph of the given function is shown.
The graph of the function [tex]y = 3.7^{-x}+2[/tex] can be draw by using transformations. First shift the graph of [tex]y = 3.7^{x}[/tex] upwards by 2 units and then replace x by -x in the function [tex]y = 3.7^x+2[/tex] and graph of the function [tex]y = 3.7^x+2[/tex] is reflected about y-axis.
Given :
[tex]y = 3.7^{-x}+2[/tex]
To graph the above function using transformations following steps can be use:
Step 1 - Draw the graph of exponential function [tex]y = 3.7^{x}[/tex].
Step 2 - Now, shift the graph upwards in y axis by 2 units. The resulting graph is of function [tex]y = 3.7^x+2[/tex].
Step 3 - Now, replace x with -x in the function [tex]y = 3.7^x+2[/tex] and graph of the function [tex]y = 3.7^x+2[/tex] is reflected about y-axis. The resulting graph is of the function [tex]y = 3.7^{-x}+2[/tex] .
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hat is the equation of a line that passes through the point (5, −4) and is parallel to the line whose equation is 2x + 5y = 10? Enter your answer in the box
List the five key elements of a two column geometric proof
Final answer:
The five key elements of a two column geometric proof include: Statement, Given, Prove, Logical Arguments, and a Diagram (if applicable). These components are crucial in presenting a clear and logical proof based on mathematical principles.
Explanation:
The five key elements of a two-column geometric proof are essential for laying out the reasoning behind geometric propositions in a clear and structured way. When constructing or analyzing these proofs, the following elements should be included:
Statement: This is what you are trying to prove. It includes the theorem, postulate, or property you intend to show as true.Given: Information that is known to be true which provides the starting point for the proof.Prove: A clear declaration of the specific statement or theorem that is to be demonstrated as true.Logical Arguments: The logical progression of statements and reasons that lead from the givens to the statement being proved.Diagram (if applicable): This is a visual representation that illustrates the problem.Each of these elements plays a crucial role in ensuring that the proof is valid, understandable, and follows a logical sequence based on accepted mathematical principles.
The quotient of 9 times an unknown number and 16 is 81. What is the value of the unknown number?
A wise man once said” 200 reduced by twice my Age is 42.” What is his age ?
D is the midpoint of CE. E has coordinates (−9, −6), and D has coordinates (7, 2). Find the coordinates of C
Kayla needs to have $560.00 to buy a new laptop. She already has $200.00 in the bank. Each month she will add $45.00 to her bank account. How many more months until she has enough money to buy her laptop?
Kayla will take 8 months to add $45.00 into her bank account to reach the amount of $560.00 so that she can buy her laptop.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
Let's say it will take an "x" number of months to have $560.00.
Total money = fixed deposit + 45(number of months)
Given that,
Fixed deposit = $200
560 = 200 + 45x
45x = 360
x = 8
Hence "Kayla will take 8 months to add $45.00 into her bank account to reach the amount of $560.00 so that she can buy her laptop".
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Find the area of a figure whose coordinates are A (-2,2) B (2,2) C (2,-2) D (-2,-2)
12 units.squared
16 units.squared
20 units.squared
24 units.squared