Between 2004 and 2010, the growth rate of the Florida Panther population was approximately 4%. What was the average annual growth rate?
The equation 22 + 0.15p =c
Why is it impossible to list the set of rational numbers using the roster method?
SIMPLIFY the expression! Please!
1+3^2 = 1+9 = 10
10/5 = 2
2-6+2 = -4+2
answer is -2
caryssa makes bracelets to sell at craft fairs. The supplies she needed to start her business cost $45. In addition, the supplies for each bracelet cost her $3. She sells her bracelets for $5. What is the minimum number of braclets she must sell to make a profit?
Find the equation of the curve that passes through the point 0, 1 6 and whose slope at each point (x, y) is − x 12y .
The equation is [tex]\(x^2 + 12y^2 - 3072 = 0\),[/tex] obtained from integrating [tex]\(12y \, dy = -x \, dx\)[/tex] with the initial condition.
To find the equation of the curve passing through the point (0, 16) with a slope given by [tex]\( \frac{{dy}}{{dx}} = -\frac{x}{12y} \),[/tex] you can use separation of variables.
Given that [tex]\( \frac{{dy}}{{dx}} = -\frac{x}{12y} \)[/tex], we can rewrite it as:
[tex]\[ 12y \, dy = -x \, dx \][/tex]
Now, integrate both sides:
[tex]\[ \int 12y \, dy = \int -x \, dx \]\[ 6y^2 = -\frac{1}{2}x^2 + C \][/tex]
Given that the curve passes through the point (0, 16), substitute these values into the equation:
[tex]\[ 6(16)^2 = -\frac{1}{2}(0)^2 + C \]\[ 6(256) = C \]\[ C = 1536 \][/tex]
Therefore, the equation of the curve is:
[tex]\[ 6y^2 = -\frac{1}{2}x^2 + 1536 \][/tex]
This can also be written in standard form as:
[tex]\[ x^2 + 12y^2 - 3072 = 0 \][/tex]
So, the equation of the curve is [tex]\( x^2 + 12y^2 - 3072 = 0 \).[/tex]
is a integer a rational number
write each rate as a fraction in lowest terms.
4.20 for 36 potatoes
Find y'' by implicit differentiation. 5x3 + 2y3 = 1
The value of y'' will be (- 5x/y² - 25x⁴/2y⁵).
What is implicit differentiation?
In implicit differentiation, we differentiate each side of an equation with two variables by treating one of the variable as a function of other.
Given that;
The equation is;
5x³ + 2y³ = 1
Now, Apply implicit differentiation rule we get;
5x³ + 2y³ = 1
After differentiation;
15x² + 6y² dy/dx = 0
dy/dx = - 15x² / 6y²
dy/dx = -5x²/2y²
Again differentiation;
d²y/dx² = -5/2 (y² × 2x - x² × 2y dy/dx) / y⁴
d²y/dx² = -5/2 (2xy² - 2x²y dy/dx) / y⁴
Substitute value of dy/dx;
d²y/dx² = - 5/2 (2xy² - 2x²y × -5x²/2y²) / y⁴
d²y/dx² = - 5/2 (2xy² + 5x⁴/y) / y⁴
d²y/dx² = - 5x/y² - 25x⁴/2y⁵
y'' = - 5x/y² - 25x⁴/2y⁵
Thus, The value of y'' will be (- 5x/y² - 25x⁴/2y⁵).
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how many gallons will it take to mow a lawn if you maintain the rate of 1/2 gallon of gasoline per 1/4 mowed
2. During a 5-day training at your department, the number of visitors tripled each day. If the training started on a Monday with 345 attendees, what was the attendance on Thursday?
The number of attendance on Thursday would be 9,315.
Given that,
During a 5-day training at your department, the number of visitors tripled each day.
Here, the training started on a Monday with 345 attendees.
Hence, the number of visitors on Tuesday is 3 times with 345 attendees.
That is, On Tuesday;
Number of attendees = 345 x 3
= 1,035
On Wednesday;
Number of attendees = 1,035 x 3
= 3,105
On Thursday;
Number of attendees = 3,105 x 3
= 9,315
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The distance d that a certain particle moves may be calculated from the expression d = at + bt2 where a and b are constants; and t is the elapsed time. what must the dimensions of the quantities a and b be, respectively?
A car travels 182 miles in 3 hours and 15 minutes. How many miles does it travel per hour?
One book cost £1.99 how much do four books cost
Can the sum of two negative numbers ever be positive?
720,808 in expanded form with exponents
The number 720,808 in expanded form with exponents is written as:
[tex]\[ 7 \times 10^5 + 2 \times 10^4 + 8 \times 10^2 + 8 \times 10^0 \][/tex]
To express 720,808 in expanded form with exponents, We break it down by place value and then represent each term using powers of 10. The breakdown is as follows:700,000 : [tex]7 \times 10^5 \\[/tex]
20,000 : [tex]2 \times 10^4 \\[/tex]
800 : [tex]8 \times 10^2 \\[/tex]
8 : [tex]8 \times 10^0[/tex]
When we combine these, we get the expanded form:[tex]\[ 7 \times 10^5 + 2 \times 10^4 + 8 \times 10^2 + 8 \times 10^0 \][/tex]
This representation helps in understanding the value of each digit based on its position in the number.
You are at a Carnival .One of the Carnival games ask you to pick a door and then pick a curtain behind the door. There are 3 doors and 4 curtains behind each door.how many choices are possible for the player ?????
There are 12 possible choices for the player.
What is combination?"It is a way of selecting items from a collection "
What is formula of combination?"[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]"
What is n factorial?n! = n × (n - 1) × . . . × 2 × 1
For given question,
There are 3 doors and 4 curtains behind each door.
The number of possible ways of selecting a door from the 3 doors.
Using combination formula,
[tex]^3C_1=\frac{3!}{1!(3-1)!}\\\\ ^3C_1=\frac{3\times 2!}{2!}\\\\ ^3C_1=3[/tex]
The number of possible ways of selecting a curtain from the 4 curtains.
Using combination formula,
[tex]^4C_1=\frac{4!}{1!(4-1)!}\\\\ ^4C_1=\frac{4\times 3!}{3!}\\\\ ^3C_1=4[/tex]
So, the number of choices for the player to pick a door and then pick a curtain behind the door :
[tex]^3C_1\times ^4C_1\\\\=3\times 4\\\\=12[/tex]
Therefore, there are 12 possible choices for the player.
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Shantel is studying for her history test. After 20 minutes she is 1/4 of the way done. How much longer will she study?
Shantel will need to study for 60 minutes more to complete her history review.
Shantel is studying history and after 20 minutes, she is [tex]\frac{1}{4}[/tex] of the way done.
To determine how much longer she will study, we need to calculate how much time is needed to complete the remaining [tex]\frac{3}{4}[/tex] of her study time.
[tex]\frac{1}{4}[/tex] of the study done in 20 minutes means she will study for 4 * 20 = 80 minutes in total.
To find out how much longer she needs to study, subtract the time she has already studied (20 minutes) from the total study time (80 minutes): 80 - 20 = 60 minutes.
Therefore, Shantel will need to study for 60 minutes more to complete her history review.
How many gallons of a 80% antifreeze solution must be mixed with 60 gallons of 30% antifreeze to get a mixture that is 70% antifreeze?
Lean wants to giftwrap a present she got for her little brother. how many square inches of giftwrap will be needed to cover a box that is 5in × 7in × 3in?
-0.7 repeating as a decimal in simplest form
what are two practical products you could add to find 990 x 37 ; 297 693 2970 6930 69300 6330 29700
Generate a process that would generate random numbers between –1 and 1 for x and y positions of 10000 points and count how many points fall with the circle, then determine an estimated version of π. (see below to generate floating point random numbers. this generation is not needed to describe the process, but to implement the process)
The question is about using the Monte Carlo method to estimate the value of π, by generating random points in a square, counting how many fall inside a unit circle, and finally using this count to calculate π.
Explanation:This question involves the implementation of a famous problem in computational mathematics known as the Monte Carlo method for estimating the value of π:
First, initialize a variable, say 'count', to 0. This variable will keep track of the number of points falling within the circle.Next, carry out a 'for' loop to generate 10000 points. Each point will have x and y coordinates, each a random floating point number between -1 and 1.For each generated point (x, y), calculate the distance from the point to the origin (0,0), which is sqrt(x^2 + y^2). If this distance is less than or equal to 1, it means that the point lies within the unit circle, so increment the 'count' variable by one.After all 10000 points have been generated and tested, 'count' will hold the total number of points lying within the circle. To determine an estimation of π, use the formula 4 * (count / total_number_of_points).This process is based on the mathematical fact that the ratio of the area of a unit circle to the square it is inscribed in is π/4.
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The floor of a one-story building is 14 feet longer than it is wide. The building has 1715 square feet of floor space. Find the length l and width w of the floor.
Final answer:
To find the floor dimensions of a building that is 14 feet longer than it is wide with an area of 1715 sq ft, we solve the quadratic equation w * (w + 14) = 1715, resulting in w=100 feet and length l=114 feet.
Explanation:
The student is asked to find the length (l) and width (w) of a one-story building floor which is 14 feet longer than it is wide, with a total area of 1715 square feet. To solve this, we set up an equation where w represents the width and w + 14 feet represents the length. Since the area of a rectangle is length times width, the equation is w * (w + 14) = 1715.
After solving this quadratic equation, we find that w=100 feet which makes the length l = w + 14 = 114 feet. Therefore, the actual dimensions of the building are 114 ft by 100 feet.
Suppose John opens a savings account with $1,000 that compounds interest daily. The APR at the time John deposits the account is 3.5%. He makes no withdrawals or deposits. What is his APY to the nearest hundredth of a percent after 1 year?
Find the quotient of 5/68
Solve for W
A=2Lw+2Lh+2wh
Let a be a rational number and b be an irrational number. Which of the following are true statements?
A. The sum of a and b is never rational
B. The product of a and b is rational
C. b^2 is sometimes rational
D. a^2 is always rational
E. √a is never rational
F. √b is never rational
What is the next letter? YBWDUF
translate into an algebraic expression: the difference of six times a number and 8