1. A biologist Studied the population of white-sided jackrabbits and black-tailed jackrabbits over a 5 year period. He modeled the population, in thousands, with the following polynomials where x is time, in years
White-sided jackrabbits: 6.5x^2-8.7x+5.9
Black-sided jackrabbits: 6.5x^2+9.2x+1.2
2. A family is having a pool built in their backyard. If their backyard is rectangular and measures 8x by 7x and the pool is circular with a radius of 3x how much of the yard will be left over after the pool is built
Answers
1. Hence, after 5 years, there are roughly 113,500 white-sided "jackrabbits" and 157,700 black-tailed "jackrabbits" living in North America.
2. Yard will be left over after the pool is built 29.48
What is polynomial ?A polynomial is a mathematical equation that only uses addition, subtraction, multiplication, and non-negative integer exponents and consists of variables (also known as indeterminates) and coefficients. Variables can be present in polynomials, which can be expressed in the following way: \(a 2x2 + a 1x + a 0 + a nxn + a n-1xn-1 +\).. where x is the variable, and the coefficients are a n, a n-1,..., a 2, a 1, a 0. The highest exponent of the variable in an expression is the polynomial's degree. For instance, the polynomial \(3x2 + 2x - 1\)has a degree of 2 since the largest exponent of x is 2. Calculus, algebra, and geometry are just a few of the mathematical disciplines where polynomials are employed.
given,
We can enter x = 5 into the corresponding polynomials to determine the population of white-sided "jackrabbits" and black-tailed "jackrabbits" over a 5-year period.
Regarding white-sided "jackrabbits":
\(8.7(5) + 5.9 - 6.5(5)2 = 113.5\) thousand
For jackrabbits with black tails:
157.7 thousand is equal to \(6.5(5)2 + 9.2(5) + 1.2.\)
Hence, after 5 years, there are roughly 113,500 white-sided "jackrabbits" and 157,700 black-tailed "jackrabbits" living in North America.
The backyard's size is 8 x 7 x 56 x 2.
The pool's surface area is:
\(\pi (3x)^{2} =9\pi x^{2}\)
Following the construction of the pool, the remaining yard space is:
\(56x^{2} -9\pi x^{2}\)\(=14.74x^{2}\)
Consequently, 14.74x2 of the yard will remain after the pool is constructed.
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Related Questions
Refer to the given terms . A pattern defines the relationship between the first two terms . Determine the relationship and identify the missing term of the second pair , such that both the pairs are analogous . AZP : ZAR :: TXK :
Answers
The missing term in the second pair is YUL.
To determine the relationship between the first two terms, let's analyze the given pattern: AZP : ZAR.
If we look closely, we can observe that each letter in the first term is shifted one position forward in the alphabet to form the corresponding letter in the second term.
So, applying the same pattern to the second pair (TXK), we need to shift each letter one position forward in the alphabet:
T + 1 = U
X + 1 = Y
K + 1 = L
Therefore, the missing term in the second pair is YUL.
The analogy between the pairs is that each letter in the first term is shifted one position forward in the alphabet to form the corresponding letter in the second term.
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What conclusion can Keisha make?
mp ng
A+B=
so the sum of a rational number and an irrational num
1
29
Answers
The sum of two rational numbers is a rational number option "the sum of two rational numbers is a rational number" is correct.
What is an irrational number?It is defined as the numbers in all real numbers which cannot be represented as rational numbers, in other words the irrational number cannot be expressed in the form of p/q form.
A rational number is a sort of real number that has the form p/q and does not equal zero.
We have two numbers:
A and B
= A + B
\(\rm = \dfrac{m}{q}+\dfrac{n}{p}\\\\\\= \dfrac{mp+nq}{pq}\)
Thus, the sum of two rational numbers is a rational number option "the sum of two rational numbers is a rational number" is correct.
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SOME ONE HELP PLEASE
Answers
Answer:
1 23/32
Step-by-step explanation:
hi, dont sweat it! i gotchu.
Two cars start moving from the same point. One travels south at 56 km/h and the other travels west at 42 km/h. At what rate (in km/h) is the distance between the cars increasing three hours later?
Answers
The distance between the cars increasing three hours later rate (in km/h) is 70km/h.
What do you mean by distance?
Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.
According to the given question,
We have given information:
Two cars start moving from the same point. One travels south at 56 km/h and the other travels west at 42 km/h.
Now, we will calculate the distance between the cars increasing three hours later,
S² + W² = D²
where S is the southbound car,
W is the westbound car,
D is the distance,
2 * S dS/dt + 2 W dW/dt = 2 D dD/dt
S dS/dt + W dW/dt = D dD/dt
In 3 hours,
S=3*56 = 168 and W = 3*42 = 126
and D = \(\sqrt{(168)^{2}+ (126)^{2}}\) = 210
168 * 56 + 126 * 42 = 210 * dD/dt
(168 * 56 + 126 * 42) / 210 = dD/dt
dD/dt = (9408+5292)/210
dD/dt = 14700/210 = 70
Therefore, the distance between the cars increasing three hours later rate (in km/h) is 70km/h.
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PLEASE HELP ME I AM STUCK!! WILL MARK BRAINLIEST
Answers
Answer:
your answer is right answer is 4
Solve the compound inequality.3x+1 <4 or 2x + 5 > 17Graph the solution on the number line.
Answers
SOLUTION:
\(\begin{gathered} 3x\text{ + 1 }\leq\text{ 4} \\ 3x\text{ }\leq\text{ 4 - 1} \\ 3x\text{ }\leq\text{ 3} \\ \frac{3x}{3}\leq\text{ }\frac{3}{3} \\ x\leq\text{ 1} \end{gathered}\)\(\begin{gathered} 2x\text{ + 5 }\ge\text{ 17} \\ 2x\text{ }\ge\text{ 17 - 5} \\ 2x\text{ }\ge\text{ 12} \\ \frac{2x}{2}\text{ }\ge\text{ }\frac{12}{2} \\ x\ge\text{ 6} \end{gathered}\)
The quantities xxx and yyy are proportional.
xxx yyy
333 303030
101010 100100100
161616 160160160
Find the constant of proportionality (r)(r)left parenthesis, r, right parenthesis in the equation y=rxy=rxy, equals, r, x.
r =r=r, equals
Answers
Answer:
The answer is 10
Step-by-step explanation:
I just know
Answer:
IT'S 10
Step-by-step explanation:
HAHAHAH HE HAD IT RIGHT LOL...
Have a good day =D
What is the Domain of f(x) = -x^3 + 6x^2 -10x + 4
Answers
We can say that the domain of f(x) is (-∞, ∞), which means that any real number can be plugged into the function and it will produce a valid output.
What is function?
In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.
The function f(x) = -x³ + 6x² -10x + 4 is a polynomial function, which means that it is defined for all real values of x. Unlike some functions (such as square roots or logarithms) which have restrictions on their input values, a polynomial function can take any real number as an input.
To express the domain of the function in interval notation, we use the notation (-∞, ∞), which represents all real numbers. The symbol ∞ stands for infinity, and the open interval notation with the parentheses indicates that there are no specific endpoints for the domain; it extends indefinitely in both directions along the real number line.
Therefore, we can say that the domain of f(x) is (-∞, ∞), which means that any real number can be plugged into the function and it will produce a valid output.
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Please help me i am so confused
Answers
The interval that will have the highest frequency will be: C. 11 - 15.
Which interval will have the highest frequency?The interval that will have the highest frequency will be 11 - 15. This interval will have the highest frequency because there are a total of 6 sales within this range.
The other intervals have sales that are 5 and below. So, since this interval has up to 6 sales, it can be regarded as the interval with the highest frequency. Frequency refers to how often something occurs. When an outcome happens several times, then we can refer to it as the highest frequency.
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What is the range of the function? f(x)=3^x−1−2
Answers
The range of the equation f(x) = 3ˣ ⁻ ¹ - 2 is y > -2
Calculating the range of the equation?From the question, we have the following parameters that can be used in our computation:
f(x) = 3ˣ ⁻ ¹ - 2
The above equation is an exponential function
The rule of an exponential function is that
The domain is the set of all real numbersHowever, the range is always greater than the constant termIn this case, it is -2
So, the range is y > -2
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2. Blake interviewed 24 students to see whether they collected sports cards and whether they participated in sports. The table below shows his data Sports-Card Collecting and Sports Participation Collects Sports Cards Does Not Collect Sports Cards Participates in Sports 6 Does Not Participate in Sports 3 7 How many total students Blake interviewed, participate in sports?
Answers
Therefore, out of the 24 students that Blake interviewed, 9 of them participate in sports.
What is equation?An equation is a mathematical statement that indicates that two expressions are equal. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The expressions on both sides of the equation are separated by an equal sign "=" which means that the two expressions have the same value.
Here,
According to the table, Blake interviewed a total of 24 students. To find out how many of these students participate in sports, we need to add up the number of students who collect sports cards and participate in sports, as well as the number of students who do not collect sports cards and participate in sports. So:
Total students who participate in sports = Number of students who collect sports cards and participate in sports + Number of students who do not collect sports cards and participate in sports
Total students who participate in sports = 6 + 3
Total students who participate in sports = 9
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7+4(3a+5b) how to distribute and combine like terms
Answers
To distribute 4 into the parentheses, multiply it to each term in the parentheses.
We can see that the terms inside are 3a and 5b, and after we multiply them by 4, we would get 12a and 20 b.
Because in the parentheses, 3a and 5b are originally being added, we also add them after we distribute 4 into the parentheses.
7+4(3a+5b)
=7+12a+20b
Now, we cannot combine like terms, since we only have one term with each variable, a and b. 7 is not being multiplied to a variable so we cannot combine that with anything either. In other words, we cannot combine like terms after the first step since there are no like terms to combine.
I hope this helps!
the following are the Scores of 20 students in a Diagostic exam: 34, 36, 66, 74, 76, 78, 84, 85, 99, 103, 121, 123, 123, 125, 130, 133, 137, 140, 145, 156, n=20 Find P43, Q3, AND D8
Answers
From the students diagnostic exam, the 43rd Percentile, 3rd Quartile and 8 Decile are 84.5, 138.5 and 140 respectively.
Understanding Percentile, Quartile and DecileWe first need to sort the scores in ascending order:
34, 36, 66, 74, 76, 78, 84, 85, 99, 103, 121, 123, 123, 125, 130, 133, 137, 140, 145, 156
P43 represents the 43rd percentile, which is the score below which 43% of the scores fall. To find P43, we need to calculate the index of the score that corresponds to the 43rd percentile:
P43 = (43/100) * (n + 1)
P43 = (43/100) * (20 + 1)
P43 = 8.44
Since P43 is not an integer, we can take the average of the scores at the indices 8 and 9 (since the index starts from 1):
P43 = (84 + 85) / 2
P43 = 84.5
Therefore, P43 is 84.5.
The third quartile, Q3, represents the score below which 75% of the scores fall. To find Q3, we calculate the index of the score that corresponds to the 75th percentile:
Q3 = (75/100) * (n + 1)
Q3 = (75/100) * (20 + 1)
Q3 = 15.75
Since Q3 is not an integer, we can take the average of the scores at the indices 15 and 16:
Q3 = (137 + 140) / 2
Q3 = 138.5
Therefore, Q3 is 138.5.
D8 represents the score below which 80% of the scores fall. To find D8, we calculate the index of the score that corresponds to the 80th percentile:
D8 = (80/100) * (n + 1)
D8 = (80/100) * (20 + 1)
D8 = 16.8
Since D8 is not an integer, we can round up to the nearest whole number and consider the score at the 17th index:
D8 = 140
Therefore, D8 is 140.
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whats 10/14 in short decimal form ?
Answers
\( = > \frac{10}{14} \\ \)
\( = > \frac{5}{7} \\ \)
\( = > 0.71428\)
PLEASEEE HELP!!!
A car dealership uses this graph and equation to show the relationship between the list price of a particular car model and the age of the car.
Y= -2,500x + 19,000
At a recent auction, the dealership purchased several of these cars that are between two and three years old.
Based on the equation, what are the minimum and maximum amounts the dealership should set as the list prices for the cars it purchased?
Minimum list price: $(10,500 , 14,000 , 6,500 , 11,500)
Maximum list price: $(10,500 , 18,500 , 14,000 , 11,500)
Answers
Answer:
minimum: 6500
maximum: 18500
Hope this helps
GLL
Step-by-step explanation:
Answer:
Correct answer is below
Step-by-step explanation:
I need Help please!!!
Answers
Step-by-step explanation:
it seems you solved the tricky part yourself already.
just to be sure, let's do the first derivative here again.
the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...
f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =
= 3t⁴ + 18t³ + 24t² + 18t + 21
f'(t) = 12t³ + 54t² + 48t + 18
and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).
we simply put the input number (2) at every place of the input variable (t).
so,
f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =
= 426
A town has a population of 50,200 and grows at a rate of 9% every year. Which equation represents the town’s population after 2 years?
Answers
Answer:
A. P = 50,200(1 + 0.09)2
Answer:
P = 50200(1+0.09)²
Step-by-step explanation:
To find the answer to this question we use the equation new value = original value x \(d^{n}\), where d is the multiplier
We are told that our original value is 50200 and to find the multiplier we have to do 1 + 0.09. This is because the population is increasing by 9% which as a decimal is 0.09!
This means that our equation would be P = 50200(1+0.09)²
Hope this helps, have a lovely day! :)
EMERGENCY PLEASE HELP
A company deposits $5,000 in a bank account that earns 3%
compound interest each year. Which function represents the value,
V(t), in dollars, of the bank account after t years?
Answers
Answer:
5150
Step-by-step explanation:
Answer: v(t) = 5,000(1.03)t
Step-by-step explanation:
HELP PLEASEEEEEEE!!!!!!
Answers
Answer: I think it is
x y
1 2
3 14
10 56
Step-by-step explanation:
So what I did is you take the 6 and multiply it by the x number then you subtract by 4
There are 108 pigeons that need pigeon coops. Each coop can hold up to 7 pigeons. How many coops are needed for all 108 pigeons?
Answers
15 coops are needed for 108 pigeons
What is unitary method ?
The unitary method is a technique for solving a problem but first finding the value of a single unit , and then finding the necessary value by multiplying the single unit value
using unitary method
Total pigeon = 108
each coop can hold = 7 pigeons
7 pigeons are held by = 1 coop
108 pigeons will be held by = 108 / 7 = 15.43 =15
15 coops are needed for 108 pigeons
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There are 108 pigeons that need pigeon coops, each coop can hold up to 7 pigeons, coops are required for all 108 pigeons.
What are pigeons?"Pigeons are gentle, plump, small-billed birds with a skin saddle (cere) between the bill and forehead."
What are coops?"Pigeon houses are also sometimes referred to as "coops" although the word seems to have originally applied to the breeding pens inside the housing."
Total number of pigeons that needed coops \(=108\)
Number of pigeons each coop can hold \(=7\)
Number of coops required
\(=\frac{108}{7} \\=15.42\\=16\)
Hence, we need approximately 16 coops for all 108 pigeons.
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Which of the following would you see on a circle graph?
OA. Percentages
OB. Bars
C. Points
OD. A y-axis
Answers
A, percentages
You would see percentages on a circle graph, because it's how many parts of the whole that they take up.
Happy to help, have a great day! :)
9. Find m DF
m
140°
DF:
=
E
44°
20. Find
mZPQR.
131*
m/POR=
Need done asap please show work
Answers
According to the angles between intersecting secant and tangent, the value of
angle DF is 52 degrees
angle PQR = 49 degrees
How to solve for angle DFThe value of angle DF is solved using the angles of intersecting secant out side the circle
The theorem give the formula in the form
44 = 1/2 (140 - DF)
88 = 140 - DF
DF = 140 - 88
DF = 52 degrees
Using intersection of tangents, for the second figure
exterior angle = 1/2 (major arc - minor arc)
major arc = 360 - 131 = 229
PQR = 1/2 (229 - 131)
PQR = 49 degrees
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For a new neighbor, 1 acre of land will be split into 5 lots.How many acres of land will be in each lot.
Answers
Hope this helps :D
What is the slope of the line that passes through the points (0, -6) and (0, -5)?
Answers
The slope of the line that passes through the points (0, -6) and (0, -5)is undefined.
What is the slope of the line that passes through the points (0, -6) and (0, -5)?Slope is line's inclination with regard to the horizontal is quantified numerically. In analytical geometry, a line, ray, or line segment's slope is the ratio of the vertical to horizontal distance between any two points on the line, ray, or line segment ("slope equals rise over run").
In differential calculus, the derivative of a function yields the slope of a line tangent to its graph, which represents the function's instantaneous rate of change with respect to changes in the independent variable.
Ok so slope is the change in y over change in x.
Your why changed from 6 to -5 so you can write this as -5 - 6
Your x didn’t change it went from 0 to 0
You can write this as 0-0
Now -11/0 is what you end up with as a slope.
Any number divided by 0 is undefined so your slope is undefined.
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88888*88888 help me please
Answers
Simplify the product using the distributive property
(3h - 5)(5h + 4)
Answers
Step-by-step explanation:
(3h - 5)(5h + 4) = 3h * 5h + 3h * 4 - 5*5h - 5 *4
= 15h^2 - 13h -20
\((3h-5)(5h+4)\)
\(=(3h+-5)(5h+4)\)
\(=(3h)(5h)+(3h)(4)+(-5)(5h)+(-5)(4)\)
\(=15h^2+12h-25h-20\)
Answer:
\(\bold{=15h^2-13h-20}\)due in 1 hour
screenshot below
Answers
Answer:
True I'm pretty sure. Just check to be sure.
Step-by-step explanation:
Please answer if your good at math and I will give brainlest.
Tell whether the pair of polygons is similar. Explain why or why not.
Answers
I need whats in the red rectangle
Answers
Answer:
9
Step-by-step explanation:
sqrt(5) + sqrt(405)
sqrt(5) + sqrt( 81*5)
sqrt(5) + sqrt(81) sqrt(5)
sqrt(5) +9 sqrt(5)
10 sqrt(5)
Please hurry and answer!
This graph gives growth of a plant overtime what is the slope of the line, and what does the slope mean in situation
select from the drop down menus to correctly complete the statement
The slope is blank which means that the plant blank by blank everyday
Answers
Using the slope of the linear function, it is found that:
The slope is of 0.5, which means that the plant grows by 0.5 inches each day.A linear function is modeled by:
\(y = mx + b\)
In which:
m is the slope, which is by how much the output y changes when the input x changes by 1.b is the y-intercept, which is the value of y when x = 0.In this problem:
x is the time in days.y is the height in inches.Two of the points are: (0,0) and (2,1).
The slope is given by change in y divided by change in x, hence:\(m = \frac{1 - 0}{2 - 0} = \frac{1}{2} = 0.5\)
Then, applying the interpretation:
The slope is of 0.5, which means that the plant grows by 0.5 inches each day.To learn more about slopes and linear functions, you can take a look at https://brainly.com/question/16302622
Answer:
hes correct. the slope is 0.5 and it grows 0.5 inches everyday
Step-by-step explanation: