Using the average rate of change, it is found that:
A. The average population decline between 1984 and 2018 was of 2.25 thousand deer a year.
B. The population would have reached 225 thousand deer between 2017 and 2018.
C.
The rates are as follows:
1994 to 2004: 0.75 thousand deer a year.2004 to 2014: -1.45 thousand deer a year.Meaning that between 1994 and 2004 there was a increase in the population of deer, and from 2004 to 2014 there was a decrease.
What is the average rate of change of a function?The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
For 1984 and 2018, we have that:
f(1984) = 250.f(2018) = 173.50.Hence the rate is:
r = (173.50 - 250)/(2018 - 1984) = -2.25 thousand deer a year.
For item b, the situation is modeled by a linear function, as follows:
D(t) = 230.50 - 1.45t.
The population would be of 225 thousand deer when D(t) = 225, hence:
230.50 - 1.45t = 225
1.45t = 5.5
t = 5.5/1.45
t = 3.79.
Hence between the years of 2017 and 2018.
For item c, the rates are as follows:
1994 to 2004: (245 - 237.50)/10 = 0.75 thousand deer a year -> increase.2004 to 2014: (230.50 - 245)/10 = -1.45 thousand deer a year -> decrease.More can be learned about the average rate of change at https://brainly.com/question/11627203
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Which inequality is true?O A. 31 - 1<8B. + 6 < 9O c. <3D. 477 > 12
The answer is D
To solve this, we can use similar values of the ones in the problems and compare it:
With a just add one to each side:
[tex]undefined[/tex]The diameter of a circle is 18 cm. Find its circumference in terms of T. Answer: C = om Submit Answer
The circumference of a circle is given by the formula:
[tex]C\text{ = 2 }\pi\text{ r}[/tex]The diameter of the circle, d = 18cm
Radius = diameter / 2
r = d/2
r = 18/2
r = 9 cm
[tex]\begin{gathered} C\text{ = 2}\pi(9) \\ C\text{ = 18}\pi \end{gathered}[/tex]Could someone please help me with this?
Answer:
1. f(4) = 4
2. g(2) = -4
3. f(-5) = -14
4. g(-3) = 21
5. f(0) = -4
6. g(0) = 0
7. f(3) - 1 = 1
8. f(1/4) = -3.5 or -7/2
9. g(1/4) = -0.9375 or -15/16
10. f(a^2) = 2a^2 - 4
11. f(k+1) = 2k - 2
12. g(2n) = 2n^2 - 8n
13. f(3x) = 6x - 4
14. f(2) + 3 = 3
15. g(-4) = 32
Step-by-step explanation:
here’s a pic of my work:
Is it true that Weight is a function of Height?
Answer:
Yes
Step-by-step explanation:
The number of height is also the number of wegt
Fifty-two percent of realtors have a college degree. If a continuing education course enrolls a random selection of 1,600 realtors every year, what is the average number of realtors attending the course with a degree each year?
SOLUTION:
The average is given by the formula;
[tex]\begin{gathered} Mean=xP(x) \\ =0.53\times1600 \\ =848 \end{gathered}[/tex]Thus, the average number of realtors who have a degree attending the course is 848
a rotation of 180 degrees maps figure A onto itself. It has
Letter A doesn't show rotational symmetry of 180 degrees.
The letter 'A' has just one vertical line of symmetry.A vertical line of symmetry is that line which runs down a picture thus dividing it into two identical halves. In other words, it's a straight standing line that divides an image or shape into two identical halves.
The rotational symmetry of a shape explains that when an object is rotated on its own axis, the form of the object looks the same. Many geometrical shapes appear to be symmetrical once they are rotated 180 degrees or with some angles, clockwise or anticlockwise. A number of the examples are square, circle, hexagon, etc.
Complete Question- A rotation of 180 degrees maps figure A onto itself. It has transformation or not?
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Add 5/6+ 3/4 + 2/3 Simplify the answer and write it as a mixed number, if possible.2122O12
In order to add those fractions, we need to write them using a commom denominator. We can do so by finding a common multiple for the original denominators:
6, 4 and 3
Since 12 is a multiple of those three numbers, we can use 12 as a new denominator for each of the fractions:
5/6 = (5 * 2)/(6 * 2) = 10/12
3/4 = (3 * 3)/(4 * 3) = 9/12
2/3 = (2 * 4)/(3 * 4) = 8/12
Notice that 10/12 is equivalent to the the original fraction 5/6, because we obtained 10/12 by multiplying both the numerator and the denominator by the same factor. The same applies to the other pairs of fractions.
Now, we can add:
5/6 + 3/4 + 2/3 = 10/12 + 9/12 + 8/12
= (10 + 9 + 8)/12
= 27/12
Now, we can simplify the result by dividing both the numerator and the denominator by the same factor. Since both 27 and 12 are multiples of 3, we can write:
27/12 = (27 : 3)/(12 : 3)
= 9/4
Now, since 9 is greater than 4, we can write the fraction 9/4 as a mixed number:
9 = 8 + 1
= 2*4 + 1
9/4 = (2*4 + 1)/4
= 2*4/4 + 1/4
= 2 + 1/4
= 2 1/4 (using the notation of mixed number)
Several students use stopwatches to measure how quickly a sensitive plantreacts to stimuli. They record the times in milliseconds. Which kind of dataare the students recording?OA. Qualitative dataOB. Audio dataC. Quantitative dataOD. Categorical data
Given: Several students use stopwatches to measure how quickly a sensitive plant reacts to stimuli. They record the times in milliseconds.
Required: To determine which kind of data the students are recording.
Explanation: The given kinds of data can be summarized as follows-
→Qualitative data determines the quality of a single data. Example: The colour of cars in a parking lot.
→Audio data have the data in the form of audio. Example: The sound of different dogs barking.
→Quantitative data represents the quantity of some data. Example: Recording the number of the height of students in a class.
→Categorical Data represents the data of various categories. Example- Recording some person's age, sex, hair colour, etc.
Hence, measuring how quickly a sensitive plant reacts to stimuli is an example of Qualitative Data.
Final Answer: Option A (Qualitative Data) is correct.
find a formula for the nth term of the arithmetic sequence the first term is 7 and the common difference is -3
The formula for the nth term of the arithmetic sequence whose first term is 7 and the common difference is -3 is - a[n] = 10 - 3n
What is an Arithmetic progression?An arithmetic progression is a sequence of numbers such that the difference between the consecutive terms is constant. A sequence -
a₁ , a₂, a₃ , a₄ ...... aₙ
will be an arithmetic progression if -
a₂ - a₁ = a₃ - a₂ = a₄ - a₃ = d (constant) is called common difference of A.P. and a₁ = 'a' as the first term.
Given is the the first term equal to 7 and the common difference equal to
- 3.
We can calculate the nth term of an A.P. using the formula -
a[n] = a + (n - 1)d
a[n] = 7 + (n - 1)(- 3)
a[n] = 7 - 3n + 3
a[n] = 10 - 3n
Therefore, the formula for the nth term of the arithmetic sequence whose first term is 7 and the common difference is -3 is -
a[n] = 10 - 3n
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The velocity of a body as a function of time is given as Vt=5e-2t+4 where t is in seconds, and V is in ms. The acceleration in ms2 at t=0.6s is .....
The velocity of a body as a function of time is given as Vt=5e-2t+4 where t is in seconds, and V is in ms acceleration at t = 0.6s is -10x 0.30119m/[tex]s^{2}[/tex].
The velocity of a body is given by
Vt=5e-2t+4
acceleration a(t)= [tex]v'(t)[/tex]
= d/dt [tex]v'(t)[/tex]
= d/dt 5e-2t+4
= -10[tex]e^{-2t}[/tex]
put t = 0.6
acceleration at t= 0.6= a(0.6)
= [tex]-10e^{-2\times0.6}[/tex]
= -10x [tex]e^{-12}[/tex]
= -10x 0.30119m/[tex]s^{2}[/tex]
What is acceleration?acceleration is the rate of change of the speed of an object with respect to time. Accelerations are vector quantities. The direction of the target's acceleration is obtained from the direction of the net force on the target.
Three types of accelerated motion
Uniform acceleration non-uniform acceleration intermediate acceleration.The term uniform acceleration refers to motion in which an object moves in a straight line with increasing speed at equal intervals of time.
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4 strings 5 strings 6 strings 25% off 4 4 8 50% off 6 8 3 Vhat is the probability that a randomly selected Simplify any fractions.
number of banjos that have 5 or 6 strings: 4 + 8 + 8 + 3 = 23
total number of banjos: 6 + 4 + 4 + 8 + 8 + 3
The standard trampoline has a diameter of 14 feet. What is its circumference?
The circumference, C, of a circle is computed as follows:
[tex]C=\pi D[/tex]where D is the diameter of the circle. Substituting with D = 14 ft, we get:
[tex]\begin{gathered} C=\pi\cdot14 \\ C\approx44\text{ ft} \end{gathered}[/tex]The circumference of the trampoline is approximately 44 feet
Lucy bought a plant and planted it in a pot near a window in her house. The initial height of the plant was 12 inches and it grew at a rate of 2 inches per month. Make a table of values and then write an equation for H, in terms of t, representing the height, in inches, of the plant tt months after Lucy bought the plant.
I need the equations
The equation for H, in terns of t, representing the height , in inches, of the plant tt months after Lucy bought the plant is :
H=12+2t
Given, A plant that Lucy had purchased was placed in a pot next to a window in her home. The plant initially stood 12 inches tall and grew at a rate of 2 inches per month.
from the given information, the equation can be framed as:
H = 12 +2t
where the initial height of the plant is increased at a rate of two inches every month.
from the table substitute the value of months in t, to find the height of the plant in that particular month.
t = 0
H=12+2(0)
H=12
hence when t=0 then H=12
t=1
H=12+2(1)
H=12+2
H=14
after a month the height of the plant changes to 14 inches.
t=2
H=12+2(2)
H=12+4
H=16
after two months the height changes to 16 inches.
t=3
H=12+2(3)
H=12+6
H=18
after three months the height changes to 18 months.
t=4
H=12+2(4)
H=12+8
H=20
finally after four months the height of the plant changes to 20 months.
hence we get the required equation as H=12+2t
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Line CD passes through points (0, 2) and (4, 6). Which equation represents line CD?
v
Consequently, y = x + 2 is the equation for the line CD.
Points C(0, 2) and D are given (4, 6).
We must identify the equation of the line CD.
Given is the equation for the line through two points
[tex]\frac{y-y_{1} }{y_{1} - y_{2} } = \frac{x-x_{1} }{x_{1} -x_{2} }[/tex]
[tex]\frac{y-2}{6-2} = \frac{x-0}{4-0}[/tex]
y - 2 = x
x - y + 2 = 0
Consequently, y = x + 2 is the equation for the line CD.
What is the equation of the line?
The set of points that make up a line in a coordinate system is represented algebraically by a line's equation. An equation of a line is an algebraic expression that represents the many points that together make up a line in the coordinate axis as a set of variables, x, and y. We may determine if a given point lies on a line using the equation of any line.
The line's equation is a linear equation of degree one. Let's learn more about the various ways a line's equation may be expressed and how to calculate it.
The slope of the line and a point on the line may be used to create the equation of a line. To better comprehend how the equation for a line is formed, let's learn more about the line's slope and the necessary point on the line. The slope of the line, which can be stated as a numeric integer, fraction, or tangent of the angle it forms with the positive x-axis, is the line's inclination with respect to the positive x-axis. The coordinate system's point with the x coordinate and the y coordinate is referred to as the point.
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7- At the school car wash, Kelly washes a car in 13 minutes, and Libby washes a car in 17 minutes, How many more minutes does it take Kelly to wash a car alone than it takes Kelly and Libby to wash a car when working together? Express your answer as a decimal to the nearest tenth.
Kelly will take 5.64 minutes more to wash the car as compared to Kelly and Libby when they are working together
Time taken by Kelly to wash the car = 13 minutes
Time taken by Libby to wash the car = 17 minutes
Time taken by Kelly and Libby to wash the car together:
LCM of 13 and 17 is 221. So, the total work required to be done is 221 units
Hence, Kelly does 17 units of work each minute and Libby does 13 units of work each minute
If both work together, they will finish the work in = Total work required to be done/ Work done in a minute by Kelly + Work done in a minute by Libby
= 221/(17+13)
= 221/30 = 7.36 minutes
The extra time taken by Kelly working alone = 13-7.36 = 5.64 minutes
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Help me please this is due tn
The length of a rectangle is (5x+1) inches. The width is (x). Express the area of the
checkerboard in terms of the variable x. Use the formula: A = L-W
14.
Answer: A = 7x
Step-by-step explanation:
Area = Length x Width
A = L * W
L = 5x + 1 W = x
Plug the length and width into the equation for area.
A = (5x + 1) * x
A = 6x + x
A = 7x
Write the correct equation for the following statement.
You decide to rent a limo for prom. The rate is $250 plus $6 per mile
traveled. Write an equation to calculate your total cost (c) at the end of
the evening for a given number of miles (m).
250+6m
If you travel 45 miles what will be your total bill at the end
of the evening?
Answer:
Easy;
Substitute m (miles) for 45.
250+6(45)
(6 dollars per mile, times 45 miles, plus the 250 flat rate)
250+270
520
So you would be charged 520 dollars total at the end of the evening.
Hope this helped!
Mr.Kermshner has 168 bandages march through June. How much is it if each bandage is 3 cents
504 bandages if it is each bandage is 3 cents.
Given,
Mr. Kermshner has 168 bandages march through June.
To find the how much is it if each bandage is 3 cents ?
Now, According to the question,
Based on the given conditions,
Formulate:
Total bandage is 168
and, each bandage is 3 cents
= 168 x 3
= 504
Alternative form = 5.04 x 10^2
Hence, 504 bandages if it is each bandage is 3 cents.
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Finding the Slope of a LineVy10What is the slope of a line that contains the points (1,9) and (4, 3)?The slope of the line is<88642N2x624.8
Given the points: (1, 9) and (4, 3)
To find the slope:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]m=\frac{3-9}{4-1}[/tex]m = -2
Walnuts make up half of the nuts in this nut bread:
It has exactly 2 pecans
The number of walnuts is double the number of pecans.
Write an equation to show how many of each nut this nut bread contain.
An equation showing how many of each nut this nut bread contains is Y = 2p + 4w + 2t.
What is an equation?An equation is a mathematical expression of equality between two variables or expressions.
Equations are shown using the equation mark, symbol, or sign (=).
The number of walnuts in the nut bread = 1/2
The number of pecan nuts = 2
The number of walnuts which is double of pecan nuts = 4 (2 x 2)
The number of other nuts = 2 since walnuts equal 1/2 of the nuts
The total number of nuts = 8 (2 pecan, 4 walnuts, and 2 others)
Let the number of nuts in the bread = Y
Let the number of walnuts, w = 4
Let the number of pecan nuts, p = 2
Let the number of other nuts, t = 2 (8 - 4 - 2)
Thus, the equation of each nut contained in the nut bread is Y = 2p + 4w + 2t.
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Distribute property of 41×8
Using distribute property on 41×8 is 328.
What is the Distributive Property?
The distributive property states that an expression which is given in form of A (B + C) can be solved as A × (B + C) = AB + AC. This distributive law is also applicable to subtraction and is expressed as, A (B - C) = AB - AC. This means operand A is distributed between the other two operands.
We know that,
Distributive property is A × (B + C) = AB + AC.
So, 41 × 8 is 41 × (5 + 3 ) = 41×5 + 41×3
41 × (5 + 3 ) = 205 + 123
41 × (5 + 3 ) = 328
Hence, using distribute property on 41×8 is 328.
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For y = 10*0.5^x (that is read y equals ten times one half to the power of x), doesthis model exponential growth or decay? Explain how you know.
f(1)=1/2 f(2)=(1/2)^2=(1/2)*(1/2)=1/4
1/2>1/4 => f(1)>f(2) => it is decreasing, because with the grow of x the value(y) is decreasing what we have shown
Solve this system of equations byusing the elimination method.x - 5y = 164x – 2y = -8([?],
Given:
There are given two equations:
[tex]\begin{gathered} x-5y=16...(1) \\ 4x-2y=-8...(2) \end{gathered}[/tex]Explanation:
To find the value by using the elimination method, we need to multiply by 4 into the equation (1) and 1 into the multiply by (2):
Then,
From the equation (1):
[tex]\begin{gathered} 4(x-5y=16) \\ 4x-20y=64...(3) \end{gathered}[/tex]And,
From the equation (2):
[tex]\begin{gathered} 1(4x-2y=-8) \\ 4x-2y=-8...(4) \end{gathered}[/tex]Now,
From the equation (3) and equation (4):
[tex]4x-20y-64=4x-2y+8[/tex]Then,
[tex]\begin{gathered} 4x-20y-64-4x+2y-8=0 \\ -20y-64+2y-8=0 \\ -18y-72=0 \\ -18y=72 \\ y=-4 \end{gathered}[/tex]Now,
Put the value of y into the equation (3):
[tex]\begin{gathered} \begin{equation*} 4x-20y=64 \end{equation*} \\ 4x-20(-4)=64 \\ 4x+80=64 \\ 4x=64-80 \\ 4x=-16 \\ x=-4 \end{gathered}[/tex]Final answer:
Hence, the value of x and y is shown below:
[tex](-4,-4)[/tex]please i need help. can someone please help me
Triangle ABC is similar to triangle DEFwhich proportion can be used to find the length of DE in centimeters?A. 4/3 = DE/9B. 5/15 = DE/4C. 4/DE = 9/3D. 9/DE = 3/5
In the given figure, Triangle ABC is similar to triangle DEF.
Applying the Similar Triangle Formula, the proportion to be used to find the length of DE is:
[tex]\frac{4\text{ cm}}{3\text{ cm}}\text{ = }\frac{DE}{9\text{ cm}}[/tex]Therefore, the answer is A.
Solve the inequality and graph the solution.
−2p + 4.5 < −2.9
number line with open circle plotted at 3.7 and arrow pointing right
number line with closed circle plotted at 3.7 and arrow pointing left
number line with open circle plotted at 3.7 and arrow pointing left
number line with closed circle plotted at 3.7 and arrow pointing right
The solution of the inequality −2p + 4.5 < −2.9 is number line with open circle plotted at 3.7 and arrow pointing right, the graph of the inequality has been plotted.
The inequality is −2p + 4.5 < −2.9
Subtract 4.5 from both side
-2p + 4.5 - 4.5 <-2.9 - 4.5
-2p < -7.4
Divide both sides by -2
-2p/-2 < -7.4/-2
p > 3.7
Draw the graph using the result of the inequality
Hence, the solution of the inequality −2p + 4.5 < −2.9 is number line with open circle plotted at 3.7 and arrow pointing right, the graph of the inequality graph has been plotted.
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Answer:
number line with open circle plotted at 3.7 and arrow pointing right
Step-by-step explanation:
hope this helps :)
The diameter of a cylindrical pipe is 7 ft. If the pipe is 42 ft long, what is it’s volume? Use the value 3.14 for n, and round your answer to the nearest whole number. Be sure to include the correct unit in your answer.
ANSWER:
1616 ft³
STEP-BY-STEP EXPLANATION:
We have that the formula to determine the volume of the cylinder is as follows:
[tex]V=\pi r^2\cdot h[/tex]The radius is equivalent to half the diameter, therefore the radius is equal to 3.5 ft (7/2) while the height, in this case, is equivalent to the length, so it is equal to 42 ft. Therefore, we replace each value and calculate the volume, like this:
[tex]\begin{gathered} V=\left(3.14\right)\left(3.5^2\right)\left(42\right) \\ \\ V=1615.53\cong1616\text{ }ft^3 \end{gathered}[/tex]The volume of the cylindrical pipe is 1616 ft³.
Solve the following using substitutionY = -2X + 10.5x - y = 4
We are to solve the equations
[tex]\begin{gathered} y=-2x+1 \\ 0.5x-y=4 \end{gathered}[/tex]The equation can be rewritten as
[tex]\begin{gathered} y+2x=1------------\text{equation 1} \\ -y+0.5x=4-----------\text{equation 2} \end{gathered}[/tex]Using substitution method
From equation 1
[tex]y=1-2x--------\text{equation 3}[/tex]Substitute 1 - 2x for y into equation 2
This gives
[tex]\begin{gathered} -(1-2x)+0.5x=4 \\ -1+2x+0.5x=4 \\ -1+2.5x=4 \\ 2.5x=4+1 \\ 2.5x=5 \\ x=\frac{5}{2.5} \\ x=2 \end{gathered}[/tex]Therefore, x = 2
Substitute 2 for x into equation 3
This gives
[tex]\begin{gathered} y=1-2(2) \\ y=1-4 \\ y=-3 \end{gathered}[/tex]Therefore the solution to the equations is
x = 2, y = -3
radius = 3 ¼ydlearning something about area of circle
Given that the radius of a circle is;
[tex]r=3\frac{1}{4}yd[/tex]Recall that the area of a circle can be calculated using the formula;
[tex]A=\pi r^2[/tex]substituting the value of r;
[tex]\begin{gathered} A=\pi(3\frac{1}{4})^2 \\ A=\pi(\frac{13}{4})^2 \\ A=\pi(\frac{169}{16}) \\ A=33.18yd^2 \end{gathered}[/tex]Therefore