Answer: 0.5
Step-by-step explanation: 5 divide by 2 = 2.5. 2.5 minus 2 = 0.5
Problem 6:
*I understand how to complete the problem but I am stuck on trying to find the common difference for population 1. It's the only thing I need help with for this problem.*
The table shows two sloth populations growing over time.
time (years since 1990)
0
1
2
3
4
5
6
7
8
population 1 (thousands)
0, 90.0
1, 76.5
2, 65.0
3, 55.3
4, 47.0
population 2 (thousands)
0, 39
1, 37
2, 35
3, 33
4, 31
1. Describe a pattern in how each population changed from one year to the next.
2. These patterns continued for many years. Based on this information, fill in the extra rows in the table.
3. On the same axes, draw graphs of the two populations over time.
4. Does Population 2 ever equal Population 1? If so, when? Explain or show your reasoning.
Graphs and functions can be used to illustrate real life events.
The pattern is that; population decreases by 15% each year, while population reduces by 2000 each yearPopulation 2 and Population 1 have equal values twiceThe table is given as:
[tex]\left[\begin{array}{cccccccccc}Time&0&1&2&3&4&5&6&7&8\\P_1&90.0&76.5&65.0&55.3&47.0\\P_2&39&37&35&33&31\end{array}\right][/tex]
(a) The pattern in each population
Population 1
This population follows a geometric pattern.
The common ratio (r) is calculated by dividing the subsequent values of population 1.
We have:
[tex]r = \frac{P_1(1)}{P_1(0)}[/tex]
This gives
[tex]r = \frac{76.5}{90.0}[/tex]
[tex]r = 0.85[/tex]
Express as percentage
[tex]r = 85\%[/tex]
Next, we calculate the scale factor (k)
[tex]k = 1 - r[/tex]
[tex]k = 1 - 85\%[/tex]
[tex]k = 15\%[/tex]
Hence, the pattern of population 1 is: the population decreases by 15% each year
Population 2
This population follows an arithmetic pattern.
The common difference (d) is calculated by subtracting the subsequent values of population 1.
We have:
[tex]d = P_2(1) - P_2(0)[/tex]
[tex]d = 37 - 39[/tex]
[tex]d = -2[/tex]
-2 indicates that the population reduces, each year by 2000
(b) Complete the table
For population 1, we keep multiplying current population by 85%.
So, we have:
[tex]P_1(5) = 47.0 \times 85\% = 40.0[/tex]
[tex]P_1(6) = 40.0 \times 85\% = 34.0[/tex]
[tex]P_1(7) = 34.0 \times 85\% = 28.9[/tex]
[tex]P_1(8) = 28.9 \times 85\% = 24.6[/tex]
For population 2, we keep adding -2 to the current population
So, we have:
[tex]P_2(5) = 31 -2 = 29[/tex]
[tex]P_2(6) = 29 -2 = 27[/tex]
[tex]P_2(7) = 27 -2 = 25[/tex]
[tex]P_2(8) = 25 -2 = 23[/tex]
So, the complete table is:
[tex]\left[\begin{array}{cccccccccc}Time&0&1&2&3&4&5&6&7&8\\P_1&90.0&76.5&65.0&55.3&47.0&40.0&34.0&28.9&24.6\\P_2&39&37&35&33&31&29&27&25&23\end{array}\right][/tex]
(c) The graph of the two populations
First, we determine the equations of both populations
Population 1
We have:
[tex]P_1(0) = 90.0[/tex]
[tex]r = 0.85[/tex]
The nth term of a geometric sequence is:
[tex]P_1(n) = P_1(0) \times r^n[/tex]
This gives
[tex]P_1(n) = 90.0 \times 0.85^n[/tex]
Population 1
We have:
[tex]P_2(0) = 39[/tex]
[tex]d = -2[/tex]
The nth term of an arithmetic sequence is:
[tex]P_2(n) = P_1(0) + nd[/tex]
This gives
[tex]P_2(n) = 39 -2 \times n[/tex]
[tex]P_2(n) = 39 -2n[/tex]
See attachment for the graphs of:
[tex]P_1(n) = 90.0 \times 0.85^n[/tex] and [tex]P_2(n) = 39 -2n[/tex]
(d) Determine if both populations ever have the same value
From the attached image, the graph of both populations intersect at:
[tex](8.891,21.218)[/tex] and [tex](16.337,6.327)[/tex]
This means that both populations have equal values, twice
Read more about graphs and functions at:
https://brainly.com/question/18806107
A garden is in the shape of a square with a perimeter of 48 feet. The garden is surrounded by two fences. One fence is around the perimeter of the garden, whereas the second fence is 3 feet from the first fence on the outside. If the material used to build the two fences is $ 1.21 per foot, what was the total cost of the fences?
These fractions are in order from least to greatest.
StartFraction 8 Over 7 EndFraction, 1 and two-fifths, x, 1 and two-thirds, 2
Which value of x would keep the list in order from least to greatest?
1 and one-sixth
StartFraction 8 Over 5 EndFraction
1 and StartFraction 7 Over 10 EndFraction
StartFraction 7 Over 3 EndFraction
Answer:
I think it is B.
Step-by-step explanation:
They don't tell where the fraction will be placed and other people got it wrong when they thought they put the fraction in the greatest spot.
The value of x could be 1 and one-sixth, or StartFraction 8 Over 5 EndFraction options (A) and (B) are correct.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
The fractions are:
8/7, 1 2/5, x, 1 2/3, 2
Or
8/7, 7/5, x, 5/3, 2
1.142, 1.4, x, 1.667, 2
x could be
x = 1 1/6 = 1.166
Thus, the value of x could be 1 and one-sixth, or StartFraction 8 Over 5 EndFraction option (A) and (B) are correct.
Learn more about the fraction here:
brainly.com/question/1301963
#SPJ6
Pythagorean Theorem:a2 + b2 = c2
Re−write the formula solving for b2 .
Answer:
b2= a2-c2. that is the formula while making b2 subject
Answer:
[tex]b=\sqrt{c^2-a^2}[/tex]
Step-by-step explanation:
a² + b² = c²
~Subtract a² to both sides
b² = c² - a²
~Take square root of both sides
b = ±√c²-a²
Best of Luck!
PLEASE HELP, GIVING BRAINLIEST!!!
These triangles are congruent by _____.
A. ASA
B. AAS
C. SSS
D. Not enough information
E. None of these
Answer:
not enough info
Step-by-step explanation:
unless there is a way to confirm the other 90° angle, u cant say anything. it would be asa if u could. not sure if this is 100% correct, the lines are perpendicular, so it would be 90, but idk lol
Answer: i think it is (A
Step-by-step explanation:
To get to school each morning, Vanessa takes a horse 19.3319.3319, point, 33 kilometers and a train 2.272.272, point, 27 kilometers. In total, the journey takes 26.4826.4826, point, 48 minutes. How many kilometers is Vanessa's journey in total?
Answer:
21.6 km
Step-by-step explanation:
Given that,
The distance covered by a horse is 19.33 km and the distance covered by the train is 2.27 km.
Time taken during entire journey is 26.48 minutes
We need to find the total kilometers of Vanessa's journey in total. It can be calculated by simply adding distance covered by a horse and by train.
Total distance = 19.33 km+2.27 km
D = 21.6 km
So, the total distance covered by Vanessa's journey is 21.6 km.
Eddie sorts his 85 baseball cards into stacks of 9 cards each. How many stacks of 9 cards can Eddie make
You are at the grocery store buying meat for a BBQ that you are hosting. The meat packets are 10.25 pounds each. If you buy 6 of those packets, how many pounds of meat will you end up buying?
Answer:
61.50 pounds
Step-by-step explanation:
10.25 x 6
PLS HELP ME I WILL GIVE BRAINLYEST
Answer:
C
Step-by-step explanation:
2 * 3 is 6
4 * 3 is 12
8 * 3 is 24
Answer:
C
Step-by-step explanation:
2,6 4,12 and 8,24 are all simplified to the fraction 1/3 so the relationship is proportional.
Also in each of the x column every number is always three times the amount.
Hope this helps! :) Plz mark as brainliest
Find Slope (-2,-2) (4,2
Answer:
4/6 or in simplest form 2/3.
Step-by-step explanation:
2-(-2)/4-(-2)= 4/6
An ice cream shop has a selection of 10 flavors of ice cream and 5 toppings. The first menu option lets you pick three flavors and two toppings for $3.75. How many combinations can be created with the first menu option, assuming you pick different flavors of ice cream and different toppings?
Answer:
Here we want to find all the possible combinations that we can make,
First, let's define the selections that we have, and the number of options for each one of these selections. (Remember that each option can be selected only once)
we have 3 flavors and 2 toppings, so let's analyze this case:
First flavor ----- here we have 10 options
Second flavor ---- because we already selected one before, now we have 9 options.
Third flavor ---- because we already selected two before, now we have 8 options.
First topping --- here we have 5 options,
Second topping --- because we already selected one before, here we have 4 options.
Now the total number of possible combinations will be equal to the product between the number of options for each selection:
C = 10*9*8*5*4 = 14,400
The sharks foot ball team lost 5 yards in each of their three downs. Since the product of 3 and -5 is -15 the team lost a total of 15 yards in those three downs
Answer:
The answer is below
Step-by-step explanation:
A football team lost 5 yards on each of 3 plays. Explain how you could use a number line to find the team's change in field position after the 3 plays.
Solution:
Number line is a straight line on which numbers are marked and are separated at regular intervals. A number line can be used for both addition and subtraction. Addition is done by counting to the right while subtraction is done by counting to the left.
Given that the football team lost 5 yards in each of their three downs, this is the same as 3(-5) = (-5) + (-5) + (-5)
Hence since it is negative we move to the left. Starting from 0, we move 5 units to the left 3 times, this gives -15
Answer:
b^itch as^s do ur own work
Step-by-step explanation:
[1\4]∧-3 -27∧4/3 pls help me solve for it
Answer:
-17
Step-by-step explanation:
Green's Gym charges a one-time application fee of $50 plus $30 per session for a personal trainer. Breakout Gym charges an annual fee of $250 plus $10 for each session with a trainer. For how many sessions is the cost of the two plans the same? Write and solve an equation to represent this problem. Make sure to create a let statement: Example: Let s = number of gym sessions.
Answer:
10 sessions
Step-by-step explanation:
let s be the number of gym session
and let y be the cost
the cost can be represented as
y=ms+c
given data
Green's Gym
c=$50
m=$30
y=30s+50------------1
Breakout Gym
c=$250
m=$10
y=10s+250------------2
equating 1 and 2 we can find s, which is the number of session
30s+50=10s+250
30s-10s=250-50
20s=200
s=200/20
s=10
therefore the number of session is 10
A line that includes the point (9, −4) has a slope of −16. What is its equation in point-slope form?
Answer:
y+4= -16(x-9)
Step-by-step explanation:
point slope form is y-y1=m(x-x1)
substitute y-(-4)= -16(x-9)
simplify y+4= -16(x-9)
y=2x+1
-4x+2y=2
How many solutions does the system have?
A none
B exactly one
C exactly two
D Infinitely many
simplify the expression :
(2 + 3p) (2) =
please help
Mrs. Dillard is installing a cubed swimming pool in her backyard. The hole that her husband dug in her backyard is 216 feet cubed. She went to the pool store to pick out a pool frame. She chose a pool frame that had a length, width, and height of 7ft. Will the pool frame she choose fit into the 216 foot cubed hole? If so, explain, if not what dimensions much she buy for the pool frame to fit?
Answer: No. The pool frame she choose will not fit into the 216 foot cubed hole. She should have picked a frame of 6ft.
Step-by-step explanation:
From the question, we are informed that Mrs. Dillard is installing a cubed swimming pool in her backyard and that the hole that her husband dug in her backyard is 216 feet cubed.
We are further told that she went to the pool store to pick out a pool frame. She chose a pool frame that had a length, width, and height of 7ft.
Since the height is 7ft, the volume will be: = 7ft × 7ft × 7ft = 343 feet cubed.
This shows that the pool frame she choose will not fit in the hole dug. She should have picked a frame of 6feet since (6ft × 6ft × 6ft) = 216 ft cubed.
3. If y = -4 when x = 1/2, find y when = 2/3. MUST SHOW ALL WORK on
separate sheet of paper.
Answer:
its 21/40
Step-by-step explanation:
A population of rats triples every 7 days. If the population starts with 5 rats, how many rats
will there be in 3 weeks?
Answer:
135 rats
Step-by-step explanation:
first do 5 x 3 (because it triples every week) that equals 15 then triple that witch is 45, then triple that one more time, 135 (because you are supposed to do 3 weeks) so its 135 rats! hoped this helped ;)
Devina made a quilt using 142 pieces of fabric. She used 4 times as many fabric pieces to make a second quilt. For her third quilt, she doubled the number of fabric pieces that she used in her second quilt. How many fabric pieces did she use in the third quilt?
Answer:
She used 1,136 fabrics in her third quilt
Step-by-step explanation:
For the first quilt, the number of fabrics used is 142
second quilt is 4 times this = 142 * 4 = 568 quilts
For the third quilt, she doubled the number of fabrics used
That will be 2 * 568 = 1,136 quilts
PLEASE HELPPP!!! Solve r to the nearest tenth of a centimetre.
Answer:
r = 2.7 cm
Step-by-step explanation:
From the figure attached,
To find the value of 'r' we will apply the sine rule in ΔRST,
sin(m∠R) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
sin(20)° = [tex]\frac{r}{SR}[/tex]
sin(20)° = [tex]\frac{r}{8}[/tex]
r = 8sin(20)°
r = 8(0.34202)
r = 2.736
r ≈ 2.7 cm
PLEASE HELP ME OUT!!
The question is in the image below next to the blue x
Answer:
y=3x +5
Step-by-step explanation:
PLSS HELP YALLLLLLLLL
Which equation shows the correct use of the Distributive Property?
−4(3/2x−1/2)=−15
A- 6x + 4 = –15
B- 2x – 1/2 = –15
C- –6x – 2 = –15
D- –6x + 2 = –15
Answer:
D
Step-by-step explanation:
Hope this helped!
Happy Halloween!
You roll a single die numbered from 1 to 6.
What is the probability of rolling an odd
number, expressed as a fraction?
Answer: SEE EXPLANTION!
Step-by-step explanation:
In rolling a die once, you do have a 1/6 chance of getting 6. In rolling a die once (for the second roll), you do have a 1/2 chance of getting an odd number (getting 1, or 3 or 5).
Thank you!
Answer:
1/2.
Step-by-step explanation:
There are 3 odd numbers on the die (1, 3, 5) and 3 even numbers (2, 4, 6). So, the probability would be 3/6 (3 odd out of a total 6 numbers), which simplfies to 1/2.
Identify the slope and the y-intercept of the line written as
L
y + 7 = ] (x + 1)
) m =
6, point: (7, 1)
m = 5, point : (-1, -7)
m = 5, point : (-7,-1)
m =
6, point : (1, -7)
Answer:
m=1/6, point: (-1,-7)
Step-by-step explanation:
the point slope form is y-y1=m(x-x1) and m is the slope and x1 is 1 and y1 is -7 so it will be y-(-7)=1/6(x-(-1)) then when you simplify it, it will be y+7=1/6(x+1)
Help! Will mark branliest
Answer:
<3 = 40 degrees
Step-by-step explanation:
90 + 58 + <1 = 180
148 + <1 = 180
<1 = 32
<1 = <2
32 = <2
<2 + <3 + 108 = 180
32 + <3 + 108 = 180
<3 + 140 = 180
<3 = 40
A complex shape made of 2 shapes. Shape 1 measures 2 centimeters by 1 centimeter. Shape 2 measures 1 centimeter by 1 centimeter. What is the area of the shape? 3 square centimeters 4 square centimeters 6 square centimeters 9 square centimeters
Answer:
77
Step-by-step explanation
add
What is the solution to the following equation? 9x -5x + 11 = 4x -11
Answer:
the answer is no solution
Step-by-step explanation:
when u solve you end up with 0= -22
Given the equation 3x – 4y = 24.
a) Find two solutions to the equation. Show your work. See pages 82 – 85 in your reference guide. Write your answer as coordinates.
b) Using your answers from part a, what is the slope of the given equation. Show your work. See pages 88 – 90 in your reference guide.
c) Convert the given equation into slope-intercept form. Show your work. See page 91 - 93 in your reference guide.
Answer:
Step-by-step explanation:
Given the equation 3x-4y = 24,
The solution of the equation of the equation will be gotten at the point where x = 0 and y = 0 as shown;
when x = 0
3(0)-4y = 24
0-4y = 24
y = 24/-4
y = -6
Also when y = 0
3x-4(0) = 24
3x = 24
x = 24/3
x = 8
Hence the solution of the equation (x, y) are (8, -6)
b) The standard from of equation of a line is y = mx+c where m is the slope. To get the slope of the line, we will need to rewire the equation in slope intercept form first.
Given 3x-4y = 24
-4y = 24-3x
-4y = -3x+24
Divide through by -4
-4y/-4 = -3x/-4 + 24/-4
y = 3/4 x - 6
Comparing
m = 3/4
Hence the slope of the line is 3/4
c) This has been done in (b) above. The equation in slope-intercept form is
y = 2/4 x - 6