The size of the red squirrel population has decreased exponentially
over the past few years in the UK.
The rate of decrease is 15% per year.
At the start of 2016 there were an estimated 10000 red squirrels in the UK.
Estimate the size of the population of red squirrels in the UK at the start of 2010.
Give your answer to 3 significant figures.
Answer:
The size of the population of red squirrels in the UK at the start of 2010 is 3772
Step-by-step explanation:
At the start of 2016 , No. of squirrels = 10000
The rate of decrease is 15% per year.
So, No. of squirrels after x years = [tex]10000(1-0.15)^x[/tex]
We are supposed to find the size of the population of red squirrels in the UK at the start of 2010.
So,No. of squirrels after 6 years = [tex]10000(1-0.15)^6=3771.49[/tex]
Hence the size of the population of red squirrels in the UK at the start of 2010 is 3772
Answer:
Step-by-step explanation:
The population in 2016 is 10,000 but we re trying to find the population in 2010.
Let the start population be P.
Then P*(1-0.15)^6 = 10000
P*(0.85)^6 = 10000
P = 10000 / (0.85)^6
P = 26514.6834
In 2010 :
P = 26500 to 3 significant figures
9. y=-2(x-3)
10. 12x + 30 y = 10
11. y = -5x+2
12. y=6+36-1)
13. y-3 = 2x
14. y=-3-4(x+9)
intercept form
Answer:
9. y= -2x+6
10. y= -0.4x+ [tex]\frac{1}{3}[/tex]
11. y = -5x+2
12. y=41
13. y=2x+3
14. y= -4x-39
Step-by-step explanation:
9.
y= -2(x-3)
y= -2x+6
10.
12x+30y=10
Subtract 12x from both sides
30y=10-12x
Divide both sides by 30
y= -0.4x+ [tex]\frac{1}{3}[/tex]
11.
y = -5x+2
(Already solved)
12.
y=6+36-1
y=41
13.
y-3=2x
Add 3 to both sides
y=2x+3
14.
y= -3-4(x+9)
y= -3-4x-36
y= -4x-39
PLEASE HELP I WILL MARK BRAINLIEST
Answer:
(cos^2(x)-1) cot (-x); last expression.
Step-by-step explanation:
You'll first need to simplify the given expression. Then look at each option. To find out whether or not two expressions are equivalent see if they have the same value irrespective of the value of the variables in them.
1) (1-cos^2(x)) cot (-x) is equivalent
2) (cos^2(x)-1) cot(x) is equivalent
3) (sin62(x)-10 tan (x) is equivalent
4) (cos^2(x)-1) cot (-x) is not equivalent.
Analyze Nick's solution. Is he correct? If not, what was
his mistake?
Yes, Nick is correct.
O No, the power multiplied to 8.64 should have an
exponent of 0.
No, he needed to subtract the coefficients.
X No, he needed to add the exponents.
Answer: No, the power multiplied to 8.64 should have an exponent of 0. B pretty much
Step-by-step explanation: just got that question trust me it’s right.
Answer:
No, the power multiplied to 8.64 should have an exponent of 0.
PLZ HELP ME W DIS ASAP!!!
Answer:81/m^7(D)
Step-by-step explanation:
81m^5/12
81/m^7
If |x−2|=p, where x<2, then x−p = (A) −2 (B) 2 (C) 2−2p (D) 2p−2 (E) |2p−2|
Answer:
A
Step-by-step explanation:
is the answer because x-x = 0
since -2 is left that's the answer!
Select the correct answer.
The sum of two numbers is -18. If the first number is 10, which equation represents this situation, and what is the second number?
A. The equation that represents this situation is 10 - x= -18. The second number is 28.
OB.
The equation that represents this situation is 10+ x=-18. The second number is -28.
C.
The equation that represents this situation is r- 10 =-18. The second number is -8.
D. The equation that represents this situation is -10+ x = -18. The second number is -8.
Answer:
Thw answer would be B
Step-by-step explanation:
Answer:
OB.
The equation that represents this situation is 10+ x=-18. The second number is -28.
Step-by-step explanation:
First, sum means added together.
Second, one value in the sum is given so:
10+(var)=-18
var=8
and if we solve, we get -28.
20 POINTS !! PLEASE ANSWER THIS QUESTION !!
Answer:
a.
Step-by-step explanation:
It is not a negative so it can’t be c or d I think it is a
Answer:b
Step-by-step explanation:
Each of three friends flips a coin 71 times. The results for each friend are shown in the tables. Find the Each of three friends flips a coin 71 times. The results for each friend are shown in the tables. Find the relative frequency for the event "heads" for each friend. If the friends combine their results to get 101 heads and 112 tails, what is the relative frequency for the event "heads"? Use pencil and paper. Suppose each friend flips a coin 710 times. Is there a value you would expect the relative frequency for the event "heads" to be close to?
For friend 1, the relative frequency is [tex]\frac{25}{71}\approx 0.352.[/tex]
For friend 2, it's [tex]\frac{53}{71}\approx 0.746,[/tex] and for friend 3, it's [tex]\frac{23}{71}\approx 0.319.[/tex]
Combining the data of all three would give a relative frequency of [tex]\frac{101}{213}\approx 0.474.[/tex]
If each friend were to flip a coin 710 times, assuming the coin to be a fair coin, we'd expect about half of the flips to be heads, so the relative frequency would be close to 0.5.
(2x+3y)+(8x+10y) simplify the following
Answer:
10x+13y
Step-by-step explanation:
remove parentheses:
2x+3y+8x+10y
add like-terms:
2x+8x+3y+10y
add numbers with the same variables/elements
10x+3y+10y-->10x+13y
hope this helps
Hello!
Answer:[tex]\boxed{ \bf The~correct~answer~is~10x~+~13y.}[/tex]
________________________________________________
Explanation:(2x + 3y) + (8x + 10y)
First, drop the brackets:
2x + 3y + 8x + 10y
Next, collect like terms:
2x + 8x + 3y + 10y
Finally, add the like terms together:
10x + 13y
Which statement is true regarding the functions on the
graph?
WN
(6)
f(3) = 9(3)
f(3) = g(6)
(6) - 9(6)
-124
Answer:
the last one
Step-by-step explanation:
Nancy prepared 12 kilograms of dough after working 6 hours. How much dough did Nancy prepare if she worked for 10 hours? Solve using unit rates.
Answer:
20 kilograms of dough
Step-by-step explanation:
Given that;
12 kilograms working 6 hours
Rate = 12/6 kilogram per hour = 2 kilogram per hour
So,
In 10 hours he would produce;
Amount of dough = Time × rate
Time = 10 hours
= 10 hours × 2 kilograms per hour
= 20 kilograms of dough
Answer:
20 kilograms of dough
Step-by-step explanation:
Given;
12 kilograms of dough for 6 hours
how many of this will be produced in 10 hours ?
= (12 x 10) / 6
= 20 kilograms of dough
=
The area of a square patio is 36 ft sq. What are the side measurements of the patio?
2 ft by 18 ft
4 ft by 9 ft
3 ft by 12 ft
6 ft by 6 ft
please hellppppp!
Answer:
6ft by 6 ft
Step-by-step explanation:
area of a square =length*width whereas they are supposed to be of the same measurements
A ball is thrown straight up from the top of a 40 feet tall building with an initial speed of 24 feet per second. The height of the ball as a function of time can be modeled by what function h(t) = _________________ 1. after how many seconds the ball hit the ground. 2.What is the maximum height of the ball? 3.How long did it take for the ball to reach its maximum height?
Answer:
1)The ball hits the ground after 3 seconds.
2)The maximum height of the ball is 49 feet
3)It takes 1.25 seconds to reach its maximum height
Step-by-step explanation:
Height of building = 40 feet
We are given that A ball is thrown straight up from the top of building with an initial speed of 24 feet per second.
So, The height of the ball as a function of time can be modeled by: [tex]h(t)=-16t^2+40t+24[/tex]
1)After how many seconds the ball hit the ground.
Substitute h(t)=0
So,[tex]-16t^2+40t+24=0\\-2t^2+5t+3=0\\2t^2-5t-3=0\\2t^2-6t+t-3=0\\2t(t-3)+1(t-3)=0\\(2t+1)(t-3)=0\\t=\frac{-1}{2} , 3[/tex]
Since time cannot be negative
So,the ball hits the ground after 3 seconds.
2)What is the maximum height of the ball?
It takes maximum height at vertex
Formula : [tex]t = \frac{-b}{2a}[/tex]
[tex]t=\frac{-40}{2(-16)}=1.25 seconds[/tex]
Substitute the value of t in function
[tex]h(1.25)=-16(1.25)^2+40(1.25)+24\\h(1.25)=49 feet[/tex]
So,the maximum height of the ball is 49 feet
3).How long did it take for the ball to reach its maximum height?
It takes 1.25 seconds to reach its maximum height
write down in terms of n an expression of the following sequences
a) 12 10 8 6 4
b) 25 20 15 10 5
Answer:
[tex]-2n+14[/tex]
[tex]-5n+30[/tex]
Step-by-step explanation:
-2 difference.
[tex]u_{n} =-2n+c[/tex]
[tex]u_{1} =-2(1)+c=12[/tex]
[tex]c=14[/tex]
-5 difference.
[tex]u_{n} =-5n+c[/tex]
[tex]u_{1} =-5(1)+c=25[/tex]
[tex]c=30[/tex]
The graph of equation (3,-2) passes through which point
Answer:
If the y-intercept is 0, then this graph passes through [3,-2][6,-4][9,-6] and so forth.
Step-by-step explanation:
Rise over run, 3 is the rise, and -2 is the run. Using this you can find any point on the line up to infinity.
Answer:
it passes through y intercept
Please mark me as a Brainliest
the scale on the map is 1: 20000. The area of a lake on a map is1.6 square centimetres. give the actual area of the lake
Answer:
6.4 × 10^8
Step-by-step explanation:
Question 7
The equation of a straight line AB is
[tex] \frac{x}{2} + \frac{y}{2} = 1[/tex]
(a) Find the gradient of line AB.
(b) Find the y-intercept of line AB.
(c) A second line PQ is parallel to the line AB and passes through a point (2, -8).
Show that the second line PQ also passes through the point(-1,-5)
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
[tex]\frac{x}{2}[/tex] + [tex]\frac{y}{2}[/tex] = 1 ( multiply through by 2 to clear the fractions )
x + y = 2 ( subtract x from both sides )
y = - x + 2 ← in slope- intercept form
(a) with slope m = - 1
(b) with y- intercept c = 2
(c)
Parallel lines have equal slopes, thus
y = - x + c ← is the partial equation of PQ
To find c substitute (2, - 8) into the partial equation
- 8 = - 2 + c ⇒ c = - 8 + 2 = - 6
y = - x - 6 ← equation of PQ
To show (- 1, - 5) lies on PQ, substitute x = - 1 into the equation and evaluate for y.
y = - (- 1) - 6 = 1 - 6 = - 5 ← the given y- coordinate
Thus PQ passes through (- 1, - 5 )
need help ezy points plz
Answer:
24 cubic inches.
Step-by-step explanation:
[tex]2a \times a^{2} +a^{3} \\2a^{3} +a^{3}[/tex]
[tex]3a^3\\3(2)^3\\3 \times 8[/tex]
If you were an integer, which integer would you be and why?
Answer:
6
Step-by-step explanation:
Because my lucky num is 6
Answer: 7
Step-by-step explanation:because it is one of my favorite integers
15) Martha wants to put carpet in a rectangular room that measures 14 feet by 16 feet. There is a section in front of
the door which measures 3 feet by 4 feet that will remain tiled. How many square feet of carpet will Martha need?
Answer:
5 ft
Step-by-step explanation:
Please answer correctly !!!!!! Will mark brainliest !!!!!!!!!!!!!
Answer:
At the time of launch height of the object was 60 meters.
Step-by-step explanation:
An object was launched from a platform and its height was modeled by the function,
h(x) = -5x² + 20x + 60
Where x = time or duration after the launch
At the time of launch, x = 0
So, by putting x = 0 in this equation,
h(0) = -5×(0) + 20×(0) + 60
h(0) = 60
Therefore, at the time of launch height of the object was 60 meters.
A person is listening to a 500 Hz tone sitting from a distance of 450 m from the sound source. What is the time interval between successive compressions from the source?
Answer:
So, the time interval between successive compression from the source is 0.002 seconds.
Step-by-step explanation:
Given that,
Frequency of the tone, f = 500 Hz
It is sitting at a distance of 450 m from the source of sound, d = 450 m
Let t is the time interval between successive compression from the source. We know that the relation between the frequency and the time period is :
[tex]T=\dfrac{1}{f}T=\dfrac{1}{500}\\\\T = 0.002 s[/tex]
So, the time interval between successive compression from the source is 0.002 seconds.A bag contains 14 green tiles,10 red tiles, and 16 blue tiles. Brodie randomly draws a tiel, records the color , and replaces the tile.if he does this 80 times, how many times should he expect to draw a red tile
Answer:
20 red tiles
Step-by-step explanation:
14 green tiles,10 red tiles, and 16 blue tiles. = 40 tiles
P(red) = 10/40 = 1/4
If we draw 80 tiles
80 * 1/4 = 20
We should expect 20 red tiles
please help i don’t know what to do and this will help me pass 7th grade thank you!!!
Height of table is 18 inches
Height of one block is 2 inches
The height would be 34 inches with 8 blocks ✌️
Answer:
Well each block is 2
Step-by-step explanation:
cause the height of the table is 18 itself it says in the table and one block just adds 2
i hope it's right sorry if it's not
I understand the struggle
Samy's car can hold 20 gallons of
gasoline in its fuel tank. It is 3/4 full. He
can travel 15 miles for every gallon of
gasoline.
Rosa car has 13 gallons of gasoline in
the fuel tank and she can travel 19 miles
for every gallon of gasoline.
If they both start at the same place and
travel at the same constant speed, who
will go farther?
Answer:.
Justification:
Answer:
Rosa will go farther.
Step-by-step explanation:
1. Samy's travel distance.
3/4 of 20
3/4 * 20 = 15 gallons
15 miles for every gallon
15 * 15 = 225
Samy's travel distance is 225 mIles
2. Rosa travel distance.
13 gallons
19 miles for every gallon
19 * 13 = 247 mIles
Rosa's travel distance is 247 mIles.
Please answer correctly !!!!!!!! Will mark brainliest !!!!!!!!
Answer:
(7,7)
Step-by-step explanation:
The maximum point in a graph is where the y value is the highest. On this graph, the point (7,7) has the highest y value of 7 of the entire graph, making it the maximum. Hope this helps!
If a line is perpendicular to a line segment, what angle do they form at their
intersection?
A. 90°
B. 45°
C. 180°
D. 09
can someone pls explain how you find the x intercept and how to solve a slope intercept form question????
Answer:
See below
Step-by-step explanation:
Let me give you an example to help;
[tex]y = 2x + 3[/tex]
This equation is in slope - intercept form, which can be demonstrated through the following notation -
[tex]y = mx + b - Where, m = slope, and, b = y - intercept[/tex]
Now to solve for the x - intercept, we will have to propose y as 0;
[tex]0 = 2x + 3,\\2x = - 3,\\x = - 3 / 2 = - 1 and 1 / 2[/tex]
Thus the x - intercept = - 1 and 1 / 2;
* Note that you can't solve a slope intercept form equation, unless it is a system of equations, and if that is the case just let me know and I can help you out with that *
Can someone please help me with this!!
Answer:
33.7°
Step-by-step explanation:
The smallest angle -> opposite of the smallest side
Smallest side = 10yards
Calling this angle a
we have 10^2 = 15^2 +18^2 -2*15*18*cosa
-> cos a=0.83
cos^-1(a)=0.83 -> a =33.7 degree
