Answer:
Initial population = 313
Population after 5 hours = [tex]3.36 \times 10^{11}[/tex]
Step-by-step explanation:
Let initial population = [tex]x[/tex]
It is given that population gets doubled every 10 minutes.
Population after 10 minutes = [tex]2x[/tex]
Population after 20 minutes = [tex]2^{2} x[/tex]
:
:
Population after 80 minutes = [tex]2^{8} x[/tex] and it is given as 80000.
[tex]\Rightarrow 2^{8} x = 80000\\\Rightarrow x = \dfrac{80000}{256}\\\Rightarrow x = 313[/tex]
So, initial population is 312.5 = ~313
To find, population after 5 hours i.e. 5 [tex]\times[/tex] 60 = 300 minutes
Population after 300 minutes =
[tex]2^{30} x\\\Rightarrow 2^{30} \times 313\\\Rightarrow 3.36 \times 10^{11}[/tex]
So, the answers are:
Initial population = 313
Population after 5 hours = [tex]3.36 \times 10^{11}[/tex]
Function g can be thought of as a translated (shifted) version of f(x)=x^2.
PLEASE HELP I NEED THISSS!!!
Answer:
g(x) = x² - 3
Step-by-step explanation:
A quadratic function has been given as,
f(x) = x²
If the function f is translated by 'h' unit down over the y-axis, the new function obtained by the translation is,
g(x) = x² - h
From the graph attached, h = 3 units (shift of 3 units downwards)
Therefore, g(x) = x² - 3 will be the translated version of f(x).
PLEASE HELP ME WITH MY MATHS HOMEWORK BELOW
if you answer it correctly i will rate you 5 stars and brainiest
Answer:
a) 52%
b) 7
Step-by-step explanation:
Total no of grids = 25
Shaded grids = 13
[tex]a) \\Percent \; of \: Shaded\: grids = \frac{13}{25} \times 100 = 13\times 4 = 52\%\\\\b)\\80\% \: of \: 25 =0.80\times 25 = 20\\No \; of \: squares\: more\: than \: 13 = 20 - 13 = 7[/tex]
Which equation is equivalent to
(1/3)^x= 27^X+2
Answer:
x=-1½
Step-by-step explanation:
1/3^x=27^x+2
3^-x=3^3x+6
-x=3x+6
-6=3x+x
-6=4x
x=-1½
If sin 30º = cos(3x), then x=_
Answer:
x = 20º
Step-by-step explanation:
we know that sin x = cos(90-x)
Hence
sin 30º = cos(90 - 30)º
sin 30º = cos 60º
hence sin 30º can be also written as cos 60º
Also, as given
sin 30º = cos(3x)
therefore
cos 60º = cos(3x)
as we have cos on both side then angle for both side will be same
60º = 3x
=> 60º / 3 = x
=> x = 20º
Then x = 20º is answer.
What is the inverse of the function f(x) =1/4x – 12?
Answer:
f(x) = 4x + 48
Step-by-step explanation:
Replace the positions of x and y and isolate y to find the inverse of a function.
y = 1/4x – 12
x = 1/4y – 12
x + 12 = y/4
4(x + 12) = y
4x + 48 = y
f(x) = 4x + 48
PLZ HELP meeeeeeeeeeeeeeeeeeeee
please see the attached picture
Hope it helps
Good luck on your assignment,
MY KEY BROKE AND ITS NOT UNNY
The probability of a biased coin landing on heads is 2/7 complete the tree diagram
Answer:
The numbers needed to fill each box are in the image attached
Step-by-step explanation:
The probability of the coin landing on heads is 2/7, so the probability of it landing on tails is 1 - 2/7 = 5/7
The probability of landing heads 2 times is:
P = (2/7) * (2/7) = 4/49
The probability of landing heads and then tails is:
P = (2/7) * (5/7) = 10/49
The probability of landing tails and then heads is:
P = (5/7) * (2/7) = 10/49
The probability of landing tails 2 times is:
P = (5/7) * (5/7) = 25/49
The numbers needed to fill each box are in the image attached.
Step-by-step:
The first flip numbers will always add up to 1 so you do
1 - 2/7= 5/7
now it gets easy...
The second flip head will be 2/7 because it is a biased dice and the second flip tail will be 5/7
This also applies for the bottom 2: 2/7 head, 5/7 tails
hope this helped :)
Charlie is helping refill ketchup bottles at his uncle's diner. He has a huge container with 2 gallons of ketchup, which he distributes evenly among 15 bottles. How much ketchup goes in each bottle? Write your answer as a proper fraction or mixed number.
Answer:
A = 2/15 gallons per bottle
Step-by-step explanation:
Given;
Total volume of ketchup V = 2 gallons
Number of bottles N = 15
The amount of ketchup per bottle A;
A = total volume of ketchup ÷ number of bottles
A = V/N
Substituting the values;
A = 2gallons ÷ 15bottles
A = 2/15 gallons per bottle
Answer:
2/15
Step-by-step explanation:
2 divided by 15 is the same or equal to 2/15
example: 2 divided by 15= 2/15
help me out please!!!!
Answer:
Answer (e)
Step-by-step explanation:
Note that this graph has a zero at x = 1 and a vertical asymptote at x = -4. Only Answer (e) corresponds to that. Try letting x = 1. y is zero, correct? Try letting x = -4. y is undefined, correct?
How do I solve this problem?
Answer:
x = 12
Step-by-step explanation:
(whole secant) x (external part) = (whole secant) x (external part)
(6+x) *6 = (4+23) * 4
(6+x) *6 = 27*4
6(6+x) = 108
Divide each side by 6
6+x =18
Subtract 6 from each side
6+x-6 =18-6
x = 12
solve for x
8x+6=10 please help me ASAP
Answer:
0.5
Step-by-step explanation:
8x+6=10
8x=10-6
8x=4
x=4/8=0.5
Please answer correctly !!!!!!!!! Will mark brainliest answer !!!!!!!!!!!!
Answer:
I think that C) and D)
Step-by-step explanation:
I think this because if you look at 3.5 secounds it came down and after 1.75 secounds the ball hit the ground. A) wouldn't be because it came down at 3.5 secounds not coming up. B) wouldn't be because the ball droped after 1.75 secounds not come up.
look at the diagram which angle is adjacent and congruent to angle AOE
Answer:
Angle EOC.Step-by-step explanation:
You can observe the figure in the image attached.
Notice that angle AOE is 90°, that is, it's a right angle. (The little red square indicates its perpendicularity).
Now, the adjacent and congruent angle to AOE is angle EOC, because they are on a straight angle, they are supplementary angles and also adjacent angles.
Right triangle LMN has vertices L(7, –3), M(7, –8), and N(10, –8). The triangle is translated on the coordinate plane so the coordinates of L’ are (–1, 8). Which rule was used to translate the image? (x, y) → (x + 6, y – 5) (x, y) → (x – 6, y + 5) (x, y) → (x + 8, y – 11) (x, y) → (x – 8, y + 11)
Answer:
d
Step-by-step explanation:
The rule that was used to translate the image is (x, y) → (x – 6, y + 11)
Translation is a way of moving an object from one location to another on the xy- plane
Given the coordinate of the right triangle LMN with vertices L(7, –3), M(7, –8), and N(10, –8)
If the triangle is translated on the coordinate plane so the coordinates of L’ are (–1, 8), the translation used will be:
L'(1, 8) = (x, y) - L(7, -3)
(X, Y) = L'(1, 8) + L(7, -3)
(X, Y) = (1+7, 8+3))
(X, Y) = (-6, 11)
Hence the rule that was used to translate the image is (x, y) → (x – 6, y + 11)
Learn more here: https://brainly.com/question/1046778
Can anyone help me solve this problem plz need need help asap!
Answer:
25
Step-by-step explanation:
(-5)^2+10(-5)(2)+25(2)^2
=25+(-100)+100
=25
What is the inverse of the function f(x) = 4x + 8
Answer:
let f(x)= y
y = 4x+8
x= 4y + 8
4y = x - 8
y = (x - 8)/4
Hope this helps.
Answer:
x/4 - 2 = y
Step-by-step explanation:
soo switch x and f(x)
x=4y+8
then bring it back to like how it was before
x-8=4y
then
(x-8)/4=y
then simplify
x/4 - 8/4 = y
which can then be simplified to
x/4 - 2 = y
To determine the annual yield (rate of return) on an investment, divide the income from the investment for the year by the original amount invested. Look at the example. Then, calculate the annual yield for the other investment
Savings account: $4 / $200 = 0.02 x 100 = 2%
Bond: $85 / $1000 = 0.085 x 100 = 8.5%
Real Estate: $6,400 / $40,000 = 0.16 x 100 = 16%
The vertices of a rectangle are A(-2, 4), B(-2,6), C(3,6), and D(3, 4). Which expression
shows how to find the length of the diagonal?
Answer:
Third option correct
Step-by-step explanation:
The diagonal is the distance between 2 of the vertices, and to end.
So the option we shall choose will contain 2 of the vertices in a distance between points equation.
Mathematically, the distance between two points is given by;
D = √(x2-x1)^2 + (y2-y1)^2
The correct option is the third option.
This is because it takes into consideration two of the vertices which are points A and point C
Answer: c the third one
Step-by-step explanation:
Marcus saved money from her allowance for some books she wanted to buy. To determine how much money she will save, she used the function rule: y = 6x. Find f (7) A. $13 B. $36 C. $42 D. $49
Answer:
$42
Step-by-step explanation:
Substitute:
Y = 6x
F = 7
So, Y = 6 * 7 = 42
Answer: 42
Step-by-step explanation:
URGENT PLEASE HELP ME I SUCK AT GEO
Answer: 225°
Step-by-step explanation:
Each rotation is 45°
From C to H, there are five rotations
5 * 45 = 225°
Answer:
D: 225 degrees
Step-by-step explanation:
You want to first find the value of each angle that comes in together at point P. To do this, you take 360 degrees/8 degrees. 360 since that is a central angle and 8 because there are 8 congruent angles that make up the central angle. You should get 45 degrees. Then since it takes 5 "45 degree turns" to get onto H, you would do 5 times 45 to get 225.
Factor the polynomial completely.
(y - 8)^2 - 16
Answer:
(y -12)(y -4)
Step-by-step explanation:
This can be factored as the difference of squares:
(y -8)² -16 = (y -8)² -4² = (y -8 -4)(y -8 +4) = (y -12)(y -4)
find the value of k for which the quadratic equation 2x^-kx+=0 have equal roots
Answer:
I'll email it to you
why is x^2-8x+20 always positive?
Answer:
cause it is
Step-by-step explanation:
it just is, sorry i can't help. maybe bc there are more positive functions then negative ones?
I need help with how to solve things like this. The units of the subway map at the right are in miles. Suppose the routes between stations are straight, find the distance you would travel between each the Elm and Symphony Stations. Round your answer to the nearest tenth of a mile. the distance between the Elm and Symphony Stations is how many miles?
Answer:
8 miles OR 8.0 miles
find the value of each trigonometric ratio. Part 1
Answer: [tex]\bold{2)\ sin\ C=\dfrac{20}{29}\qquad 3)\ tan\ A=\dfrac{8}{15}\qquad 4)\ tan\ Z=\dfrac{4}{3}}[/tex]
Step-by-step explanation:
[tex]2) \sin C=\dfrac{\text{side opposite of}\ \angle C}{\text{hypotenuse of triangle}}=\large\boxed{\dfrac{20}{29}}\\\\\\3) \tan A=\dfrac{\text{side opposite of}\ \angle A}{\text{side adjacent to}\ \angle A}=\large\boxed{\dfrac{8}{15}}\\\\\\4) \tan Z=\dfrac{\text{side opposite of}\ \angle Z}{\text{side adjacent to}\ \angle Z}=\dfrac{40}{30}\quad \rightarrow \large\boxed{\dfrac{4}{3}}[/tex]
Which function grows at the fastest rate for increasing values of x? h(x)=2x f(x)=8x2−3x g(x)=19x p(x)=5x3+3
The function p(x) = 5x³ + 3 grows at the fastest rate for increasing values of x.
What is a function?A function is a relation between two sets one is called domain and the other one is range.
Given functions are:
h(x) = 2x
f(x) = 8x² − 3x
g(x) = 19x
p(x) = 5x³ + 3
Here, p(x) = 5x³ + 3 is the only cubic function.
As the degree of the function p(x) is highest among all.
Therefore, this function p(x) grows at the fastest rate for increasing values of x.
Learn more about function here:
https://brainly.com/question/5607159
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Please answer correctly !! Will mark brainliest !!!!!!!!!
Answer:
6 seconds
Step-by-step explanation:
h(x) = 0 m , when the ball is on the ground.
h(x) = - (x-2)² + 16
0 = - (x-2)² + 16
(x-2)² = 16
√(x-2)² = +/- √16
(x-2) = 4 , (x-2) = - 4
x - 2 = 4 , x = -2
x = 6
We can use only positive solution.
..solve the following as fast as
you can using the properties
of additition and multiplication
a)365+94+35
b)896+423+104
c)379×25×4
d)89×125×8
Pls answer fast
Answer:
i hope this will help you
Step-by-step explanation:
a 365+94+35
=494
b 896+423+104
=1423
c 379×25×4
=45480
d 89×125×8
=89000
PLEASE HELP ME According to this diagram, what is cos 23°?
67
13
5
90°
12
12
O
A.
B.
13
12
0
D.
13
E.
5
12
OF.
12
13
Answer:
F. [tex]\frac{12}{13}[/tex]
Step-by-step explanation:
[tex]cos = \frac{adjacent}{hypotenuse}[/tex]
The hypotenuse of a right triangle is the angle that is opposite and not touching the 90 degree angle. In this case, the hypotenuse is 13.
The adjacent side is the side that is touching the angle but not the hypotenuse. That makes the adjacent side in this case 12.
That means that [tex]cos = \frac{12}{13}[/tex].
I hope this helps!
Answer:it’s f.12/13
Step-by-step explanation:
big brain
£750 is divided between Bridget, Caroline & Sarah so that Bridget gets twice as much as Caroline, and Caroline gets three times as much as Sarah. How much does Caroline get?
Answer: £225
Step-by-step explanation:
Amount shared = £750
Let Sarah's share = y
Therefore,
Caroline's share = 3y
Bridget's share = 2(3y) = 6y
Mathematically,
y + 3y + 6y = £750
10y = £750
y = £750/10
y = £75
Caroline's share = 3y
Caroline's share = 3 × £75 = £225
Caroline's share is £225