A city starts with a population of 500,000 people in 2007. Its population declines according to the equation
P(t) = 500,000e -0.099t
where P is the population in t years later. Approximately when will the population be half the initial amount?
Answer:
2014
Step-by-step explanation:
Given the exponential growth function :
P(t) = 500,000e^-0.099t
Where P is population in t years later
When the population will 1/2 the initial amount
1/2 the initial amount = 1/2 * 500,000 = 250,000
P(t) = 250,000
250,000 = 500000e^-0.099t
250,000/500000 = e^-0.099t
In(0.5) = - 0.099t
t = −0.69314 / - 0.099
t = 7.0014
t = 7
Year which population = 500,000 = 2007
Hence, half the population will be attained on (2007 + 7) = 2014
After 7 years population of the city will be half of the initial amount.
Population function:
[tex]P(t) = 500000 e^{-0.099t}[/tex]
Initial population means population at t=0
P(0) = 500000
Half of initial population = 250000
So, we need to calculate the time t when the population will be half of the initial amount.
[tex]250000= 500000 e^{-0.099t}\\\\e^{-0.099t} = \frac{1}{2}[/tex]
Taking log both sides
-0.099t (log e)= log (1/2)
What is the logarithm of e?The logarithm of e is 1 when considering the base of the log as e.
So, -0.099 t= -0.693
t=7
Therefore, After 7 years population of the city will be half of the initial amount.
To get more about logarithm visit:
https://brainly.com/question/11495859
What is the value of 378÷(710⋅−30)?
Answer:
0.555882
Step-by-step explanation:
John is playing a game of darts. The probability that he throws a dart into the center of the dart board (the Bull’s eye) is. The probability that he throws the dart into the 10-point ring is. What is the probability that he either hits a Bull’s eye or scores 10 points?.
The probability that the John either hits a Bull’s eye or scores 10 points in the game of darts is 2/5.
What is probability?Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event. The probability of an event can not be more than the number 1.
John is playing a game of darts. In this game of dart,
The probability that he throws a dart into the center of the dart board (the Bull’s eye) is 1/10. The probability that he throws the dart into the 10-point ring is 3/10.The probability that he either hits a Bull’s eye or scores 10 points is equal to the sum of the probability he hits the bull's eye and the probability that he throws the dart into the 10-points ring.
Let, the probability that he either hits a Bull’s eye or scores 10 points is P. Thus,
[tex]P=\dfrac{1}{10}+\dfrac{3}{10}\\P=\dfrac{4}{10}\\P=\dfrac{2}{5}[/tex]
Hence, the probability that the John either hits a Bull’s eye or scores 10 points in the game of darts is 2/5.
Learn more about the probability here;
https://brainly.com/question/24756209
Answer:
Option D is the correct answer
Step-by-step explanation:
D.[tex]\frac{2}{5}[/tex]
Select the correct answer. Find the solution(s) for x in the equation below. x2-9x+20=0
The formula to find the volume of a sphere is V=3.14r^3 where r is the
radius of the sphere. What is the formula in terms of r?
PLEASE HELP!
divide by 3.14 on both sides first.
V/3.14 = r^3
Now cube root both sides.
3√(V/3.14) = r
r = 3√(V/3.14)
r is the cube root of v/3.14.
Find the value of f(-3) if f(x) = -3x + 7
Answer:
f(-3) = -3(-3) + 7
= 9 + 7
= 16
ASAP!! I need help. -w-Which answer choice shows 5 +0.9 + 0.06 written in standard form?
OA) 0.0596
OB) 0.596
OC) 5.96
OD) 59.6
Answer:
Hey!
Your answer is 5.96!
Step-by-step explanation:
5 + 0.9 = 5.9
IF WE ADD 0.06...it makes 5.96
(the 6 is in the hundredth column so it goes AFTER the 9)
This fives us 5.96!
I HOPE THIS HELPED YOU!What is the answer to this figure when I solve for x?
x / 9.8 = 6.4 / 11.2
x = 6.4 / 11.2 * 9.8 = 5.6
PLEASE HELP!!
Question: Select All Equations Where C=9
Is A Solution
*Choose 2 Answers*
Answer: d and e
Step-by-step explanation:
a) 4 - 9 = 5 FALSE
b) 20 = 14 + 9 FALSE
c) 15 = 9 - 6 FALSE
d) 9 divided by 3 = 3 TRUE
e) 36 = 4 x 9 TRUE
Answer is D and E
Step-by-step explanation:
Option D u will multiply each side by the LCM which is 3 and u will get the answer to be C=9
option E u will divide both side by 4 and u will get the answer to be C=9
How much can a computer technician earn in two
years? Assume there are no raises in that time.
Helpppppppp
Answer:
$72,920
Step-by-step explanation:
36,460 x 2 = 72,920
Whats the area?/ ty show work!
Answer:
25
Step-by-step explanation:
4 times 3 is 12
5 times 3 is 15
15 plus 12 is 25
Hello!
(4*3) + (3*5)
= 12+15
= 27
Juan solved the problem in the example by dividing the figure into a rectangular prism and a trangular prism. show how to find the volume this way
Answer:
Huh?
Step-by-step explanation:
I don't understand
what is the remainder of -x^3-x^2+3 / x+3
Answer:
21
Step-by-step explanation:
The remainder on dividing f(x) by (x + h) is f(- h)
Given
f(x) = - x³ - x² + 3 , then
f(- 3) = - (- 3)³ - (- 3)² + 3 = - (- 27) - (9) + 3 = 27 - 9 + 3 = 21 ← remainder
if 2:5=x:20 then x=?
a)50 b)2 c)1/2 d)8
Answer:
x = 8
Step-by-step explanation:
Write as fraction form
[tex]\frac{2}{5}=\frac{x}{20}[/tex]
[tex]\mathrm{Switch\:sides}[/tex]
[tex]\frac{x}{20}=\frac{2}{5}[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:}10[/tex]
[tex]\frac{x}{20}\cdot \:10=\frac{2}{5}\cdot \:10[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]\frac{x}{2}=4[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:}2[/tex]
[tex]\frac{2x}{2}=4\cdot \:2[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]x=8[/tex]
Hence, Answer is [D} x = 8
~Learn with Lenvy~
Solution:
Given:
[tex]2:5 = x:20[/tex]
We know that:
Since the LHS and the RHS are equal, they form a proportion[tex]\text{a:b} = \text{c:d} \rightarrow \text{ad} = \text{bc}[/tex]To find x, let's multiply the extremes and put the product on one side. Then multiply the middles and put the product on the other side.
⇒ [tex]2:5 = x:20[/tex]⇒ [tex]2 \times 20= x \times 5[/tex]Now, solve for x.
⇒ [tex]2 \times 20= x \times 5[/tex]⇒ [tex]40 = 5x[/tex]⇒ [tex]\frac{40}{5} = \frac{5x}{5}[/tex]⇒ [tex]\boxed{x = 8}[/tex]which of the following is a quadratic inequality
y>x3+x2
y
y2+3x+4
Answer:
y>x3+x2
Step-by-step explanation:
it has the greater than sign
what is 0.728416 rounded to the nearest tenth
Answer:
0.7
Step-by-step explanation:
In order to determine if the tenth place is rounded up one number or stay the same, you have to look at the hundredths place. In this scenario it's the 2.
0.728416
If the hundredths place is 5 or greater, you round up in the tenth place. If the hundredths place is 4 or less you keep the same number in the tenth place.
2/3 divided by 1/4? Thank you
Answer:
2.66666666667
Step-by-step explanation:
two over three divided by one over four is 2.66666666667
Prove triangle ABC is congruent to triangle CDA
Answer:
Step-by-step explanation:
If the circumference of a circle is increased by 40%,
then the area of the circle is increased by
A. 18%. B. 20%. C. 40%. D. 96%.
Answer:
96%
Step-by-step explanation:
c=100=22/7D
D=7/22×100
get the radius and find the area
R=D/2
A=pi×r^2
repeat that assuming
C=140
get the area
find the %age
A2_A1=Area difference
A(diff)/A1×100=96.01%
[tex]r_{2}[/tex]Answer:
D) 96%
Step-by-step explanation:
let the circumference of circle be C = 2π[tex]r_{1}[/tex] and [tex]r_{1}[/tex] = [tex]d_{1}[/tex]/2
Initial radius (radius before increment) = [tex]r_{1}[/tex]
initial diameter (diameter before increment) = [tex]d_{1}[/tex]
Increasing the circumference of a circle other factors are constant except the radius which can be used to find the diameter hence increasing the circumference of a circle is equivalent to increasing the diameter
area of the circle before increment [tex]A_{1}[/tex] = π[tex]r_{1}[/tex]²
[tex]A_{1}[/tex] = π × ([tex]d_{1}[/tex]/2)²
[tex]A_{1}[/tex] = π[tex]d_{1}[/tex]²/4
Increment of circumference results to increment of only the diameter
diameter after increment by 40%, [tex]d_{2}[/tex] = 1.4[tex]d_{1}[/tex]
1.4 represents increment by 40%
radius after increment [tex]r_{2}[/tex] = [tex]d_{2}[/tex]/2 = 1.4[tex]d_{1}[/tex]/2 = 0.7[tex]d_{1}[/tex]
area after increment, [tex]A_{2}[/tex] = π[tex]r^{2} _{2}[/tex]
[tex]A_{2}[/tex] = π(0.7[tex]d_{1}[/tex])²
[tex]A_{2}[/tex] = π × 0.49[tex]d_{1}[/tex]²
Change in area = [tex]A_{2}[/tex] - [tex]A_{1}[/tex]
[tex]A_{2}[/tex] - [tex]A_{1}[/tex] = π × 0.49[tex]d_{1}[/tex]² - π [tex]d_{1}[/tex]²/4
[tex]A_{2}[/tex] - [tex]A_{1}[/tex] = π [tex]d_{1}[/tex]²(0.49 - ¼)
[tex]A_{2}[/tex] - [tex]A_{1}[/tex] = π [tex]d_{1}[/tex]²(0.49 - 0.25)
[tex]A_{2}[/tex] - [tex]A_{1}[/tex] = 0.24 π[tex]d_{1}[/tex]²
Percentage increment = ([tex]A_{2}[/tex] - [tex]A_{1}[/tex]/ [tex]A_{1}[/tex]) × 100
= ((0.24 π[tex]d_{1}[/tex]²)/(π[tex]d_{1}[/tex]²/4)) × 100
= (0.24 × 4 ) × 100
= 0.96 × 100
= 96 %
Hope it was useful
How many colors are there (estimate)
Answer:
There is very very very near 1,000,000 (shades included in those colors)
Step-by-step explanation:
Hi!there are about 18 decillion colors.So how do we know there are 18 decillion colors? First of all, scientists have determined that in the lab we can see about 1,000 levels of dark-light and about 100 levels each of red-green and yellow-blue. So that's about 10 million colors right there. And then you have to allow for other matters.
Two congruent trapezoids are joined at the dotted line as shown in the model below.
What is the area of both trapezoids in square centimeters
Let's see.
[tex]\\ \sf\Rrightarrow Area=\dfrac{1}{2}(Sum\:of\: parallel\:sides)Height[/tex]
[tex]\\ \sf\Rrightarrow Area=\dfrac{1}{2}(6+9)(4)[/tex]
[tex]\\ \sf\Rrightarrow Area=2(14)[/tex]
[tex]\\ \sf\Rrightarrow Area=28cm^2[/tex]
Area of both=2(28)=56cm^2Select the correct answer from the drop-down menu
23
Central angle BAC of circle A measures 20" radians. Arc BC has a length of 63.487 centimeters. What is the radius of the circle?
The radius of circle A is ✓ centimeters.
Answer:
r = 55.2 cm
Step-by-step explanation:
the arc length is calculated as
arc = circumference × fraction of circle
= 2πr × [tex]\frac{\frac{23}{20}\pi }{2\pi }[/tex] ( r is the radius )
given arc = 63.48π , then
2πr × [tex]\frac{\frac{23}{20}\pi }{2\pi }[/tex] = 63.48π ( cancel 2π on numerator/ denominator )
r × [tex]\frac{23}{20}[/tex] π = 63.48π ( divide both sides by π )
[tex]\frac{23r}{20}[/tex] = 63.48 ( multiply both sides by 20 to clear the fraction )
23r = 1269.6 ( divide both sides by 23 )
r = 55.2 cm
Answer: 55.2
Step-by-step explanation:
got it correct on my test!
what is an equation of the line through (3, -1) and (2, 14)?
Step-by-step explanation:
no explanations.I have done the whole sum
Match each set of numbers with their least common multiple.
504
288
84
44
200
108
22 and 4=
9, 8, 7=
27, 12,,36=
25 , 8=
14 ,12=
32, 24 18=
Answer:
22 and 4 = 44 9, 8, 7= 504 27, 12, 36= 108 25, 8= 200 14, 12= 84 32, 24, 18= 288
Step-by-step explanation:
Christie has $200 in her bank account. Every month, she deposits $20 into her account. The equation of the line that models the amount of money, y, in her account x years from now is y = x=
Answer:
The equation is y = x20 + 200
Step-by-step explanation:
Sorry if this is not what you are looking for.
Showing all necessary working out, evaluate 7/10 - 1/4
Answer:
[tex]\frac{9}{20}[/tex]
Step-by-step explanation:
[tex]\frac{7}{10}-\frac{1}{4}[/tex]
Find lcm : 20
[tex]=\frac{14}{20}-\frac{5}{20}[/tex]
[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{c}-\frac{b}{c}=\frac{a-b}{c}[/tex]
[tex]=\frac{14-5}{20}[/tex]
[tex]\mathrm{Subtract\:the\:numbers:}\:14-5=9[/tex]
[tex]=\frac{9}{20}[/tex]
~Learn with Lenvy~
Daniel drinks a 96 ounce energy drink containing 89 calories per 24 ounces. How many calories did he drink?
Answer:
356
Step-by-step explanation:
Pease Help. Will mark Brainliest
Answer:
the answer is b
Step-by-step explanation:
Answer:
The Answer will be B
Step-by-step explanation:
an equilateral triangle has two sides given as (3x-2)cm and (18+x)cm what is the perimeter
Answer:
84 cm
Step-by-step explanation:
Equilateral triangle have sides that measure the same
so
3x-2 = 18+x
Subtract x from each side
3x-2-x =18+x-x
2x-2 = 18
Add 2 to each side
2x-2+2 = 18+2
2x= 20
Divide by 2
2x/2 = 20/2
x = 10
The side measures18+x = 18+10 = 28
The perimeter is 3 times the length of one side
3*28 = 84
help pls and tysmm!!
At the market, Joey buys 3 avocados for $0.40 Each and 5 lemons for $0.40 each. The cashier in training rings up 3x0.40 and then 5x0.40 to get the total. The experienced cashier says to add the 3 plus 5 in his head and then ring up 8x0.40. What property says that these two totals would be the same
Answer:
Distributive property
Step-by-step explanation:
Distributive property states that,
multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
That is,
a(b + c) = ab + ac
3 avocados cost $0.40 each
3x0.40
= $1.2
5 lemons cost $0.40 each.
5x0.40
= $2
Total = $1.2 + $2
= $3.2
Using distributive property
(3+5)0.40
= 8(0.40)
= $3.2
Answer: Distributive property
Step-by-step explanation:
The Distributive property is the same as a(b + c) = ab + ac