Using an exponential equation, it is found that the estimate for the park's elephant population for the year 2020 is of 12967.
An increasing exponential equation is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.In this problem:
In 2010, there were 8350 elephants, hence [tex]A(0) = 8350[/tex].Growth rate of 4.5%, hence [tex]r = 0.045[/tex]Then:
[tex]A(t) = 8350(1 + 0.045)^t[/tex]
[tex]A(t) = 8350(1.045)^t[/tex]
2020 is 10 years after 2010, hence, we have to find A(10).
[tex]A(10) = 8350(1.045)^{10} = 12967[/tex]
The estimate for the park's elephant population for the year 2020 is of 12967.
A similar problem is given at https://brainly.com/question/22733028
Compound Interest. Pre calc.
Ignore what I have written so far.
a) The initial number of infections refers to the time t = 0, not 1. At the start, there are
[tex]P(0) = \dfrac{700}{1 + 49e^{-0}} = \dfrac{700}2 = \boxed{350}[/tex]
infected students.
b) Here you look for the time t such that P(t) = 600. We have
[tex]\dfrac{700}{1+49e^{-0.3t}} = 600[/tex]
[tex]\dfrac{700}{600} = 1+49e^{-0.3t}[/tex]
[tex]\dfrac76 = 1+49e^{-0.3t}[/tex]
[tex]\dfrac16 = 49e^{-0.3t}[/tex]
[tex]\dfrac1{294} = e^{-0.3t}[/tex]
[tex]\ln\left(\dfrac1{294}\right) = \ln\left(e^{-0.3t}\right)[/tex]
[tex]-\ln(294) = -0.3t \ln(e)[/tex]
[tex]\ln(294) = \dfrac3{10}t[/tex]
[tex]t = \dfrac{10}3 \ln(294) \approx 18.945[/tex]
Rounding up, the school will close after around 19 days.
The price of a packet of sweets has increased by 25% since last year.
If a packet of sweets cost £1.60 last year, how much does it cost now?
Step-by-step explanation:
25% of 1.60
25 ÷ 100 × 1.60
= 0.4
Cost of sweets this year : 1.60 + 0.4
= 2
5+8 = 13 but 8+5 = 14 explain
Answer:
Their both the same answers which is 13
Step-by-step explanation:
Why is unit rate the only attribute we use to compare proportional relationships?
Answer:
Because its an internationally accepted method.
Step-by-step explanation:
Aiden receives a pay rise of 15%, which increases their pay to $17,250. Calculate his salary before the increase.
Answer:
$15,000
Step-by-step explanation:
Let P represent Aiden's current pay.
If they receive a pay rise of 15%, that means they receive their original pay plus 15% of that original pay.
P + 0.15P = 17250
1.15P = 17250
P = 17250/1.15 = 15000
His salary before the increase was $15,000.
Answer:
$14662.5
Step-by-step explanation:
Aiden receives a pay rise of 15%
increases their pay to $17,250
15% of $17,250 is $2587.5 therefore $17,250 - $2587.5 is his salary before the increase which is 14662.5 so aiden had $14662.5 before his salary increase
PLEASE HELP QUESTION 4 ILL GIVE BRAINLIEST
Answer:
7
Step-by-step explanation:
We take the information in the problem and translate it into a linear equation of the form 3x-8=13. Combining like terms we get 3x=21. next divide both sides by 3 for a final answer of x=7
the length of a rectangle is (2x + 1) the width of the rectangle is (x^2 + 2x - 1). which expression represents the perimeter of the rectangle?
Answer:
(2x+1+x^2+2x-1)*2=2x^2+8x
Step-by-step explanation:
Simplify.
–36 + (–74)
–110
–100
38
110
-------------------------------
- 36 + (-74)
- 36 - 74
- 110
<3
Complete the square leave your answer in root form. 2x² - 6x - 3 = 0
Answer:
x = 1.5 ± √3.75
Step-by-step explanation:
There are several variations of completing the sqaure.
This is the one I use.
-------------------------------------
2x² - 6x - 3 = 0
add 3 to both sides
2x² - 6x = 3
the x² coefficient must be 1
so divide both sides by 2
x² - 3x = 1.5
use half the x coefficient (-3/2 = -1.5) as the complete the square term
(x - 1.5)² = 1.5 + (-1.5)²
(x - 1.5)² = 1.5 + 2.25
(x - 1.5)² = 3.75
Take the square root of both sides
x - 1.5 = ± √3.75
add 1.5 to both sides
x = 1.5 ± √3.75
Answer:
x = 1.5 + √3.75 ; x = 1.5 - √3.75
Step-by-step explanation:
2x² - 6x -3 = 0
Add 3 to both sides
2x² - 6x = 3
Divide the entire equation by the coefficient of x²
[tex]\dfrac{2x^{2}}{2}-\dfrac{6x}{2}=\dfrac{3}{2}\\[/tex]
x² - 3x = 1.5
Divide the coefficient of x by 2 and then square it and add to both sides.
3/2 = 1.5
1.5² = 2.25
Add 2.25 to both sides
x² - 3x + 2.25 = 1.5+2.25
(x - 1.5)² = 3.75
Take square root,
x - 1.5 = ±√3.75
x = 1.5 ± √3.75
Please help I’ll give brainylist in return thank you
Jill invests $7,972 in a retirement account with a fixed annual interest rate compounded continuously. After 15 years, the balance reaches
$16,876.72. What is the interest rate of the account?
The interest rate of Jill's account as described is; 0.51%
The amount invested by Jill is $7,972.
According to compound interest;
A = P {1 + (r/n)}^nt.In which case;
A = final amount = $16,876.72P = principal amount = $7,972r = interest rate = ?n = number of times interest is compounded per time = 1t = time = 15Therefore;
$16,876.72 = $7,972 (1 + r/1)^(1×15)$16,876.72/$7,972 = (1 + r/1)^(1×15)2.117 = (1 + r/1)^(1×15)[tex]1 + r = \sqrt[15]{2.117} [/tex]
1 + r = 1.051r = 1.051 - 1r = 0.051The interest rate is therefore; 0.51%
Read . more:
https://brainly.com/question/18187284
help me plz i have 5 more
Answer:
1343
Step-by-step explanation:
Jayla's dog eats 0. 78 pounds of food a day. To the nearest pound, how much does her dog eat in 7 days?.
Answer:
5.46 pounds
Step-by-step explanation:
0.78 x 7 = 5.46
A automobile manufacture can put together 7 cars in 2 day. How many cars can be produced in 12 days.
Answer:
147
Step-by-step explanation:
ADD IT
sophie drove 189 miles in 7 hours if she continued at the same rate how long would it take to travel 216 miles
Answer:
8 Hours
Step-by-step explanation:
If she drove 189 miles in 7 hours, that means she was driving 27 miles an hour, we find this number by dividing 189 by 7.
To find how long it would take to travel 216 miles, we divide 216 by 27, which gives us 8. Meaning it would take 8 hours to drive 216 miles assuming she goes at the same rate
Answer:
It would take her 8 hours.
Step-by-step explanation:
1. 189 ÷ 7, to determine miles per hour. This equals 27, which means that she drives 27 miles every 1 hour.
2. 216 ÷ 27, to determine how long it would take to travel 216 miles. This equals 8, which means that it takes her 8 hours to drive 216 miles.
hope this helps!
(1 point) PLEASE HELP
2. A drama club is planning a bus trip to New York City to see a Broadway play. The cost per
person for the bus rental varies inversely to the number of people going on the trip. It will cost
$30 per person if 44 people go on the trip. How much will it cost per person if 60 people go on
the trip? Round your answer to the nearest cent, if necessary.
O $22.00
$40.91
$1,320.00
O $21.29
Answer:
I would guess $21.29, Not completely sure though lol
Step-by-step explanation:
Hope this helps!! lol
Answer:
22
Step-by-step explanation:
if you don't understand it just tell me I'll re-do it. bye.
(- 10.7) and (-3.5)
Answer:
-14.2
Step-by-step explanation:
Algebra 2 please help
Answer:
B
Step-by-step explanation:
B
What is the y-intercept?
Answer:
y- intercept = 4
Step-by-step explanation:
The y- intercept is the point on the y- axis where the graph crosses the y- axis
In this case that is the point (0, 4 ) , then
y- intercept = 4
Identify the similar triangles.
ΔHFE=
ΔHFE=
∆HFE is similar to ∆HFG and ∆ HEG (they all are right triangles and have the same, shape.)
The given triangle ΔHFE is similar to triangle GFH and triangle GHE.
What are similar triangles?Similar triangles are two triangles that have the same shape but may differ in size. They have corresponding angles that are congruent and corresponding sides that are proportional.
Here,
Since triangle HFE is similar to triangle GFH,
∠HEF = ∠GHF,
∠FHE = ∠HGF, and ∠HFE = ∠HFG
Similarly
ΔHFE is similar to triangle ΔGHE.
Similar triangles are useful in many areas of mathematics and in the real world, such as in architecture, engineering, and cartography, where they are used to make scale models of buildings and other structures.
Thus, the given triangle ΔHFE is similar to triangle GFH and triangle GHE.
Learn more about similar triangles here:
https://brainly.com/question/12101336
#SPJ2
Last week Grace spent $125 on groceries. This week her spending increased by 35%. How much did she spend on groceries this week?
round 49.07583 to the nearest place value given; tenth, hundredth, thousandth ten-thousandth, unit?
Answer:
tenth- 49.1
Hundredth- 49.08
thousandsths- 49.076
ten-thousandths- 49.0758
Please solve with explanation will give brainliest
divide -b⁷ + 3b³ + 4b³ + 3b² by 2b²
plz solve this fast plz
Answer:
[tex] - \frac{1}{2} ( {b}^{6} - 7 {b}^{2} - 3)[/tex]
See image for solutionPLEASE HELP ME OUT!!
Convert the following
1,000 mL = _______ L
4,500 mg = _______ g
25 cm = ________ mm
Answer:
1,000ML = 1 L
4,500MG = 4.5G
25CM = 250MM
Stuck on no.2 so any help will be appreciated : )
Answer:
Step-by-step explanation:
[tex]\dfrac{x^{m}}{x^{n}}=x^{m-n}\\\\\\a)\dfrac{a^{5}}{a^{3}}=a^{5-3}=a^{2}\\\\\\b)\dfrac{c^{4}}{c^{3}}=c^{4-3}= c^{1} =c[/tex]
Answer:
A) a^2
B) c
Step-by-step explanation: hope this helps
Also you have to like multiply all of the numbers or sum.
Answer:
174 m^2
Step-by-step explanation:
9 * 5 = 45
9 * 5 = 45
9 * 3 = 27
9 * 3 = 27
5 * 3 = 15
5 * 3 =15
45+45+27+27+15+15 = 174 m^2
Hope this is helpful.
Answer:
174 m²
Step-by-step explanation:
9 * 5 = 45 (that's the bottom and top areas)
9 * 3 = 27 (that's both the bigger sides areas)
5 * 3 = 15 (that's both the smaller sides areas)
Now you have to double:
45 * 2 = 90
27 * 2 = 54
15 * 2 = 30
Now sum:
90 + 30 + 54 = 174
Helppp on mathhh pls it’s due tomorrow
Answer:
1. 20 km
2. 0.5 hours
3. 40 km
4. 1.5 hours
5. A, 40 km/hr
6. 80 km/hr, 40 km/hr
Step-by-step explanation:
2. The lines of Car A and Car B at 0.5 hours, meaning the cars have been traveling for 0.5 hours before they met.
1. From 0 hours to 0.5 hours, Car A traveled from 20 km to 40 km. The distance traveled before Car A met Car B was 40 km - 20 km = 20 km.
3. Cars A and B travel at the same speed starting at the 0.5 hour, 40 km point. They are traveling at the same speed from 0.5 hours to 1.5 hours since they share the same line and therefore the same slope. From the point at which Cars A and B met, they traveled from 40 km to 80 km. They traveled at the same speed for 80 km - 40 km = 40 km.
4. Both cars reached point C at the same time of 1.5 hours.
5. Car A had constant speed sicne the lines "Car A" and "Cars A and B" had the same slope. The speed is equal to the slope of the line: [tex]Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{80-20}{1.5-0} = 40 km/hr[/tex]
6.
First speed: [tex]Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{40-0}{0.5-0} = 80 km/hr[/tex]
Second speed: [tex]Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}} = \frac{80-40}{1.5-0.5} = 40 km/hr[/tex]
A license plate consist of 3 digits, 3 letters determine the number of different license plate if the first letter must be N,M, or P and repetition and numbers is not permitted
Answer:
1800.
Step-by-step explanation:
If N is the first letter the next 2 letters will be the number of permutations of 2 from 25 = 25!/ (25-2)!
= 600.
If the first number is M or P the number is the same so that makes 1800 possibilities.
state and prove angle sum property of a triangle
Statement:-
The sum of all the interior angles of a triangle is 180°. This is known ad the angle sum property of a triangle.
Proof :-
Consider a
