Johnny's assumption is that, none of the residents of the town will live up to 231 years.
The parameters are given as:
[tex]\mathbf{P_o = 10000}[/tex]--- the population in 2005
[tex]\mathbf{r = 0.3\%}[/tex] -- the rate at which the population declines
To model a population, we make use of the following exponential function
[tex]\mathbf{P = P_o \times(1 -r)^t}[/tex]
Where P is the current population in t years.
So, we have:
[tex]\mathbf{P = 10000 \times(1 -0.3\%)^t}[/tex]
When the population reaches half of the initial population, then P = 5000.
So, we have:
[tex]\mathbf{5000 = 10000 \times(1 -0.3\%)^t}[/tex]
Divide both sides by 10000
[tex]\mathbf{0.5 = (1 -0.3\%)^t}[/tex]
[tex]\mathbf{0.5 = (0.997)^t}[/tex]
Take logarithm of both sides
[tex]\mathbf{log(0.5) = log(0.997)^t}[/tex]
Rewrite the equation as
[tex]\mathbf{log(0.5) = tlog(0.997)}[/tex]
Make t the subject
[tex]\mathbf{t = \frac{log(0.5)}{log(0.997)}}[/tex]
[tex]\mathbf{t = 231}[/tex]
This means that the population will halve its initial population in 231 years.
Johnny's assumption is that, none of the residents of the town will live up to 231 years.
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Find x and y.
Answer:
x = 36°y = 48°Step-by-step explanation:
Given:
ΔABC ≅ ΔFDEWe can tell that y = 48° because ΔABC ≅ ΔFDE. We can also tell that ∠DEF = 108 because ΔABC ≅ ΔFDE.Let's first try to simplify ∠CAB in ΔABC. Then we can find the 'x' in ΔFDE with the help of ΔABC.
ΔABC = 108 + 48 + ∠CAB = 180°
=> 156 + ∠CAB = 180°
=> ∠CAB = 24°
=> 48 + 108 + 2x - 48 = 180°
=> 108 + 2x = 180°
=> 2x = 72°
=> x = 36°
So, after working on this problem, we can conclude that 'x = 36°' and 'y = 48°'. Hoped this helped.
Answer: x=36, y=48
Step-by-step explanation:
The sum of the angles in a triangle is 180. From triangle ABC we see that:
108 + 48 + Z = 180, where Z is the unknown third angle.
156 + Z = 180
Z= 24 (angle CAB).
Since the triangles are similar, we can say angle EDF(y) is equal to angle CAB (48). Thus,
y = 48
we can also say that angle CAB is the same as angle DFE:
24 = (2x-y)
24=2x-48
72=2x
x=36
plzzz help?????????????????????
Answer:
Step-by-step explanation:
Pythagorean theorem: base ² +altitude² = hypotenuse²
1) hypotenuse² = base² + altitude²
x² = 6² + 3²
= 36 + 9
= 45
x = √45
x = 6.7 cm
4) base ² +altitude² = hypotenuse²
x ² + 3.7 ² = 4.2 ²
x ² + 13.69 = 17.64
x ² = 17.64 - 13.69 = 3.95
x = √3.95
x = 1.99 cm
10)c ² = a ² + b ²
= 3 ² +4 ²
= 9 + 16
c ² = 25
c = √25 = 5
11) a ² + b ² = c ²
9 ² +b² = 13 ²
81 + b² = 169
b² = 169 - 81 = 88
b = 9.38
12) a² + b² = c²
12² + b² = 22²
144 + b² = 484
b² = 484 - 144 = 340
b =√340 = 18.44
Please help! It’s due today
Solve: 5|9 – 3x|– 7 = 38
Answer:
x = 0
Step-by-step explanation:
Find the factorization of the polynomial below. 81X2 - 18x+1
A. (18x-1)2
B. (9x-1)2
C. (9x + 1)2
D. (18x + 1)2
Answer:
B.(9 x -1)^{2}
Step-by-step explanation:
Rewrite the expression into the form of a^2\pm 2ab+b^2:(9 x)^{2} - 2 \times 9 x + 1^{2}
Factor the expression using a^{2}\pm 2ab+b^{2}=(a\pm b)^{2}:(9 x -1)^{2}
we have 81x^2 - 18x+1 = (9x)^2 -2.9x + 1 = (9x -1)^2
ok done. Thank to me :>
The first three terms of a geometric sequence are as follows.
2, -8, 32
Find the next two terms of this sequence.
Give exact values (not decimal approximations).
Answer:
-128, 512
Step-by-step explanation:
-8/2 = -4, 32/-8 = -4, so the ratio r = -4. 32*-4 = -128, -128*-4 = 512
decrease £67 by 26% give your answer in pounds
Answer:
£ 49.58
Step-by-step explanation:
26% of 67 = 0.26 * 67 = £17.42
67 - 17.42 = £49.58
If x= √3, find the value of x⁴.
Answer:
9
Step-by-step explanation:
Hi there!
We're given that x=√3, and we want to find the value of [tex]x^4[/tex]
We can substitute √3 as x, and then raise it to the 4th power, but if you don't know what that number is, it might be difficult to figure it out.
An easier way would be to write [tex]x^4[/tex] as x² * x², which in that case, we can multiply √3 by itself, multiply √3 by itself again, and then multiply those 2 numbers together.
If we do it this way, it'll look something like this (remember: x² is equal to x*x, or (x)²:
(√3)² * (√3)²
The order of operations will ask us to first take care of what's in the parentheses, and then to raise the numbers to their powers. Starting with the number on the left of the multiplication sign,
(√3)² = (√3)(√3)=3
And then the number on the right of the multiplication sign:
(√3)² = (√3)(√3)=3
Substitute these numbers in as (√3)² and (√3)²:
3 * 3 = 9
Therefore, x² * x², or [tex]x^4[/tex] is equal to 9
Hope this helps!
The sides of a triangle are in the ratio 4:4:3.What kind of triangle is it
Answer:
Isosceles triangle. An Isosceles triangle is a triangle that has 2 equal sides and 2 equal angles
Step-by-step explanation:
Triangle PQR is an isosceles triangle with the coordinates P(2, 3), Q(5, 10), and R(8,3).
What is the area of triangle PQR
Answer:
b
Step-by-step explanation:
I HAVE A SEMICIRCLE WITH A DIAMETER 16cm. How do I find the perimeter of the SEMICIRCLE
Answer:
Perimeter of Semicircle
The perimeter of a semicircle is the sum of the half of the circumference of the circle and diameter. As the perimeter of a circle is 2πr or πd. So, the perimeter of a semicircle is 1/2 (πd) + d or πr + 2r, where r is the radius.21-Oct-202
Answer:
Perimeter is 41.1327 centimeters
Step-by-step explanation:
The perimeter of a semi-circle is the circumference of the full circle plus the length of the diameter.
To find the circumference of a circle, just multiply the diameter by pi:
[tex]c=\pi\times d\\c=\pi\times 16\\c=50.2655[/tex]
Now, add the diameter to half of it:
[tex]p=\frac{c}{2}+d\\p=\frac{50.2655}{2}+16\\p=25.1327+16\\p=41.1327[/tex]
0 4
2 10
4 16
6 22
what is the slope?
what is the y-intercept?
proportional or not proportional?
I think is non proportion
What number has 7 as 1/10
I need help with 12 please
A smart watch was marked 150 and is sold at 120. Find discount percentage
Step-by-step explanation:
100 % = 150
1% = 100%/100 = 150/100 = 1.5
the discount was 150 - 120 = 30.
how many percent are in 30 ? that is our discount preventative.
30/1.5 = 20
so, the watch was sold with 20% discount.
Review the graph. On a coordinate plane, a parabola opens up and goes through (negative 2, 5), has vertex (0, 1), and goes through (2, 5). Another parabola opens to the right and goes through (8, 4), has vertex (negative 8, 0), and goes through (8, negative 4). Everything inside of the first parabola and above the second parabola within the first parabola is shaded. Which system of inequalities has the solution set shown in the graph?
Answer:
The value of h is h = -1.5
Step-by-step explanation:
The quadratic equation is represented by a parabola, the vertex form of the equation is y = a(x - h)² + k, where
(h , k) are the coordinates of its vertex point
a is the coefficient of x²
∵ The graph is a parabola opens up
∵ It has a vertex at (-1.5, 0)
∵ The vertex of the parabola is (h , k)
∴ h = -1.5 and k = 0
∵ The graph shows f(x) = (x - h)²
∵ The coordinates of the vertex are (h , k)
∵ h = -1.5 and k = 0
∴ h = -1.5
The value of h is h = -1.5
The value of h is h = -1.5
We have given that,
On a coordinate plane, a parabola opens up and goes through (negative 2, 5), has vertex (0, 1), and goes through (2, 5). Another parabola opens to the right and goes through (8, 4), has vertex (negative 8, 0), and goes through (8, negative 4).
The quadratic equation is represented by a parabola,
What is the vertex form of the parabola?The vertex form of the equation is y = a(x - h)² + k, where
(h, k) are the coordinates of its vertex point
a is the coefficient of x²
∵ The graph is a parabola that opens up
∵ It has a vertex at (-1.5, 0)
∵ The vertex of the parabola is (h , k)
∴ h = -1.5 and k = 0
∵ The graph shows f(x) = (x - h)²
∵ The coordinates of the vertex are (h, k)
∵ h = -1.5 and k = 0
∴ h = -1.5
The value of h is h = -1.5.
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can someone please help me i’m not doing so well in this new topic
Answer:
m<H= 80*
m<P= 80*
m<I= 33*
M<Q= 33*
M<J=67*
M<R=67*
Step-by-step explanation:
Given States that ️ HIJ = ️ PQR
<H=<P
2x=x+40
2x-x=x-x+40
x=40
<I=<Q
<J=<R
ALL TRIANGLES MEASURE 180*
Y= the measure of <R and <J
2x+33+y=180
2(40)+33+y=180
80+33+y=180
113+y=180
113-113+y=180-113
y=67
Answer:
See answer below
Step-by-step explanation:
If ΔHIJ ≅ ΔPQR ,then you know six congruent parts:
∠H ≅ ∠P ; ∠I ≅ ∠Q; ∠J ≅ ∠R and HI ≅ PQ; HJ ≅ PQ ; IJ ≅ QR
∠H ≅ ∠P ∠I ≅ ∠Q
2x = x + 40° ∠I = 35°
x = 40°
So ∠H = 2x = 2(40) = 80° Δ HIJ = 180°
∠P = x + 40 = 40 + 40 = 80° ∠H + ∠I + ∠J = 180°
∠Q = 35° 80° + 35° + ∠J = 180°
∠ I = 35° 115° + ∠J = 180°
∠ J = 65° ∠J = 65°
∠R = 65° ∠J ≅ ∠R
6
How much
10 500
A pile of bricks weighs 22 kg.
18750g of bricks are removed. What weight is left?
Answer:
3,250g
Step-by-step explanation:
22kg = 22,000g - 18,750g = 3250g
Please give me the answer
Answer:
8%
If you need the work comment on this post.
0.35 is best known as what number
In Joe's fish tank, there are 5 goldfish and 12 snails. How does the ratio 5:17 describe Joe's fish
tank?
Choose the correct answer below.
O A. The ratio 5:17 compares the number of snails to the number of goldfish.
OB. The ratio 5:17 compares the number of snails to the total number of animals.
OC. The ratio 5:17 compares the number of goldfish to the total number of animals.
OD. The ratio 5:17 compares the number of goldfish to the number of snails.
Answer:
OC. 5:17 compares the amount og goldfish he has to the amount of total animals he has
Melanie got a new job through the Jones Employment Agency. The job pays $32, 400 per year, and the angency fee is equal to 45% of one months pay. How much must Melanie pay the agency?
Answer:
The answer is $1,215
Step-by-step explanation:
I did $32,000 divided by 12 (months on an year) and got $2,700 per month, now we just do 0.45 x $2,700 and thats how I got the answer!
(X-5)(X+6)
Expand and simplify
Answer:
Step-by-step explanation:
(x - 5)(x + 6) = x *(x + 6) - 5*(x + 6)
=x * x + 6 *x + x*(-5) + 6*(-5)
= x² + 6x - 5x - 30 {Combine like terms}
= x² + x - 30
A car travels 23 km in 15 minutes. How fast is it going in kilometres per hour?
Answer:
96 km/h.
Step-by-step explanation:
23 x
-- = ----
15 60
60/15 = 4
24 x 4 = 96
x = 96
2. It’s time for Ronda to start repaying her student loans, which are amortized over the next 10 years. Her first month’s payment due is $396. How much should she expect to pay next month?
Based on the amount that she paid in the first month, the amount Ronda will pay for the next month is $396.
When a loan is amortized, it means that one can pay it off by paying the same amount every period until they would have paid off both the loan and the associated interest.
The amortized amount contains:
A portion going towards the principal(debt )A portion going towards the interest accumulated.In conclusion, as the amount is the same every time, Ronda will have to pay the same amount of $396 the next month.
Find out more at https://brainly.com/question/12256592.
How to find an area of a trapezium
Answer:
A = 87.5 sq cm
Step-by-step explanation:
A = 1/2·h·(sum of bases)
A = 1/2 · 7 · (10 + 15)
A = 3.5(25)
A = 87.5 sq cm
The midpoint of DF is E(-5, 4). If the coordinates of Fare (-4, 2), What are the coordinates of D?
Answer:
(-6,6)
Step-by-step explanation:
ABC is a right angle triangle. Calculate the length of BC
Give your answer correct in 1 decimal place
AB= 6.7 cm
AC= 16 cm
Answer:
I don't know sorry I haven't studied this at all I am in 7th grade only so
Choose the expression that correctly compares 0.501 and 0.051
Answer:
0.501>0.051
Step-by-step explanation:
Answer:
0.501 > 0.051
Step-by-step explanation: blah
BRAINLIEST x 3
It is kinda late and I need to finish my work
Please help me
If you answer this I will create two other posts to give you extra brainliests
1002828197382728173927937294729929382991divided by 182883929190.837283828281-737273728377273737272
Answer:
4.766141725565771e23
Step-by-step explanation: it is impossibel to explane so coculated it and i got 4.766141725565771e23. so there you go.