Answer:
4
Step-by-step explanation:
Every year, the world grows by 1.1%. Converting to a decimal, we can divide by 100 to get 1.1% = 0.011. This means that the world grows by 0.011 exponentially each year. To put this into an expression, we can add 1 to our percentage to get 1.011. This represents 1 = 100% (the original population) and the growth of 1.1% = 0.011. We multiply the rate including the growth by the population to get the population after one year. After the first year, we have
population * 1.011 as the new population after one year. We do that for every year, so the second year's population is population*(1.011)*(1.011) and so on. If x represents the amount of years, then the population can be represented as
(original population)*1.011ˣ
Therefore, to get from 7 billion to 7.31 billion, we have
7 billion * 1.011ˣ = 7.31 billion
divide both sides by 7 billion to relatively isolate the x
1.011ˣ = 7.31/7
Another way of writing this is
log (base 1.011) (7.31/7) = x
≈ 3.96
Rounding to the nearest whole number, we get 4 as our answer
The number of years it takes for the population to grow from 7 billion to 7.31 billion is;
n = 4 years.
We are told that the population of the world grows exponentially by 1.1% per year. This is equivalent to growth of 0.011 per year exponentially.
Now, since the exponential rate is 0.011 per year, thus, if the original population is P, then after a year, the new population will be;
P_1 = 1.011¹ × P
After 2 years, it will be;
P_2 = 1.011² × P
Thus, if n represents the number of years after the initial population, then population after n years if original population is P is;
P_n = 1.011ⁿ × P
Now, we are told that the population grew from 7 billion to 7.31 billion.
Thus;
P = 7 billion
P = 7 billion P_n = 7.31 billion
Thus;
7 billion × 1.011ⁿ = 7.31 billion
divide both sides by 7 billion to get;
1.011ⁿ = 7.31/7
1.011ⁿ = 1.044285
n log 1.011 = log 1.044285
n = 0.018819/0.004751156
n ≈ 4 years
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how many axes of symmetry does a square have
Answer:
four lines axes of symmetry does a square have
Solving equations involving vertical angles
Given the figure below, find the values of x and z.
Answer:
[tex]x=5\\z=94[/tex]
Step-by-step explanation:
As they are vertical angles
∴[tex]7x+51=86\\=>7x=35\\x=5[/tex]
And,
∴[tex]86+86+z+z=360\\=>2z=188\\z=94[/tex]
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Calculate the length of segment AB on the graph below.
A. Square root of 5
B. Square root of 73
C. Square root of 65
D. Square root of 90
Answer:
D
Step-by-step explanation:
Substitute the co-ordinates if a and b in the distance formula and you will get the answer as sq root of 90 which is D
Find all y-intercepts of the following function. Express your answer as a coordinate
point in simplest form.
X-4
F(x)=————————
X^2+5x-36
Step-by-step explanation:
to find y intercept, put x to be 0
hence,y int is -36
also, to find x int put y to be 0 and factorise the equation
hence, x are - 9 and 4
finally, the answer in a co ordinate are
(4,-36) , (-9,-36)
on a number line to suppose point it has a coordinate of two and EG equals eight what are the possible coordinates of point G
Answer:
I don't understand please can you explain to me
if this trapezoid is moved through the translation (x+3,y-2) what will the coordinates of B` be
Answer:
-2, 2
Step-by-step explanation:
Melany wants to hang a canvas, which is 8 feet wide, on his wall. Where on the
canvas should Melany mark the location of the hangers if the canvas requires a
hanger every 1/5 of its length, excluding the edges? Justify your answer.
The length of the canvas where Melany will mark the position of the hanger is 1.6 feet.
The given parameters:
length of the canvas = 8 feet
dimension of the hanger = [tex]\frac{1}{5} \ of \ the \ shoe's \ length[/tex]
To find:
the length of the canvas where Melany will mark the position of the hanger.The length of the canvas where Melany will mark the position of the hanger is calculated as follows:
[tex]location \ of \ the \ hanger = \frac{1}{5} \times 8\ ft\\\\location \ of \ the \ hanger = 1.6 \ ft[/tex]
Thus, the length of the canvas where Melany will mark the position of the hanger is 1.6 feet.
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can anyone help me please on this function.
USE (m a t h w a y) its real easy to use
Step-by-step explanation:
Find the exact solution of -x^2+3x+7=0 by using the Quadratic Formula?
can any one solve this please....I kinda need this
9514 1404 393
Answer:
t₂ = 2t₃ = 2Step-by-step explanation:
The given expression says ...
[tex]t_n+1=3\\\\t_n=2\qquad\text{for any value of n}\\\\t_2=2\\\\t_3=2[/tex]
Answer:
[tex]here \: tn + 1 = 3 \\ tn = 2 \\ put \: n = 1 \\ t1 = 2 \\ n = 2 \\ t2 = 2 \\ n = 3 \\ t3 = 2 \\ for \: all \: n \: values \: = 2 \\ thank \: you[/tex]
I needddddd heelllpppp pleaseeee
Answer:
3/2
Step-by-step explanation:
Csc(theta) = 1/Sin(theta)
So we have to find the side opposite theta.
a = 3*sqrt(5)
b = ?
c = 9
a^2 + b^2 = c^2
(3sqrt(5)) ^2 + b^2 = 9^2
9*5 + b^2 = 81
b^2 = 81 = 45
b^2 = 36
sqrt(b^2) = sqrt(36)
b = 6
Sin(theta) = 6/9
Csc(theta) = 1 / sin(theta) = 9/6
Csc(theta = 3/2
Problem 3
Answer: 3/2=====================================================
Explanation:
Use the pythagorean theorem to find the length of the missing side.
[tex]a^2 + b^2 = c^2\\\\a^2 + (3\sqrt{5})^2 = 9^2\\\\a^2+3^2*(\sqrt{5})^2 = 9^2\\\\a^2 + 9(5) = 81\\\\a^2 + 45 = 81\\\\a^2 = 81-45\\\\a^2 = 36\\\\a = \sqrt{36}\\\\a = 6\\\\[/tex]
This is the length of the missing vertical side. This side is opposite the angle theta.
[tex]\csc = \text{cosecant}\\\\\csc(\theta) = \frac{\text{hypotenuse}}{\text{opposite}}\\\\\csc(\theta) = \frac{9}{6}\\\\\csc(\theta) = \frac{3*3}{3*2}\\\\\csc(\theta) = \frac{3}{2}\\\\[/tex]
Alternatively, you can compute it like this
[tex]\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin(\theta) = \frac{6}{9}\\\\\sin(\theta) = \frac{2}{3}\\\\\csc(\theta) = \frac{1}{\sin(\theta)}\\\\\csc(\theta) = 1 \div \sin(\theta)\\\\\csc(\theta) = 1 \div \frac{2}{3}\\\\\csc(\theta) = \frac{3}{2}\\\\[/tex]
is 9.40 equal to 9.4
Answer:
no
Step-by-step explanation:
if it was 9.04 it would
its not equal because 9.40 is 10^2 but 9.4 is 10^1
if a=3x and b = 3x-4i, find the value of a3b In fully simplified form
C^-24 times c^9 times c^-87 answer using positive exponents
Answer:
1/c^102
Step-by-step explanation:
C^-24 * c^9 * c^-87
When we multiply exponents with the same base, we add the exponents
c^(-24+9+-87)
c^(-102)
We know that a^-b = 1/a^b
1/c^102
Answer:
Step-by-step explanation:
[tex]a^{m} *a^{n} = a^{m+n}\\\\\ a^{-m}=\dfrac{1}{a^{m}}\\\\\\c^{-24}*c^{9}*c^{-87}=c^{-24+9-87}\\\\=c^{-102}\\\\=\dfrac{1}{c^{102}}[/tex]
Write -5i, 2, and 7 in the simplest polynomial function given the roots
Answer:
x^4-9x^3+39x^2-225x+350
Step-by-step explanation:
The simplest polynomial you can get with that roots are (x-5i)(x+5i)(x-2)(x-7)=x^4-9x^3+39x^2-225x+350
Pls help me in this my math exam is Tom and I wanna know how to solve theese
Step-by-step explanation:
[tex]thank \: you[/tex]
A wedding planner uses 72 ivy stems for 18 centerpieces. When sh arrives at the venue , she realizes she will only need 16 centerpieces. How many ivy stems should she use so that the ratio of ivy stems to centerpieces stays the same ?
Answer:
64 ivy stems
Step-by-step explanation:
72 ivy stems / 18 centerpieces = 4 ivy stems / 1 centerpiece
Create an equation with x being the amount of ivy stems needed.
x / 16 = 4
x = 64
A _______ is a collection of values.
A. data summary
B. data volume
C. data summation
D. data set
pls help
A data summation is a collection of values.
Kai took a trip from Stratford to Paris in 2013, and needed to exchange 500 British
pounds for euros. The exchange rate was 1 pound to 1.23 euros. How many euros did Kai
receive in this exchange?
Answer:
500pounds×1.23euros
=615eurosCan someone help me with this??
Carlos and Pamela are going on a road trip. They are driving a total of 650 miles in three days to reach the destination. They took it easy the first day. On the second day, they drove twice as many miles as the first day. On the third day, they drove 50 miles more than the second day. How many miles did they drive each day?
Answer:
Carlos and Pamela drove 120 miles on the first day, 240 miles on the second day, and 290 miles on the third day.
Step-by-step explanation:
Let x be the number of miles driven on the first day.
Then they drove twice as many miles, or 2x on the second day
and 50 miles more than the second day's, so 2x + 50
The total is 650 across all three days, so we'll take the sum.
x + 2x + (2x + 50) = 650
Combine like terms on the left
5x + 50 = 650
Subtract 50 on both sides
5x = 600
Divide by 5 on both sides
x = 120
Check work:
120 + 2(120) + 2(120) + 50 = 650
120 + 240 + 240 + 50 = 650
600 + 50 = 650
650 = 650
So they drove 120 miles on the first day
2*120 = 240 miles on the second day
and 2*120 + 50 = 240 + 50 = 290 miles on the third day
(7x2 - 2x - 5)(3x2 + 2x - 3)
Answer:
21x4 + 8x3 - 40x2 + 15
Step-by-step explanation:
expand using distributive property.
what is 98 divided by 5
Answer:
19.6
Step-by-step explanation:
the answer to the question is 19.6
Answer:
19.6
Step-by-step explanation:
We have to do long devision:
5 goes into 9 how many times? Once. So our first number will be one.
9 - 5(1) = 4
Bring the 4 down. Then bring the 8 from 98 down.
5 goes into 48 how many times? Nine times. So our second number will be nine.
48 - 5(9) = 3
Bring the 3 down. Since there is no numbers left from 98, add a decimal and then a zero to make the number 98.0.
5 goes into 30 how many times? Six times. So our third number will be six. Don't forget to add the decimal before the six!
30 - 5(6) = 0
This diagram was created by starting with points A and
B and using only straightedge and compass to construct
the rest. All steps of the construction are visible.
Describe precisely the straightedge and compass moves
required to construct the line CD in this diagram.
The drawing instruments required for a construction, is dependent on the type of construction performed
The straightedge and the compass moves required to construct the line CD in the diagram are;
Move 1: Place the compass at point A and draw circle A with center at A and radius ABMove 2: Place the compass at any point of the circumference of circle A and label the point, at point B. Draw a second circle with the same radius AB and center at point B with the compassMove 3: Label the point the two circles intersect as points C and DMove 4: Place the straightedge at points C and D and construct the straight line CDLearn more about technical drawing here:
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Answer:
Move 1: Place the compass at point A and draw circle A with center at A and radius AB
Move 2: Place the compass at any point of the circumference of circle A and label the point, at point B. Draw a second circle with the same radius AB and center at point B with the compass
Move 3: Label the point the two circles intersect as points C and D
Move 4: Place the straightedge at points C and D and construct the straight line CD
Step-by-step explanation:
the heights of five basketball players are 184 cm, 190 cm, 198 cm, and 202 cm. what is the average height of the five players?
Answer:
93.5
Step-by-step explanation:
Also you only wrote down four numbers not 5 so I calculated it using those four numbers
Answer: 193.5
Step-by-step explanation:
184 + 190 + 198 + 202 = 774
first we add all the numbers together
774/4 = 193.5
then we divide the numbers by the amount of things we have in this case we have four players (last basketball player height not given) so we divide that by our added number and get 193.5cm
if you rolled a die what is the probability that you would roll a 4 or 5
Answer:
1/3
a dice has 6 sides and the probability of getting 4 or 5 is just 2/6 which simplifies to 1/3
By rationalizing the denominator of
[tex] \frac{ \sqrt{2} }{ \sqrt{5 + \sqrt{3} } } [/tex]
Salma got the answer as:
a)
[tex] \frac{ \sqrt{2} }{ \sqrt{5 - \sqrt{3} } } [/tex]
b)
[tex] \frac{ \sqrt{2( \sqrt{5 - \sqrt{3)} } } }{2} [/tex]
c)
[tex] \frac{ \sqrt{2( \sqrt{5 + \sqrt{3}) } } }{2} [/tex]
d)
[tex] \sqrt{5 - \sqrt{3} } [/tex]
Answer:
D
Step-by-step explanation:
What is 7 divided by 329
Answer:
47
Step-by-step explanation:
Do long division.
7 goes into 32, 4 times.
32 - 28= 4
7 goes into 49, 7 times.
Therefore 47 is correct.
please help with these 5 math questions for 25 points!
Answer:
1)C 2)A 3)D
Step-by-step explanation:
600 miles/day into miles per hour
what is the opposite of
A) 7 & B) -3
A -7 , -3
B -7 -3
C -7 , 3
D 7 , 3