Using an exponential function, it is found that it will take 31.7 years for the state's population to be of at least 30 million people.
An increasing exponential function is given 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:
The initial population is of 16 million people, hence [tex]A(0) = 16[/tex].The growth rate is of 2%, hence [tex]r = 0.02[/tex]Then:
[tex]A(t) = A(0)(1 + r)^t[/tex]
[tex]A(t) = 16(1 + 0.02)^t[/tex]
[tex]A(t) = 16(1.02)^t[/tex]
It will be 30 million after t years, for which A(t) = 30, hence:
[tex]A(t) = 16(1.02)^t[/tex]
[tex]30 = 16(1.02)^t[/tex]
[tex](1.02)^t = \frac{30}{16}[/tex]
[tex](1.02)^t = 1.875[/tex]
[tex]\log{(1.02)^t} = \log{1.875}[/tex]
[tex]t\log{1.02} = \log{1.875}[/tex]
[tex]t = \frac{\log{1.875}}{\log{1.02}}[/tex]
[tex]t = 31.7[/tex]
It will take 31.7 years for the state's population to be of at least 30 million people.
A similar problem is given at https://brainly.com/question/14773454
-2r+11=13 2r=2 r= I need help
Answer:
-2r = 2 - Subtract 11 from both sides
r = -1
is it an inverse or a reciprocal? Pls help ASAP!!!
Answer:
An inverse of a fraction is a reciprocal of a fraction. In other words, flipping the numerator and denominator provides the reciprocal of fraction. For example, the reciprocal of fraction 3/5 is 5/3.
Step-by-step explanation:
when you have an inequality with a variable on both sides what would you use to put all variables on one side and all constants on the other?
Answer:
Properties of Inequality
Addition Property of Inequality[tex]x - 3 = 9\\x-3 +3 = 9 + 3\\x= 9 + 3[/tex]
Subtraction Property of Inequality[tex]x+3<9\\x+3-3<9-3\\x<9-3[/tex]
Multiplication Property of Inequality[tex]\frac{1}{2}x<4\\\frac{2}{1} * \frac{1}{2}x < 4 * \frac{2}{1}\\x < 8[/tex]
Division Property of Inequality[tex]2x < 4\\\frac{2x}{2} < \frac{4}{2}\\x < 2[/tex]
Note: When you multiply or divide with a negative number. Flip the sign.
Step-by-step explanation:
search it up
2. Which of the following shows a translation of f(x) two units to the left?
f(x - 2)
f(x)-
f(x + 2)
f(x) + 2
Answer:
f(x + 2)
Step-by-step explanation:
Given f(x) then f(x + a) is a horizontal translation of f(x)
• If a > 0 then a shift to the left of a units
• If a < 0 then a shift to the left of a units
Here f(x) is translated 2 units to the left , then f(x + 2)
Solve for r.
-27 = r/10 - 36
r =
what is the value of x?
Answer:
so x = 80
Step-by-step explanation:
Any triangle, no matter what type will add up to a total of 180, so 70+30= 100, and you now subtract that 100 from 180 and you 80
what type of graph is used to display categorical data?
Answer:
bar chart..
Step-by-step explanation:
The sum of two consecutive even numbers is 214. What are the numbers?
Step-by-step explanation:
since they are consecutive even numbers, one is bigger by 2 than the other number.
so,
x + (x + 2) = 214
2x + 2 = 214
x + 1 = 107
x = 106
so, the 2 numbers are 106 and 108.
What is one geometrical fact explained in the lecture that reflects the mathematical technique da Vinci used in The Last Supper? a. He doesn?t use mathematics in the painting. B. He uses trigonometry to find the exact place where each thing should be located and create the picture plane. C. He uses the coffers of the ceiling to place Jesus in the mathematical center, and to create an illusion that extends the room beyond what is visible.
Answer:
C. He uses the coffers of the ceiling to place Jesus in the mathematical center, and to create an illusion that extends the room beyond what is visible.
Step-by-step explanation:
See attached. We can see that this option is the best as it reflects what we can see in the painting.
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
Answer:
c
Step-by-step explanation:
Use the definite integral and the Fundamental Theorem of Calculus to solve the following problem. A ball is thrown upward from a height of 1.2 m at an initial speed of 58 m/sec. Acceleration resulting from gravity is -9.8 m/sec^2. Find the following:
v(t)= _________
h(t)= ________
If v(t) and h(t) denote the ball's velocity and height at time t, respectively, then we have h(0) = 1.2 m and v(0) = 58 m/s.
The ball is in free fall after being tossed, so its acceleration is constant at any time t :
[tex]a(t) = -9.8 \dfrac{\rm m}{\mathrm s^2}[/tex]
By the fundamental theorem of calculus, the velocity function is given by
[tex]\displaystyle v(t) = v(0) + \int_0^t a(u) \, du[/tex]
Compute the integral:
[tex]\displaystyle v(t) = 58 \frac{\rm m}{\rm s} - \left(9.8 \frac{\rm m}{\mathrm s^2}\right) \int_0^t du[/tex]
[tex]\displaystyle v(t) = 58 \frac{\rm m}{\rm s} - \left(9.8 \frac{\rm m}{\mathrm s^2}\right) (t - 0)[/tex]
[tex]\displaystyle \boxed{v(t) = 58 \frac{\rm m}{\rm s} - \left(9.8 \frac{\rm m}{\mathrm s^2}\right) t}[/tex]
Similarly, the height function is given by
[tex]\displaystyle h(t) = h(0) + \int_0^t v(u) \, du[/tex]
[tex]\displaystyle h(t) = 1.2 \, \mathrm m + \int_0^t \left(58 \frac{\rm m}{\rm s} - \left(9.8 \frac{\rm m}{\mathrm s^2}\right) t\right) \, du[/tex]
[tex]\displaystyle h(t) = 1.2 \, \mathrm m + \left(58 \frac{\rm m}{\rm s}\right) (t - 0) - \frac12 \left(9.8 \frac{\rm m}{\mathrm s^2}\right) (t^2 - 0^2)[/tex]
[tex]\displaystyle \boxed{h(t) = 1.2 \, \mathrm m + \left(58 \frac{\rm m}{\rm s}\right) t - \frac12 \left(9.8 \frac{\rm m}{\mathrm s^2}\right) t^2}[/tex]
Answer:
V(t) = 58-9.8t
h(t)=1.2+58t-4.9[tex]t^{2}[/tex]
Step-by-step explanation:
Using the standard formula
a=V f-Vi/t --rearrange
at=V f-Vi
V f=V i + a t
therefore
V(t)=58-9.8t
same with height
H= Hi+Vit+1/2at^2
therefore
h(t)=1.2+58t-4.9t^2
What is the solution to -4(8 - 3x) >_6x -8?
O x >_-4/3
O x<_-4/3
O x>_4
Ox<_4
Mrs. Ashton buys journals for the students in her language arts class. She pays $64.48 for all of the journals. If there are 26 students in her class, how much does each journal cost?
Answer:
Each journal costs $2.48
Step-by-step explanation:
Let X be the cost of a single journal.
You can write this equation to represent the problem:
26x = 64.48
(26 times the cost of the journal is $64.48)
Then just solve for x by dividing both sides by 26:
[tex]26x=64.48\\\frac{26x}{26} =\frac{64.48}{26}\\x=2.48[/tex]
Each journal costs $2.48
If 2x-3y=3 find 16^x/64^y
a. 4
b. 8
c. 16
d. 64
Answer:
D. 64
Step-by-step explanation:
Did you mean: if 2x−3y=3 what is 16x64y? That fraction equals 42x−3y, so the answer would be 43, which is 64.
answer and please show the work.
Answer:
[tex]y=\displaystyle\frac{1}{2} x-3[/tex]
Step-by-step explanation:
Hi there!
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x=0)
1) Determine the slope (m)
[tex]m=\displaystyle\frac{y_2-y_1}{x_2-x_1}[/tex] where two points on the line are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the given points (4,-1) and (0,3)
[tex]m=\displaystyle\frac{-1-(-3)}{4-0}\\\\m=\displaystyle\frac{2}{4}\\\\m=\displaystyle\frac{1}{2}[/tex]
Therefore, the slope of the line is [tex]\displaystyle\frac{1}{2}[/tex]. Plug this into [tex]y=mx+b[/tex] :
[tex]y=\displaystyle\frac{1}{2} x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=\displaystyle\frac{1}{2} x+b[/tex]
The y-intercept occurs when x=0. Because we're given that (0,-3), the y-intercept is therefore -3.
[tex]y=\displaystyle\frac{1}{2} x-3[/tex]
I hope this helps!
At 9:00 on Saturday morning, two bicyclists heading in opposite directions pass each other on a bicycle path. The bicyclist heading north is riding 4 km/hour faster than the bicyclist heading south. At 10:15, they are 40 km apart. Find the two bicyclists’ rates.
A. northbound bicyclist = 19 km/h; southbound bicyclist = 15 km/h
B. northbound bicyclist = 18 km/h; southbound bicyclist = 13 km/h
C. northbound bicyclist = 16 km/h; southbound bicyclist = 10 km/h
D. northbound bicyclist = 18 km/h; southbound bicyclist = 14 km/h
Answer:
D Option is the correct one.
Step-by-step explanation:
As,
Distance covered = 40km = 40000m(1k=1000m)
time = 10:15-9:00 = 1:15hours = 75mins
We need to find the rates of the bicyclist in one hour so, for this first we need to calculate the total distance which covered in one hour.
For calculating distance for one hour,
40000/75 = 533.33m/min (means they covered 533.33m distance in one min)
for one hour:
533.33*60= 32000m = 32km
They covered 32km distance in one hour.
Now from the given options D is the correct one because according to give condition north bicyclist covered 4km more that south one. And other reason is we also need to check the sum of distance covered by the both cyclist which must be equal to 32km.
So for A,
Sum = 19 + 15 =34 (wrong not equal to 32)
For B,
Sum = 18 + 13 = 31 (wrong)
For C,
Sum = 16 + 10 = 26(wrong)
For D,
Sum = 18 + 14 = 32 (Right)
And second distance b/w both distance is 4km.
18-14 = 4(Right)
So, D option is the right one.
I hope it will help you.
cho tâp m của 120 số tự nhiên mà mỗi số thì chia hết cho 5 hoặc chia hết cho 7 hoặc chia hết cho 5 và 7 . Biết rằng số ấy có 71 số chia hết cho 5 và 63 chia hết cho 7. Hỏi tập M có bao nhiêu số chia hết cho 35?
Answer:
I don't understand you
Step-by-step explanation:
plss translate to English
Please Help Me :) I'm giving brainliest to correct answers only and No LiNkS.
Answer:
c
Step-by-step explanation:
it makes the most sense
Community planners are planning to build a new community garden. They agree that the garden will be rectangular in shape, but the proposed dimensions changed. At the most recent meeting, it was determined that the length would remain at 15.8 yards but that the width would increase by 5.2 yards. So, the garden would now cover an area of 327.65 square yards.
Which equation can be used to determine the original width of the garden, w?
1: 327.65 = 5.2 (w + 15.8)
2: 327.65 = 15.8(w +5.2)
3: 327.65 = 2 (w +21)
Answer:
2)
Step-by-step explanation:
To find the original width, multiply 15.8 by w, and by 5.2.
You'll get 327.65 = 15.8w + 82.16.
Next, do the opposite of the symbol from both sides, 327.65 - 82.16 = 15.8w + 82.16.
The constant is 82.16, and the symbol is +, the opposite of plus is -, and thus subtract the constant from both sides.
You'll get 245.49 = 15.8w.
Now do the opposite of the symbol (a number next to a variable is multiplication, so do division, and divide 15.8 on both sides.
245.49/15.8 = 15.8w/15.8, which equals 15.5373417722.
Help ASAP will mark Brainly to who ever answers 1st
Answer:
Step-by-step explanation:
the bottom left is the answer. I hope this helps.
What is equivalent to 1/3 P +15
Answer:
1/3(p + 45)
Step-by-step explanation:
1/3 p + 15 is the same as 1/3(p + 45)
-Chetan K
Artem drives 12.6 miles in 12 minutes. He passes a sign which gives the speed limit as 50 mph. By how much, in mph, did Artem's average speed exceed the speed limit?
What is the slope I need the answer fast
gradient=∆ in y values /∆ in x values
Step-by-step explanation:
pick any two points through which the line is passing through then label the values (any) x¹ and y¹ then x² and y². then subtract y²-y¹/x²-x¹
I'm confused on if it's 3 or 2
Answer:
it's 3 cause if u do 1 2 3 there are 3 hearts and they are broke up in half so 6
kimi is running for student body president. her friend, sarah, already helped by posting 12 of her campaign signs around the school. now kimi id posting the rest at a rate og 1.5 signs per minute. write an equation that shows the total number of signs posted, y, depends on the number of minutes
helppp yalll my mind is closed
Answer:
16
Step-by-step explanation:
(Trust me)
Five students sold lemonade and earned a total of $21.30. If they equally split their earnings, how much would each student receive?
Answer:
$4.26 each
Step-by-step explanation:
21.30 divided by 5 equals 4.26
(had to do it in words because I only have + - = )
What is -12 3/4 + -5 1/2? Write your answer as a mixed number in simplest terms.
need help plssss!!!!
should I call 911 !!!!!!!!!!!!!!
hi! I need help ! Triangles geometry angles table.
Answer:
145°
Step-by-step explanation:
[Finding the non-label angled in the triangle] 180° - 75° = 105°
Finding 3: (x = angle 3)
[Sum of a triangle's angles] 105° + 40° + x (angle 3) = 180
[combine like terms] 145° + x = 180°
[subtracting 145 from both sides] 35° = x
() We can test that this is correct by adding 40 and 35 together, to get angle 1 as it is an exterior angle
Finding 4: (x = angle 4)
180 - 35 = 145°
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
if a system of linear equations has infinitely many solutions