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
Find the equation of the line that goes through the points (4, –1) and (2, –5).
Use slope formula,m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction,to find the slope of a line that passes through the points.
m =
Use slope-intercept form, y = mx + b, to find the y-intercept (b) of the line.
b =
Write the equation in slope-intercept form, y = mx + b.
Answer:
y= 2x -9
Step-by-step explanation:
Slope-intercept form
y= mx +c, where m is the slope and c is the y-intercept.
[tex]\boxed{slope = \frac{ y_{1} - y_2}{x_1 - x_{2}} }[/tex]
Slope
[tex] = \frac{ - 1 - ( - 5)}{4 - 2} [/tex]
[tex] = \frac{ - 1 + 5}{2} [/tex]
[tex] = \frac{4}{2} [/tex]
= 2
Substitute m= 2 into the equation:
y= 2x +c
To find the value of c, substitute a pair of coordinates.
When x= 4, y= -1,
-1= 2(4) +c
-1= 8 +c
c= -1 -8
c= -9
Thus, the equation of the line is y= 2x -9.
marciano has 85 dollars to spend at a fair he spends 30 on admission and 12 on snacks he wants to plag a game that costs 1.50 per game write an inequality using a variable to find the maximum number of times Marciano can play the game using the inequality determine the maximum number of times he can play the game
Answer: 28.666666666666667
Step-by-step explanation: 85 - 30 - 12 = 43. 43 ÷ 1.50 = 28.666666666666667
What is the total surface area of a cylinder with a diameter of 10.8 and a height of 2.6?
Answer:
271.433606 (in, cm, or whichever unit)
Step-by-step explanation:
To find the areas of the ends of the cylinder, the circles, you would use the formula:
2(π * r²)
The diameter is twice the length of the radius so to find the radius, you would divide the length of the diameter in half. So with a diameter of 10.8 units, it would become 5.4 units.
2(π * 5.4²) = 183.217684
To find the surface area of the rectangle of the cylinder, you would multiply the circumference of the base of the cylinder by the height. The formula to find the circumference is 2πr. The circumference would be 33.9292007 units. 33.9292007 * 2.6 = 88.2159218.
Then add the areas to find the total.
183.217684 + 88.2159218 = 271.433606
Pls help with this question!!!!
There are 75 dimes in the box. This is because all of the pennies, nickels and quarters is 14.20$. So subtracting the full total 21.70 bu 14.20 gives us 7.50$. Which is 75 dimes.
answer please
urgently....
Answer: Picture is cropped can you send the full photo
Step-by-step explanation:
Please send the full photo
help please !!!!!!!!!
What is the answer to this Multi Step equation?
2y+29-8y=5
Answer:
Y=4
Step-by-step explanation:
Let's solve your equation step-by-step.
2y+29−8y=5
Step 1: Simplify both sides of the equation.
2y+29−8y=5
2y+29+−8y=5
(2y+−8y)+(29)=5(Combine Like Terms)
−6y+29=5
−6y+29=5
Step 2: Subtract 29 from both sides.
−6y+29−29=5−29
−6y=−24
Step 3: Divide both sides by -6.
−6y/-6=-24/-6
y=4
Hope this Helps
Type the correct answer in each box. Spell all words correctly, and use numerals instead of words for numbers.
Brad and Laura are playing a board game. In the game, a player rolls two standard number cubes to move his or her game piece along
a path on the board. On the first three turns in the game, both number cubes land on six each turn.
The theoretical probability of rolling a six on both number cubes three times in a row is 1/?
(are/ are not)
Based on the probability of rolling a six on both number cubes three times in a row, Brad and Laura
likely using unfair number cubes.
Answer:
1/46,656 and Brad and Laura ARE like using unfair number cubes.
Step-by-step explanation:
plz help!!!!!!!!!!!!!!!
Answer:
equation of line of best fit: y = -.018x + 7.3
y-intercept = 7.3
correlation coefficient = -.018
correlation coefficient indicates there is no correlation between the x-and-y values
Step-by-step explanation:
A car agency shows a new car with a price of AED 45,000. The company predicted that the cost of the
car would depreciate 10% each year for three years and then depreciate 8% each year after that. Find
the value of the vehicle in 8 years.
HELP ME PLSSS
Answer:
$8640
Step-by-step explanation:
Step 1:
The total amount of the car currently is $45,000. The car depreciates by 10% for the next 3 years. Then multiply 3 to 45,000.
3 × 45,000 = 135,000
The price then decreases by 10%. So, find 10% of 135,000
[tex]10\% = \frac{10}{100}[/tex]
[tex]135000=\frac{135000}{1}[/tex]
[tex]\frac{10}{100}\times \frac{135000}{1}[/tex]
Cross cancel the zeros
[tex]\frac{10}{1}\times \frac{1350}{1}[/tex]
Multiply across
[tex]10\times1350 = 13500[/tex]
Therefore, for the three years, the cars price is now $13,500.
Step 2:
The next step is the same as the first one. But now the car currently is $13,500. And The car depreciates by 8% for the next years. We have to find the value in 8 years. Then multiply 8 to 13,500.
8 × 13,500 = 108,000
Now, find 8% of 108,000
[tex]8\% = \frac{8}{100}[/tex]
[tex]108000=\frac{108000}{1}[/tex]
[tex]\frac{8}{100}\times \frac{108000}{1}[/tex]
Cross cancel the zeros
[tex]\frac{8}{1}\times \frac{1080}{1}[/tex]
Multiply across
[tex]8\times1080 = 8640[/tex]
Therefore, the value of the vehicle in 8 years is $8640.
The sum of three times a number and −4 is at most 17.
Answer:
7
Step-by-step explanation:
17 +4 = 21
21/3 = 7
5. The lengths of the sides of a triangle are x, 2x + 1 and 5x + 4 inches. If the perimeter is 53
inches, what is the value of x?
Equation: Xt2x+/+5x+4-53
Solution:
Answer:
x = 6
Step-by-step explanation:
The perimeter is the sum of the 3 sides
Sum the 3 sides and equate to 53
x + 2x + 1 + 5x + 4 = 53 , simplify left side
8x + 5 = 53 ( subtract 5 from both sides )
8x = 48 ( divide both sides by 8 )
x = 6
Graph the equation
Y= 1/4x^2-2x
See attached
(If this is incorrect, please add in parentheses so I can make sure I have the order correct. Thank you.)
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
Find the perimeter. Simplify your answer.
Calculate the simple interest on investing $650 for 3 years at rate of 11% per annum.
Answer:
214.5 usd
Step-by-step explanation:
blc we will do 650 times 11 .over 100 to get the annual the multiply it by 3
HOPE HELPED!!
Please help me, I’m stuck on this question.
Solve
3h/7 − 11 =2 23/28
Solve for h, and provide your answer.
Please include explanation and all your steps toward the answer
Thank you!
3h/7-11=2×23/28
h=25/2
Can someone help ????
Answer:
432
Step-by-step explanation:
Answer:
432
Step-by-step explanation:
[tex]\frac{(14-3^{2}+1 )^{2} }{1/3.\frac{1}{4} }[/tex]
Now, at first, we solve the numerator:
[tex](14-3^{2}+1 )^{2}[/tex]
=[tex](14-9+1)^{2}[/tex]
=[tex](15-9)^{2}[/tex]
= [tex]6^{2}[/tex]
= 36
Now let's solve the denominator:
1 ÷ 3 × [tex]\frac{1}{4}[/tex]
=[tex]\frac{1}{3} . \frac{1}{4}[/tex]
=[tex]\frac{1}{12}[/tex]
Hence,
[tex]\frac{(14-3^{2}+1 )^{2} }{1/3.\frac{1}{4} }[/tex]
= [tex]\frac{36}{1/12}[/tex]
= 36 x 12
= 432
This is probably easy oh well
(2.5×10^6)–(2.3×10^6)
Answer:
2×[tex]10^{5}[/tex]
aka 200000
Step-by-step explanation:
Need this question done asap ⏰
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
Let's consider the points (0 , -1) and (1 , 2) to find the slope of given line ~
[tex] \dfrac{y_2 - y_1}{x_2 - x_1} [/tex][tex] \dfrac{2 - ( - 1)}{1 - 0} [/tex][tex] \dfrac{2 + 1}{1} [/tex][tex]3[/tex]I hope it helps ~
Answer:
After looking at the image you posted, I deduced that the correct answer should be slope= 3.
Step-by-step explanation:
I came to this conculsion by using the formule slope= [tex]\frac{rise}{run}[/tex] or [tex]\frac{y-axis}{x-axis}[/tex]
Firstly:
I identified the position of the two points. The first points position being (-1, 0) and the second being (1, 2).
Secondly:
I then found the difference between the two points on the graph to be
(1,3) or (x=1, y=3).
Thus:
The [tex]\frac{rise}{run}[/tex] of the two points is [tex]\frac{y=3}{x=1}[/tex] or 3.
Which of the following expresses (2.4 on going) as a fraction in simplest form?
2 and 1/4th
2 and 2/5ths
2 and 11/25ths
2 and 4/9ths
Answer:
2 and 4/9ths
Step-by-step explanation:
2 ⁴/9 is equal to 2.4 constant
The theater manager needs to set up 54 chairs for a show each row can be holed up to eight chairs the manager puts as many chairs in each row as possible how many rolls will the manager set up
Answer:
7 not 7 full rows though
Step-by-step explanation:
What is the measure of angle x?
Answer:
See below:
Step-by-step explanation:
Hello! My name is Galaxy and I will be helping you today!
We can solve this problem in two steps, one being comprehension and another being solving. I'll start off with comprehension.
Comprehension
We can start to solve this problem by looking at it.
We can see that there is a right angle, therefore the angles that are in it are Complementary (Add up to 90).
That means that 30+3x=90.
We can now begin solving.
Solving
We can start solving by setting up an equation.
[tex]30+3x=90[/tex]
We can do this because we know due to the law of complementary angles that 30 and 3x MUST equal to 90.
[tex]3x=60\\x=20[/tex]
We can do basic algebra, we can find out that x is equal to 20 degrees. Let's now check our answer.
[tex]30+3(20)=90?\\30+60=90?\\90=90[/tex]
Therefore the answer is x=20 degrees
Cheers!
please answer this fast question in the image.
Answer:
[tex]\frac{5}{2}[/tex]
Step-by-step explanation:
slope m = [tex]\frac{rise}{run}[/tex] = [tex]\frac{y2 - y1}{x2-x1}[/tex]= [tex]\frac{4-(-1)}{2-0} = \frac{5}{2}[/tex]
Which of the following equations represents a quadratic relation?
Question 1 options:
2x+y=3
y=2x2+1
y=3x+1
y=2x3
Answer:
y=2x^2+1
Step-by-step explanation:
a quadratic equation has a x^2 term
A you-pick blueberry farm offers 6 lbs of blueberry for $16.50.
Sketch a graph of the relationship between cost and pounds of blueberries
Answer:
Step-by-step explanation:
Lol hi
Question 13 options:
Isaac drops an apple from the top of a lighthouse, 154 feet above the ground.
The equation to represent the height of the apple at a given time is h=−16t2+154,
where h is the height of the apple, and t is the number of seconds after the apple is dropped.
How many seconds (t) will it take for the apple to hit the ground (h = 0)?
[Find the value of t, rounded to the nearest tenth.]
Answer:
3.1 sec.
Step-by-step explanation:
Owen invested $81,000 in an account paying an interest rate of 3\tfrac{7}{8}3 8 7 % compounded continuously. Zoe invested $81,000 in an account paying an interest rate of 3\tfrac{1}{4}3 4 1 % compounded monthly. After 9 years, how much more money would Owen have in his account than Zoe, to the nearest dollar?
Answer: $6322
114800.8806 - 108478.6929
= 6322.1877
Rounded to the nearest dollar = $6322
Answer:6761
Step-by-step explanation:
Kamal solved an equation as shown below.
3(x-8)= x+2x+7
3x-24 - 3x+7
-24 - 7
What is the solution to Kamal's equation?
0-24
O 7
O no solution
O infinitely many solutions
Answer:
no solution
Step-by-step explanation:
3(x-8)=x+2x+7
3x-24=3x+7
there is no solution bc both sides, when simplified, that x is not defined.
you end up canceling the 3x in both sides and so,
-24 does not equal 7
Answer:
A
Step-by-step explanation:
What is the answer to this question?
Answer:
Perimiter would be 30cm
Step-by-step explanation:
3+3+6+3+6+3+6