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
Your visually impaired friend asked you to enlarge your notes from class so he can study. You took notes on 8.5-inch by 11-inch paper. The enlarged copy has a smaller side with a length of 10 inches. What is the scale factor of this dilation?
Find the scale factor.
Answer:FINDING A SCALE FACTOR Your visually impaired friend asked you to enlarge your notes from class so be can study. You took notes on 8.5-inch by 11-inch.
Step-by-step explanation:thank you
The scale factor is 20/17.
According to the question, you took notes on a paper with dimensions 8.5 inches × 11 inches.
the breadth of the paper is 8.5 inches
the length of the paper is 11 inches
Now, to make an enlarged copy, you used a paper that has its smaller side dimension of 10 inches.
Which means the breadth of the new paper is 10 inches.
So, if we calculate the ratio of the breadths we get the scale factor.
k = 10 / 8.5
k = 20/17 is the scale factor of dilation.
Learn more about scale factor:
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Nick sketches the graph of y = 0.5' for x 20 y 0.5 of Make one criticism of his sketch.
Answer:
the graph would just be a straight line going up at points (0, 0.5)
Step-by-step explanation:
This would have no slope
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?
Please help me answer this ASAP
Answer:
1.15x - 0.7x
Step-by-step explanation:
You take the manufacturer’s price and add 15 percent, then subtract 70 percent of the used price from the retail price to get the answer.
Sales tax in a certain community is 7%. If the sales tax on a new car was $1,400, what was the selling price of the car
Answer:
20,000
Step-by-step explanation:
Answer:
%7 1400
100 x
7x=140000
x=20000$
Find the values of x and y.
Answer:
y= 132, x= 32.6
Step-by-step explanation:
Let me know if this is right!
Hope it helps
Find the measure of the angle marked with a question mark using inverse trig
functions. Round your answer to the nearest degree. Enter the number only.
I need the answer quick
Applying the tangent ratio, the value of x in the right triangle is approximately: 5.
What is the Tangent Ratio?Tangent ratio that can be applied to solve a right triangle is expressed as: tan ∅ = opp/adj.
Given the following:
∅ = 63°Opp = 10 Adj. = xtan 63 = 10/x
x = 10/tan 63
x ≈ 5
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what is the coordinates of the point?
Answer:
Step-by-step explanation:
3,2
Answer:
2,3 because the point is inside the origin or equivalent so the answer has to be 2,3
Nina gets paid $200 a week plus an extra $5 per handbag
she sells. Write an equation for this problem, and identify
the slope and y-intercept
Answer:
y=5x+200
Step-by-step explanation:
x=number of handbags
y-intercept=200
slope=5
please give me brainly since I'm trying to level up!
HELP! HL theorem. Congruent. Geometry algebra. Triangles. Shapes. Math.
Answer:
x = 3
Step-by-step explanation:
x² + 15 = x² + 5x
15 = 5x
15 ÷ 5 = x
3 = x
What is the value of x in the equation ?
Answer:
[tex]x=2[/tex]
Step-by-step explanation:
This is our equation
[tex]2.5\left(6x-4\right)=10+4\left(1.5+0.5x\right)[/tex]
First off we can distribute the 2.5 and the 4
Now our equation is [tex]15x-10=10+6+2x[/tex]
subtract [tex]2x[/tex] from both sides
[tex]13x-10=16[/tex]
add [tex]10[/tex] to both sides
[tex]13x=26[/tex]
Divide both sides by [tex]13[/tex]
[tex]x=2[/tex]
Please help me! Bots keeps answering my questions and I really need an answer
Answer:
D) the bridge is about 381.16 ft. above the river, and the length of the bridge above the arch is 1,792.58 ft
Richard sold cupcakes and cookies yesterday. Each cupcake sold for $1.75 and each cookie sold for $0.75. At the end of the day, Richard had sold $49.25 worth of cookies and cupcakes. If he sold 35 cupcakes and cookies combined, how many cupcakes were sold and how many cookies were sold?
Answer:
20 cupcakes
15 cookies
Step-by-step explanation:
20*$1.75=$35
15*$0.75=$14.25
$35+$14.25=$49.25
Answer:
23 cupcakes and 12 cookies
Step-by-step explanation:
Having trouble using logarithmic differentiation!
Answer:
Having trouble using logarithmic differentiation!
A single basket basketball match will be organized by forming 3 teams in equal numbers from a group of 9 students. In how many ways can these three teams be formed?
~combination
[tex] \large \sf C(n,r) = \frac{n!}{(n-r)! .r!} [/tex]
[tex] \large \sf = C(9,3) = \frac{9!}{(9-3)!.3!} [/tex]
[tex] \large \sf = \frac{9!}{6!.3!} [/tex]
[tex] \large \sf= \frac{(9.8.7.6.5.4.3.2.1)}{(6.5.4.3.2.1).(3.2.1)} [/tex]
[tex] \large \sf = \frac{362880}{720.6} [/tex]
[tex] \large \sf = \frac{362880}{4320} [/tex]
[tex] \large \sf = \boxed{84}\: ✓[/tex]
~ nice to help you ^^
what is the slope of the line
Answer:
slope = 3/2
Step-by-step explanation:
Step 1: Select two points from the graph.
(3,0) and (1,-3) are two points on the graph.Step 2: Apply the formula to find slope- [tex]\frac{y_2-y_1}{x_2-x_1}[/tex].
[tex]\frac{-3-0}{1-3}[/tex] [tex]\frac{-3}{-2}[/tex] [tex]\frac{3}{2}[/tex]Therefore, the slope is 3/2.
How to convert minutes and seconds into grades.
Answer:
Step-by-step explanation:
To convert time to time, kernel time with 24 (number of time in a day).
To convert time to minutes, kernel with time with 1440 (number of minutes in a day = 24 * 60).
To convert s to seconds, multiply the time by 86400 (number of s in a day = 24 * 60 * 60).
Chad collected 256 M&Ms but lost 5/8 of them on his way to
sehool through a hole in his
bag. When he arrived at school how many M&Ms did Chad have left?
Chad had 96 M&Ms left when he arrived at school.
Chad initially collected 256 M&Ms.
However, he lost 5/8 of them on his way to school through a hole in his bag.
To determine how many M&Ms Chad had left when he arrived at school, we need to calculate the fraction that represents the M&Ms he did not lose.
If Chad lost 5/8 of the M&Ms, it means he kept 1 - 5/8 = 3/8 of them.
To find the number of M&Ms Chad had left, we multiply 3/8 by the total number of M&Ms he initially collected:
(3/8) [tex]\times[/tex] 256 = (3 [tex]\times[/tex] 256) / 8 = 768 / 8 = 96.
Therefore, Chad had 96 M&Ms left when he arrived at school.
In summary, Chad initially collected 256 M&Ms but lost 5/8 of them, leaving him with 3/8 of the total.
Multiplying 3/8 by 256 gives us 96 M&Ms, which is the number of M&Ms Chad had left when he arrived at school.
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The quotient of k and 9 is greater than 1/3
the value of y varies directly with X. Which function represents the relationship between X and Y if y equals 15/6 when x equals 20
Answer:
y = (1/8)x
Step-by-step explanation:
The relevant basic formula is y = kx, where k is the constant of proportionality.
We must find k. To do this, let y = 15/6 and x = 20 in the above formula:
15/6 = k(20)
We solve for k by dividing both sides by 20: 15/(6*20) = k = 1/8
Then the specific formula for this situation is y = (1/8)x
given m||n, determine the value of x (4x-7) (3x+9)
Step-by-step explanation:
7×4-=28-×3×9=27×28-=756-
What is the length of segment AB?
A-5
B-6
C-8
D-10
a student says that if 5x^2 = 20, then x must be equal to 2. do u agre or disagree with the student? justify your answer.
Answer:
The student is correct.
Step-by-step explanation:
Given that 5x² = 20:
It is true that the value of x = 2 because 2² = 4, and when you multiply 4 with 5, you'll get a product of 20:
5x² = 20
5(2)² = 20
5(4) = 20
20 = 20
Therefore, the student is correct that x = 2.
David was thinking of a number. David doubles it, then adds 3 to get an answer of 81. 6. What was the original number?.
Answer:
The answer is 39.3
Step-by-step explanation:
81.6 - 3 = 78.6
78.6 ÷ 2 = 39.3
What is 2 1/4 divided by 4 2/3
Answer: (27/56)
Step-by-step explanation:
(2 1/4)/(4 2/3)
(9/4)/(14/3) [Convert the integers on both sides to leave just fractions.
(9/4)*(3/14) [Invert the denominator and multiply times the numerator]
(27/56)
[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]
[tex] \frac{27}{56} \\ \\ in \: \: alternate \: \: form \\ \\ 0.482142857[/tex]
Step-by-step explanation:
[tex]2 \frac{1}{4} \div 4 \frac{2}{3} [/tex]
convert the mixed number to an improper fraction[tex] \frac{9}{4} \div \frac{14}{3} [/tex]
to divide by a fraction, multiply the reciprocal of that fraction[tex] \frac{9}{4} \times \frac{3}{14} [/tex]
multiply the fraction[tex] = \frac{27}{56} \\ \\ in \: alternate \: \: form \\ \\ 0.482142857[/tex]
hope it helps[tex] \: \: \: \: \: \: \: \: \: [/tex]
Help !! I don’t understand
Answer: .8, -.9, -.5, .9 (estimates)
Step-by-step explanation: correlation coefficients are between -1.0 and 1.0.
-1.0 means a perfectly negative correlation, which will be a straight line going down from left to right
0 means no correlation, it's just random points on the graph with no sense of direction or relationship
1.0 means a perfectly positive correlation, which will be a straight line going up from left to right
the more line-like the shape the data points make are, the further away the correlation coefficient is from 0. you can tell if it's negaitive or positive from the direction of the line.
Nate earns extra money on the weekends mowing lawns. He charges $14.00$ to work for the first hour. He charges $10.50 for each additional hour. Let hh equal the number of hours after the first hour. Which expression represents how much Nate charges?
Answer:
m=14+10.50h
Step-by-step explanation:
h represents hours. m represents how much he makes
he's going to get 14 dollars, plus 10.50 times however many hours he works.
Enter the value of x that makes the equation 3x + 4 + 2x + 2 = -24
answer? and how would I answer this.
Answer:
x = -6
Step-by-step explanation:
Combine like terms.
5x + 6 = -24
Subtract 6 from both sides.
5x = -30
Divide by 5 on both sides.
x = -6
Follow Me:-
[tex]3x + 4 + 2x + 2 = - 24 \\ \\ = > 5x + 6 = - 24 \\ \\ = > 5x = - 24 - 6 \\ \\ = > 5x = - 30 \\ \\ = > x = \cancel \frac{ - 30}{5} \\ \\ = > x = - 6[/tex]
Hope This HelpsPlease answer below :) I will mark the brainiest answer
Answer:The last option is correct.
Step-by-step explanation:
There is a proportional relationship between minutes and dollars per minute, shown on a graph of printing expenses. The graph passes through the point (1, 3.40). What is the slope of the graph? What is the unit rate? Complete the explanation.
Answer:
Below!
Step-by-step explanation:
The slope is 1. The unit rate is $4.75/min If the graph of a proportional relationship passes through the point (1 , R) then r equals the slope and the unit rate. $4.75 per min.
The slope of the graph resembles the unit rate.
The unit rate is the amount it cost per minute.
The graph passes through the point (1, 3.40), which means it is at x = 1, the rate is $4.75.