In 2010, a city's population was 1,405,233 and it was decreasing at a rate of 1.1%. At this rate when will the city's population fall below 1,200,000?
a. 2024
b. 2027
c. 2036
d. 2049
A log function is a way to find how much a number must be raised in order to get the desired number. The population of the city will be 1,200,000 in the year 2024.
What is Logarithm?A log function is a way to find how much a number must be raised in order to get the desired number.
[tex]a^c =b[/tex]
can be written as
[tex]\rm{log_ab=c[/tex]
where a is the base to which the power is to be raised,
b is the desired number that we want when power is to be raised,
c is the power that must be raised to a to get b.
For example, let's assume we need to raise the power for 10 to make it 1000 in this case log will help us to know that the power must be raised by 3.
The decrease in the population of the city can be written as,
[tex]\rm Final\ population=(Initial\ population)\times (1-r)^n[/tex]
[tex]1,200,000=1,405,233(1-0.011)^n\\\\0.8539=(0.989)^n\\\\\rm log(0.8539)=n\ log(0.989)\\\\n= \dfrac{log(0.8539)}{log(0.989)}\\\\n=14.279 \approx 14.3[/tex]
Since the initial population was 1,405,000 in the year 2010, then the population of the 1,200,000 will be 14 years later.
Thus, the population of the city will be 1,200,000 in the year 2024.
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Which one is it? Will give brainiest
Eliminate the parameter to find a cartesian equation of the curve. x = 3sin(t), y = 4cos(t)
To eliminate the parameter and find the cartesian equation of the curve x=3sin(t), y=4cos(t), we can use trigonometric identities. The cartesian equation of the curve is (x/3)^2 + (y/4)^2 = 1.
Explanation:To eliminate the parameter and find the cartesian equation of the curve x=3sin(t), y=4cos(t), we can use trigonometric identities. Starting with the given equations:
x = 3sin(t)
y = 4cos(t)
We can rewrite the equation for x as:
x/3 = sin(t)
And the equation for y as:
y/4 = cos(t)
Using the identities sin2(t) + cos2(t) = 1, we can square both equations and add them together:
(x/3)2 + (y/4)2 = (sin2(t) + cos2(t)) = 1
This is the cartesian equation of the curve.
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Can derivatives be used to measure the the slope of the tangent line at x=a
The coach attempts to determine an association between shirt size and hat size. Which is most likely true?
Answer:
There is likely an association because 0.8 is not similar to ≈ 0.33.
The spring has a stiffness k=200n/m and is unstretched when the 25 kg block is at
a. Determine the acceleration of the block when s=0.4m. The contact surface between the block and the plane has
This is a Physics problem involving Hooke's Law and Newton's second law of motion. The acceleration of a 25kg block when a spring it's resting on is extended by 0.4m is determined. The calculated acceleration is -3.2m/s², indicating the direction is opposite to the direction of displacement.
Explanation:The subject matter of this question is physics, specifically the area of mechanics dealing with forces, mass, and acceleration (Newton's Laws). The stiffness of a spring is given as k=200N/m and it is unstretched when the 25 kg block is resting on it. We're tasked with finding the acceleration of the block when the spring is extended by s=0.4m.
Firstly, let's find the force on the block using Hooke's Law which states that the force exerted by a spring is equal to the spring constant times the displacement (F=-kx). So, F=-200N/m*(0.4m)=-80N. The negative sign just indicates that the force is in the opposite direction of the displacement.
Secondly, we apply Newton's second law of motion (F=ma), where m is the mass and a is the acceleration. Rearranging the equation to find acceleration gives us a=F/m. Substituting our values gives a=-80N/25kg = -3.2m/s². The negative sign here indicates the direction of the acceleration, opposite to the direction of displacement. So, the acceleration of the block when the spring is extended by 0.4m is -3.2m/s².
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if a recipe calls for 0.800 kg of flour , about how many ounces of flour does it need? (1lb=16 oz, 1 lb = 0.454 kg )
5.8 oz
11.0oz
28.2oz
227oz
Answer: The correct option is (C) 28.2 oz.
Step-by-step explanation: Given that a recipe calls for 0.800 kg of flour.
We are to find the number of ounces of flour that the recipe needs.
Given that
1 lb=16 oz and 1 lb = 0.454 kg
We will be using the UNITARY method for solving the given problem.
We have
0.454 kg = 1 lb
So, 1 kg will be equal to [tex]\dfrac{1}{0.454}~\textup{lb}.[/tex]
Therefore, 0.8000 kg is equal to
[tex]\dfrac{1}{0.454}\times 0.800=1.762~\textup{lb}.[/tex]
Now, 1 lb = 16 oz.
So, 1.762 lb = 16 × 1.762 = 28.19 = 28.2 oz.
Thus, the recipe needs 28.2 oz of flour.
Option (C) is CORRECT.
divide (x^3-20x+16)divide (x-4)
A triangle has sides with lengths: 6, 9, and 5. How do you find the area of the triangle using Heron's formula?
Please help with geometry
Solve for m -20+14m=10m+16
Assume we have two lines which are perpendicular. If one line has a slope of 3, what is the slope of the other line? Enter your answer as an integer or fraction in lowest terms.
The slope of a line perpendicular to a line with a slope of 3 is -1/3. This is because perpendicular lines have negative reciprocal slopes.
Explanation:In mathematics, when two lines are perpendicular, their slopes are negative reciprocals of each other because the product of their slopes equals to -1. This means that if one line has a slope of 3, the slope of the other line would be the negative reciprocal of 3, which is -1/3. So, the slope of the other line is -1/3.
To understand this further, let's delve into the figure of Slope and the Algebra of Straight Lines. Here, 'm' represents the slope which is the rise over the run and 'b' is the y-intercept, which is the point at which the line crosses the y-axis. Considering the fact that the slope of the line is 3, there is an increase of 3 in the y-coordinate (or vertical axis) for every increase of 1 in the x-coordinate (or horizontal axis).
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Find the missing values given that cos(theta) = 1.
Sin(Theta):
Csc(Theta)
Sec(Theta):
Cot(Theta):
Rebecca is planting an orange grove that covers 32 acres she uses the same amount of ground space for each tree Rebecca plants 15 trees in a section of the grove that measures 250 feet by 25 feet what is the population density of this section of the grove use 1 acre= 43,560 square feet
If you take 5 quizzes and get scores of 95%, 95%, 80%, 85%, and 75%, how would you find your mean quiz score?
The mean of the quiz scores is given by the equation M = 86 %
What is Mean?The mean value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.
Mean = Sum of Values / Number of Values
Given data ,
Let the mean of the quizzes be represented as M
Now , the equation will be
Let the number of quizzes be n = 5
Let the scores of each quizzes be represented by set A
Set A = { 95% , 95%, 80%, 85%, 75% }
So , the mean of the quizzes M = sum of the quizzes / number of quizzes
Substituting the values in the equation , we get
The mean of the quizzes M = ( 95% + 95% + 80% + 85% + 75% ) / 5
The mean of the quizzes M = ( 430/5 )
The mean of the quizzes M = 86 %
Therefore , the value of M is 86 %
Hence , the mean of the quizzes is 86 %
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!!!!!!!!!!!!!which answe
Answer:
I think it's D
Step-by-step explanation:
A gas station sells regular gas for $2.20 per gallon and premium gas for $3.00 a gallon. at the end of a business day 300 gallons of gas has been sold, and receipts totaled $700. how many gallons of each type of gas had been sold
Solve 5x = 10x - 5(2x-3) for x. Show your work.
Eliminate parentheses using the distributive property.
... 5x = 10x -10x +15
Collect terms, then divide by the coefficient of x.
... 5x = 15
... x = 3
Jayden wants to find the dimensions of this parallelogram. He knows that the first step is to find the value of x. Which of these equations will result in the correct value of x?
A. 2x – 1 = x + 8
B. 2x – 1 = x + 1
C. x + 1 + 2x – 1 = 180
D. x + 1 = x + 1
Answer:
2x – 1 = x + 8
Step-by-step explanation:
A graph of a linear function intersects the coordinate axes in points (1, 0) and (0, 2). What is the equation of this function?
Please answer! Thank you!!!
What is the vertex of the absolute value function defined by f (x) = |x - 7| + 1?
A. (7,1)
B. (-7, -1)
C. (-7, 1)
D. (7, -1)
What’s the answer for No.29 & 30 please hurry
In the figure above, Angle FEB is a central angle. True or False?
A. True
B. False
We know that the central angle is an angle subtended at the center of the circle by any two points on the circle.
In the given figure of the circle, the center of the circle is C. Hence, the central angle must be subtended at the center C.
Since, angle FEB is not subtended at the center of the circle.
Hence, angle FEB is not a central angle.
Therefore, the given statement is FALSE.
Aaron took three times as many pictures as jennifer.jennifer has 16 fewer pictures than aaron.which system of equations can be used to find the number of oictures each person took?
how do you evaluate 71 - b, if b is 27
Mrs. rifkin had 84 oranges. 24 of her oranges were rotten; the rest were either ripe or unripe. there were 18 more ripe oranges than unripe oranges. find the ratio of the number of ripe oranges to the number of rotten oranges to the number of unripe oranges.
What is the sum of the arithmetic sequence 153, 139, 125, ..., if there are 22 terms?
Answer:
Sum of the sequence = 132.
Step-by-step explanation:
The given sequence is 153, 139, 125,.......n terms.
Sum of the arithmetic sequence will be
S = n/2[2a + (n -1)d]
where n = number of terms
a = first term of the sequence
d = common difference
for the given sequence
a = 153
n = 22
d = 139 - 153 = -14
Therefore sum of 22 terms of the sequence will be
S = (22/2)[2×153 - (22-1)14]
= 11×[306 - 21×14]
= 11×[306 - 294] = 11×12 = 132
Sum of 22 terms of this sequence is 132.
Find the ranges of the function ƒ(x) = |x + 4| + 1 and the range of the exponential function g(x) represented by the graph below.
Are they the same? Explain.
Determine whether quantities vary directly or inversely and find the constant of variation. It takes four identical water pumps 6 hours to fill a pool. How long would it take three of these same pumps to fill the pool, assuming they all pump at the same rate?
Let the number of water pumps be n and the time taken to fill the pool is t.
Now, we can see that higher the number of water pumps, lesser the time to fill the pool.
It means quantities vary indirectly.
Thus, [tex]n=\frac{k}{t} , \text{ where k is the constant of variation}[/tex]
Now, we have been given that It takes four identical water pumps 6 hours to fill a pool.
Thus, we have
[tex]4=\frac{k}{6} \\ \\ k=24[/tex]
Hence, constant of variation is 24.
Now, we have to find the time that three pumps will take to fill the same pool.
[tex]3=\frac{24}{t} \\ \\ 3y=24\\ \\ y=\frac{24}{3} \\ \\ y=8[/tex]
Hence, it will take 8 hours to fill the pool by three identical pumps.
Find the volume of a cube that is 7 cm on each edge.
Final answer:
The volume of a cube with each edge measuring 7 cm is calculated using the formula V = s^3, which results in a volume of 343 cubic centimeters (cm3).
Explanation:
To find the volume of a cube that is 7 cm on each edge, we use the formula for the volume of a cube, which is V = s3, where s is the length of one side of the cube. In this case, s is 7 cm. Therefore, the volume can be calculated as follows:
V = 7 cm imes 7 cm imes 7 cm = 343 cm3
So the volume of the cube is 343 cubic centimeters (cm3).