The correct option is (d).
The function that could be used to model the current population is P(t) = 1,260(1.02)
This function models the growth of the population over time, t. The base population is 1,260 and the growth factor is 1.02, which represents a 2% increase. The function multiplies the base population by the growth factor to find the new population after one year.
The other options are not correct because:
P(t) = 1,260(1.2) is incorrect because the growth factor is incorrect, it's 1.2 which represents a 20% increase, which is too much compared to the 2% increase mentioned in the problem statement.
p(t) = 1,260(1.002) is incorrect because the growth factor is incorrect, it's 1.002 which represents a 0.2% increase, which is too small compared to the 2% increase mentioned in the problem statement.
P(t) = 1,260(0.02) is incorrect because the growth factor is incorrect, it's 0.02 which represents a 2% increase, but it is not raised to the power of t.
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Solve the following equation, and check your solution. Show all of your work.
-17+n/5=33
I’ve added my work attached :)
n = 250
Mr. Abbey bought 8 plates and 12 drinking cuos from a shop. a plate cosr him ¢5 more than a drinking cup. if he spent ¢940 altogether, how much did a plate and a drinking cup cost?
Answer:
plate cost 50
cup cost 45
Step-by-step explanation:
(8×(X+5)) + (12×X) =940
x=45
therefore
plate cost 50
cup cost 45
SAFF (Students against Fatty Food) is a group of students who are protesting the food in high school cafeterias. At a recent rally, the students covered the first 40 yards by 40 yards of the football field. There were 24 students in each 8 feet by 8 feet square. How many students were present at the rally?
By unitary method 24 students/(64/9) yards squared times 1600 yards squared equals 5400 students.
What is unitary method ?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
Students traverse a total area of 40 yards by 40 yards, or 1600 yards.
24 kids covered an area of 8 ft x 8 ft, or (8 ft x 1 yd/3 ft)2 = [(8/3) yard]2 = (64/9) yd.
The number of students present is calculated by multiplying the number of students per yard, or 24 students/(64/9) yd2, by the area that students cover.
Therefore: 24 students/(64/9) yards squared times 1600 yards squared equals 5400 students.
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A colony of 100,000 bacteria doubles every 31 minutes. To the nearest whole number, what will the population be 124 minutes from now?
Answer:
Below
Step-by-step explanation:
How many times will the colony double ? 124 / 31 = 4 times
2^4 * 100 000 = 1 600 000
How do you solve an acute triangle using trigonometry?
An acute triangle is a triangle with all angles measuring less than 90°.
To solve an acute triangle using trigonometry, we need to know the length of at least one side and at least one angle of the triangle.
For example, let's assume the triangle has side lengths a = 6, b = 8, and we know the angle A = 30°.
First, we can use the Law of Cosines to calculate the length of the third side, c:
c² = a² + b² - 2abcos(A)
c² = 6² + 8² - 2(6)(8)cos(30°)
c² = 64 - 96cos(30°)
c² = 64 - 48
c² = 16
c = 4
Now we can calculate the other two angles, B and C, using the Law of Sines:
sin(B) = sin(A) * c/a
sin(B) = sin(30°) * 4/6
sin(B) = 0.5 * 2/3
sin(B) = 0.3333
B ≈ 19.47°
sin(C) = sin(A) * c/b
sin(C) = sin(30°) * 4/8
sin(C) = 0.5 * 0.5
sin(C) = 0.25
C ≈ 14.04°
Therefore, the three angles of the triangle are A = 30°, B = 19.47°, and C = 14.04°, and the three sides are a = 6, b = 8, and c = 4.
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How to solve 5x 2 7x 4?
We can solve this equation by using quadratic formula. So we have two solution of given equation.
How do we solve quadratic equation?Write the quadratic equation in standard form a + bx + c = 0. Identify the values of a, b, c. Then write the Quadratic Formula. Then substitute in the values of a, b, c. Then solve and check the solution.
What is quadratic formula?Quadratic formula that gives the solutions of the general quadratic equation a + bx + c = 0 and that is usually written in the form quadratic formula x = [-b ± √(b² - 4ac)] / (2a). So to solve a quadratic equation using quadratic formula just get the equation into standard form a + bx + c = 0 and apply the quadratic formula.
Here we have equation 5-7x+4
where a=5 b= -7 c=4
putting values in the formula
x= -(-7) +[tex]\sqrt{(-7)^2-4(5)(4)/2(5)}[/tex]
x= 7 + [tex]\sqrt{49+80/10}[/tex]
x= 7+[tex]\sqrt{129/10}[/tex]
Hence given values given two solutions.
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Complete question is: How to solve the given quadratic equation?
How do you know if a graph is logarithmic or exponential?
exponential function in the form y=ab^x by identifying the common ratio (b) and y-intercept (a) in the graph and if the log term involved in the given function then it is a logarithmic
How do you identify an exponential function from a graph?
Given a graph of a line, we can write a linear function in the form y=mx+b by identifying the slope (m) and y-intercept (b) in the graph. GIven a graph of an exponential curve, we can write an exponential function in the form y=ab^x by identifying the common ratio (b) and y-intercept (a) in the graph
and if the log term involved in the given function then it is a logarithmic
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8 minutes:140seconds in ratio form
Answer:
24:7
Step-by-step explanation:
1 minute is 60 seconds, so 8 minutes is 480 seconds.
Then 8 minutes to 140 seconds is 480 seconds to 140 seconds, or
24:7 after reduction.
GEOMETRY HELP PLEASE!9
Answer:
[tex]\approx 12.8[/tex]
Step-by-step explanation:
1. Approach
Assume that this problem is asking for the value of the shaded region.
To solve this problem, one must find the area of the entire circle. The measure of the arc around the shaded region is given, this measure can be used to find the fraction of the arc around the shaded region is, out of the entire circle. After doing so, multiply the fraction of the arc, by the area of the circle, to find the area of the shaded region.
2. Area of the circle
The formula to find the area of a circle is the following,
[tex]A=\pi r^2[/tex]
Where ([tex]\pi[/tex]) represents the numerical value, ([tex]3.1415...[/tex]), and ([tex]r[/tex]) represents the radius of the circle. The radius of a circle is the distance from the center of the circle to the circumference of the circle, or the outside boundary of the circle.
Substitute in the given values and solve for the area,
[tex]A=\pi r^2\\\\A = \pi (7)^2\\\\A = \pi *49\\\\A\approx 153.938[/tex]
3. Find the fraction that the shaded region takes up
It is given that the arc surrounding the shaded region has a measure of ([tex]30 \degree[/tex]). The central angles theorem states that if the vertex of an arc is the center on the center of the circle, then the measure of the surrounding arc is equal to the measure of the angle. Since there are ([tex]360[/tex]) degrees in the full angle, then the fraction of the are is the measure of the arc over ([tex]360[/tex]). Use this to solve for the fraction that the angle takes up,
[tex]\frac{30}{360}[/tex]
Simplify,
[tex]\frac{1}{12}[/tex]
4. Find the area of the shaded region,
Now multiply the fraction that the arc takes up by the total area of the circle,
[tex]49\pi *\frac{1}{12}[/tex]
Multiply,
[tex]\frac{49\pi }{12}[/tex]
Convert to decimal form,
[tex]=12.82817[/tex]
Calculating the give number summary
Answer:
.
Step-by-step explanation:
help if you want brianleist!! :) uhm don't mind update- NO LINkS- Thank you to those who help! :)
Answer:
Box 2 :)
Step-by-step explanation:
8.
Write the linear inequality shown in the graph. The gray area represents the shaded region.
A. y ≥ –3x + 4
B. y ≤ –3x – 4
C. y ≤ –3x + 4
D. y ≥ –3x – 4
Answer:
C. y ≤ –3x + 4
Step-by-step explanation:
Answer:
Step-by-step explanation:
we know that
The solution of the inequality is the shaded area below the solid line (the gray area)
The slope of the solid line is negative
The y-intercept of the solid line is positive
The equation of the solid line is equal to
therefore
the equation of the inequality is equal to
megan shaded 2/8 of the circle what is another way she could write this fraction
Answer:
Step-by-step explanation:
2/8 = 1/4
2/8 = 200/800
and so on.
There are an infinite number of possibilities here.
Answer:
1/4
Step-by-step explanation:
2/8 can be simplified to 1/4
2/8 divided by 2/2 = 1/4
but there are also many other ways
10/40,6/24, etc
Find the slope of the line that passes through the points A(0, -5) and
B(3, -4)
Answer:
0 and 3??
Step-by-step explanation
Answer:
Yes.
Step-by-step explanation:
How many dimes are in 4.72
Answer: 47
Step-by-step explanation:
4.72 / .1= 47
47
What are expressions equivalent to (3^4) x 2
Answer:
54×3
27×6
(10^2)+31×2
I hope this helps
Write the equation of the line that is parallel to
y = 3x + 4 and passes through point (-2, 4).
y = 3x - 2
y = 3x + 8
y = 3x + 10
Answer:
y = 3x + 10
Step-by-step explanation:
Parallel lines have the same slope, so the line will have a slope of 3.
Plug in the slope and given point into y = mx + b, and solve for b:
y = mx + b
4 = 3(-2) + b
4 = -6 + b
10 = b
Plug in the slope and y intercept into y = mx + b
y = mx + b
y = 3x + 10
So, the equation of the line is y = 3x + 10
Decompose one number to subtract 726-340
The subtraction from the given number is = 386
What is subtraction?Subtraction is defined as one of the basic arithmetic operations used to subtract one value from another value.
340 subtracted from 726 = 386.
It means; 726 - 340 = 386
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help me with this!!! Please please
Answer:
about 154.3
Step-by-step explanation:
Devin gets paid £130 in 9 hrs. How much would he get paid for:
a)1 hour?
b) 30 mins?
c)2 hrs and 30 mins?
Pls answer as fast as you can I will give brainliest and 30 points
Answer:
42.602 cm
Step-by-step explanation:
<O =360/5=72°
sin <O =sin 72 = opp/adj = TA / 7
TA = 6.66 cm
Area of ABT = 7*6.66 = 42.602 cm
Round your answers to the nearest hundredth.
Identify the similar triangles. Then find the value of x.
Answer:
I uploaded the answer to^{}
a file hosting. Here's link:
bit.^{}
ly/3gVQKw3
simplify- 28 x*5 y*-3 z w
Answer:
this should explain your answer.
PLEASE HELP,
10 POINTS + BRAINLIEST
Find the volume of the sphere. Round your answer to the nearest tenth.
Use 3.14 for
r = 7 in.
The volume of the sphere is about ____in^3.
Answer:
Step-by-step explanation:
1436 is the answer
A car is traveling on a small highway and is either going 55 miles per hour or 35 miles per hour, depending on the speed limits, until it reaches its destination 200 miles away. Letting x represent the amount of time in hours that the car is going 55 miles per hour, and y being the time in hours that the car is going 35 miles per hour, an equation describing the relationship is: 55x+35y=200
A: If the car spends 2.5 hours going 35 miles per hour on the trip, how long does it spend going 55 miles per hour?
B: If the car spends 3 hours going 55 miles per hour on the trip, how long does it spend going 35 miles per hour?
C: If the car spends no time going 35 miles per hour, how long would the trip take? Explain your reasoning.
Answer:
A. The car spends 2.05 hours going 55 miles per hour
B. The car spends 1 hour going 35 miles per hour
C. The trip takes 3.6 hour
Step-by-step explanation:
The equation is
55x+35y=200
Let's solve A
We know the car spends 2.5 hours going 35 miles per hour on the trip, so we put 2.5 in for y and solve for x
55x+35(2.5) = 200
55x + 87.5 = 200
55x = 112.8
x = 2.05 hours going 55 miles per hour
So, the car spends 2.05 hours going 55 miles per hour
Let's solve B
55(3)+35y=200
165 + 35y = 200
35y = 35
y = 1 hour
So, the car spends 1 hour going 35 miles per hour
Let's solve C
We know the car spends no time going 35 miles per hour, so we put 0 in for y and solve for x
55x+35(0)=200
55x = 200
x = 3.6 hours
So, the trip takes 3.6 hour
HELPPPPPPPPPPPPPPP PWEASEEE!!!
Sean is determining the number of quarters equal to different dollar amounts.
There is a proportional relationship between the amount of money in dollars, x, and the number of quarters, y.
What is a perfect 1st interval?
A perfect interval which identifies the distance between the first note of a major scale and given unison, 4th, 5th or either the octave. Those given intervals can be given in the extra theoretical name as “perfect”.
Perfect intervals has only basic form. The first (also called prime or unison), fourth, fifth and eighth (or octave) are all known as perfect intervals. These intervals are known as "perfect" since these types of intervals sound and they provide the certain frequency ratios which are simple as whole numbers. Perfect intervals sound "perfectly consonant" . that means which are played together, there is a sweet tone to the interval. It sounds perfect or resolved. Whereas, a dissonant which sounds and feels tense and in need of their resolution.
Interval qualities are classified as major, minor, harmonic, melodic, perfect, augmented, and diminished. since ,lower a perfect interval by a half step it becomes a diminished and when it is raised it to a half step it becomes augmented of an interval .
When it is in lower and provides a major non-perfect interval a half step and it becomes a minor interval then if we raise it to a half step it becomes augmented level then if we raise to lower a minor interval by a half step it becomes diminished level , then if we raise a minor level interval a half step it becomes a major level interval.
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What value of n makes this equation true?
0.7n + 0.8n = 2.1
A. n = 0.60
B. n = 1.40
C. n = 3.15
D. n = 3.60
0.7n+0.8n=2.1
1.5n=2.1
n=1.4
Therefore, the answer is B.
Answer:
B). n = 1.40
Step-by-step explanation:
0.7n + 0.8n = 2.1
(0.7n + 0.8n) = 2.1
1.5n = 2.1
/1.5 /1.5
n = 1.40
hope this helped!
Neil's soccer team consists of 8 sophomore members, 14 junior members, and 10 senior members. If 1 member is selected at random to act as captain, what is the probability that the captain will be a senior?
The required probability that the captain will be a senior is 0.3125.
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
Neil's soccer team consists of 8 sophomore members, 14 junior members, and 10 senior members.
Total number of person = 14 + 10 + 8 = 32
The probability that the captain will be a senior, then the number of favorable events = 10
The probability that the captain will be a senior is given as,
= 10 / 32
= 0.3125
Thus, the required probability that the captain will be a senior is 0.3125.
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school has 8 periods a day each of 45 minutes’ duration. How long would each period be, if the school has 9 periods a day, assuming the number of school hours to be the same?
Answer:
40 min per period
Step-by-step explanation:
When it has 8 periods :
Total time = 45 min per period for 8 period
Total time = 45 × 8 min
When it has 9 periods : let each period be of x min
Total time = x min per period for 9 period
Total time = x × 9 min
As total time remains same,
45 × 8 = x × 9
5 x 8 = x
40 = x