the trigonometric function of all the given question is obtained.
What is Trigonometric Functions?
Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.
Given: Cos θ = (3/5), Find: Csc θ = 5/4
Given: Sin θ = (5/6), Find: Cot θ = 11/5
Given: tan θ = (3/4), Find: Cot θ= 4/3
Given: Sec θ = (7/2), Find: Cos θ= 2/7
Given: Sin θ = (2/3), Find: Cosec θ=3/2
Given: Sin θ = (2/3), Find: Cos θ=5/3
Given: Tan θ = (6/4), Find: Sin θ=6/7.21
Given: Tan θ = (7/5), Find: Cos θ=5/8.6
Given: Tan θ = (7/5), Find: Sec θ= 8.6/5
Hence the above trigonometric function of all the given question is obtained.
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What is 80% of a 25 question test?; How many questions do you have to get right out of 20 to get 80 %?
To get 80% percentage you need to attempt 20 question
Percentage:
In mathematics, a percentage (from Latin: per centum, "by a hundred") is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%",although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number (pure number); it has no unit of measurement.
For example, 45% (read as "forty-five per cent") is equal to the fraction
45/100, the ratio 45:55 (or 45:100 when comparing to the total rather than the other portion), or 0.45. Percentages are often used to express a proportionate part of a total.
now we need to find 80% of a 25 question test
80% of 25 can be written as 80% × 25
= 80/100 × 25
= 20
To get 80% you need to attempt 20 question
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10. assume that the annual earnings of 23 college students are used in a simple random sample with a mean of $4590 and a standard deviation of $860. construct a confidence interval for the standard deviation if we want a 99% confidence level for our interval
Using the t-distribution, the 99% confidence intervals for the given standard deviation are given as follows: (5053.39 , 4126.61)
Given that,
Number of college students = 23
A simple random sample with a mean = $4590
A simple random sample with a standard deviation = $860
What is a t-distribution confidence interval?The t distributions is wide (has thicker tailed) for smaller sample sizes, reflecting that s can be smaller than σ. The thick tails ensure that the 80%, 95%, 99% confidence intervals are wider than those of a standard normal distribution (so are better for capturing the population mean).
The confidence interval is:
= μ ± [tex]t\frac{s}{\sqrt{n} }[/tex]
In which:
μ is the sample mean.
t is the critical value.
n is the sample size.
s is the standard deviation for the sample.
The critical value, using a t-distribution calculator, for a two-tailed 99% confidence interval, with 23 - 1 = 22 df,
Upon using a t -table or a calculator, we see that the critical t -value for this 99% confidence interval is t0.005=2.581
The parameters are:
μ = $4590
n = 23
Hence, with s = 860, the bounds of the interval are:
= μ ± [tex]t\frac{s}{\sqrt{n} }[/tex]
= 4590 ± 2.581 [tex]\frac{860}{\sqrt{23} }[/tex]
= 4590 ± 2.581 [tex]\frac{860}{4.79}[/tex]
= 4590 ± 2.581 (179.54)
= 4590 ± 463.39
Then,
= 4590 + 463.39 , 4590 - 463.39
= 5053.39 , 4126.61
Therefore,
Using the t-distribution, the 99% confidence intervals for the given standard deviation are given as follows: (5053.39 , 4126.61)
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The ratio of dye to pounds of clothing is constant. A worker develops the chart below to show the amount of dye needed for different amounts of clothing.
Clothes Dyeing
Weight of clothing (pounds)
Cups of dye
21
3
42
9
84
12
105
15
For which weight of clothing is the ratio of weight to dye different from the other ratios?
21 pounds
42 pounds
84 pounds
105 pounds
The weight of clothing is the ratio of weight to dye is different from the other ratios is B. 42 pounds.
How to calculate the ratio?Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
It should be noted that from the information given, others have a ratio of 1:7. This is different for 42 pounds since the ratio is:
= 42/9
= 14:3
In conclusion, the correct option is B.
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The water in the swimming pool was as blue as the sky.
True or false. The author uses this figurative language to help the reader understand the color of the water.
True
False
Answer:
true
Step-by-step explanation:
the author compares the color of the water to the color of the sky. so that makes it figurative language.
hope this helps.
Hari's weekly allowance varies depending on the number of chores he does. He received $24 in allowance the week he did 20 chores, and $16 in allowance the week he did 4 chores. Write an equation for his allowance in slope-intercept form.
Answer:
24 / 16
Step-by-step explanation:
divide and do the thing
Serena buys 15 shirts with five $100.00. She gets $22 change, What is the cost per shirt?
Answer:
98.53
Step-by-step explanation:
[tex]100 \times 5 = 1500 \\ 1500 - 22 = 1478 \\ 1478 \div 15 = 98.53[/tex]
Mai had $210 in her checking
account at the beginning of the month.
She wrote checks for $32 and $9.59. At
the end of the month, the bank credited
her account with $0.84 interest. How
much money did Mai have in the
account then?
Please explain the answer!
Answer: She had 167.57 remaining in her account
Step-by-step explanation:
You add all her expenses and then subtract it from the beginning balance
Determine the singular points of the given differential equation. Classify each singular point as regular or irregular. (Enter your answers as a comma-separated list. Include both real and complex singular points. If there are no singular points in a certain category, enter NONE.) (x3 + 25x)y" – 5xy' + 6y = 0 regular singular points X = irregular singular points X =
After solving, the regular singular points are x=0, 5i, -5i.
We have to determine the singular points of the given differential equation. Classify each singular point as regular or irregular.
(x^3+25x)y"–5xy'+6y = 0
On comparing with the equation P(x)y''+Q(x)y'+R(x)y=0
P(x) = (x^3+25x)
P(x)=0
x^3+25x = 0
x=0, 5i, –5i be the singular point.
Now write equation 1 in the standard form
Divide by x^3+25x on both side, we get;
y"–5x/(x^3+25x) y'+6/(x^3+25x) y = 0
y"–5/(x^2+25) y'+6/x(x^2+25) y = 0
Comparing with the standard form of equation;
y''+P(x)y'+Q(x)y = 0
P(x) = –5/(x^2+25) Q(x)=6/x(x^2+25)
We know that if [tex]\lim_{x \to x_{o}}(x-x_{o})p(x)\text{ and }\lim_{x \to x_{o}}(x-x_{o})^2q(x)[/tex] exist finite. Then the singular point [tex]x_{o}[/tex] is regular singular point else irregular singular point.
(a) At [tex]x_{o}[/tex]=0
[tex]\lim_{x \to 0}(x-0)p(x)=\lim_{x \to 0}\frac{-5x}{x^2+25}[/tex]
[tex]\lim_{x \to 0}(x-0)p(x)[/tex] = 0 (Finite)
[tex]\lim_{x \to 0}(x-0)^2p(x)=\lim_{x \to 0}\frac{6x^2}{x(x^2+25)}[/tex]
[tex]\lim_{x \to 0}(x-0)^2p(x)=\lim_{x \to 0}\frac{6x}{(x^2+25)}[/tex]
[tex]\lim_{x \to 0}(x-0)p(x)[/tex] = 0 (Finite)
So x=0 is a regular singular point.
(b) At [tex]x_{o}[/tex]=5i
[tex]\lim_{x \to 5i}(x-5i)p(x)=\lim_{x \to 5i}\frac{-5(x-5i)}{(x+5i)(x-5i)}[/tex]
[tex]\lim_{x \to 5i}(x-5i)p(x)=\lim_{x \to 5i}\frac{-5}{(x+5i)}[/tex]
[tex]\lim_{x \to 5i}(x-5i)p(x)[/tex] = -1/i (Finite)
[tex]\lim_{x \to 5i}(x-5i)p(x)=\lim_{x \to 5i}\frac{6(x-5i)^2}{x(x+5i)(x-5i)}[/tex]
[tex]\lim_{x \to 5i}(x-5i)p(x)=\lim_{x \to 5i}\frac{6(x-5i)}{x(x+5i)}[/tex]
[tex]\lim_{x \to 5i}(x-5i)p(x)[/tex] = 0 (Finite)
So x=5i is a regular singular point.
(c) At [tex]x_{o}[/tex]=-5i
[tex]\lim_{x \to -5i}(x+5i)p(x)=\lim_{x \to -5i}\frac{-5(x+5i)}{(x+5i)(x-5i)}[/tex]
[tex]\lim_{x \to -5i}(x+5i)p(x)=\lim_{x \to -5i}\frac{-5}{(x-5i)}[/tex]
[tex]\lim_{x \to -5i}(x+5i)p(x)[/tex] = 1/i (Finite)
[tex]\lim_{x \to -5i}(x+5i)p(x)=\lim_{x \to -5i}\frac{6(x+5i)^2}{x(x+5i)(x-5i)}[/tex]
[tex]\lim_{x \to -5i}(x+5i)p(x)=\lim_{x \to -5i}\frac{6(x+5i)}{x(x-5i)}[/tex]
[tex]\lim_{x \to -5i}(x+5i)p(x)[/tex] = 0 (Finite)
So x=-5i is a regular singular point.
Hence, the regular singular points are x=0, 5i, -5i.
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Solve the system using either Gaussian elimination with back-substitution or Gauss-Jordan elimination. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, express x, y, and z in terms of the parameter t.)
3x+3y+12z=9
x+y+4z=3
2x+5y+20z=15
-x+2y+8z=6
(x, y, z) = ( _____ )
The solution for the given system of equation is (x,y,z) is = (0 , (3-4t) , t) .
In the question ,
it is given that the system of equations are ,
3x + 3y + 12z = 9
x + y + 4z = 3
2x + 5y + 20z = 15
-x + 2y + 8z = 6
we have to solve the equations for x, y , z.
writing the given equations in augmented matrix form ,
we get ,
[tex]\left[\begin{array}{ccc}3&3&12\\1&1&4\\2&5&20\\-1&2&8\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}9\\3\\15\\6\end{array}\right][/tex]
Applying the operation , R₁/3 ⇒ R₁
[tex]\left[\begin{array}{ccc}1&1&4\\1&1&4\\2&5&20\\-1&2&8\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}3\\3\\15\\6\end{array}\right][/tex]
Applying the row operation , R₂ - R₁ ⇒ R₂ .
[tex]\left[\begin{array}{ccc}1&1&4\\0&0&0\\2&5&20\\-1&2&8\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}3\\0\\15\\6\end{array}\right][/tex]
After applying more row operations , in the above matrix ,
to make the lower triangle matrix 0 ,
we get ,
[tex]\left[\begin{array}{ccc}1&0&0\\0&1&4\\0&0&0\\0&0&0\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}0\\3\\0\\0\end{array}\right][/tex]
The above result can be expressed as x = 0,
and y + 4z = 3 .
So , the system of equations have infinite solutions .
So , the solution x, y, and z expressed in terms of the parameter t is
(0 , (3-4t) , t) .
Therefore , the solution is (x,y,z) is = (0 , (3-4t) , t) .
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Consider a population with data values of:
12, 8, 28, 22, 12, 30, 14.
The population standard deviation is closest to: ____.
a) 8.64.
b) 64.00.
c) 74.67.
d) 8.00.
Answer:
D)8.00
σ = √64
= 8
(x^3+5x^2+7x+2)/(x+2)
In ΔOPQ, \overline{OQ} OQ is extended through point Q to point R, \text{m}\angle PQR = (7x-19)^{\circ}m∠PQR=(7x−19) ∘ , \text{m}\angle OPQ = (2x-3)^{\circ}m∠OPQ=(2x−3) ∘ , and \text{m}\angle QOP = (x+16)^{\circ}m∠QOP=(x+16) ∘ . Find \text{m}\angle PQR.m∠PQR.
The sum of two interior angles other than the adjacent angle of extended length will be equal to the external angle of extended length thus m∠PQR will be 18°.
What is an angle?An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus. The identical endpoint of the two rays known as the vertex is referenced as an angle's sides.
In any triangle, the sum of two interior angles other than the adjacent angle of extended length will be equal to the external angle of extended length.
In the given triangle,
m∠PQR = m∠OPQ + m∠POQ
4x - 10 = x + 9 + x - 5
4x - 10 = 2x + 4
2x = 14
x = 7
So,
m∠PQR = 4(7) - 10 = 18°
Hence the measure of m∠PQR will be 18° for the given triangle.
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based on the graph below, which of the following statements is true? select one:
a. has a derivative that is zero at two values of x, one is a local maximum on the interval while the other is neither a local maximum nor a minimum. b. has a derivative that is zero at two values of x, both being local maxima. c. has a derivative that is zero at one value of x where it is a local minimum. d. has a derivative that is zero at two values of x, one is a local minimum on the interval while the other is neither a local maximum nor a minimum. e. has a derivative that is zero at two values of x, one is a local maximum while the other is a local minimum.
A local minimum or a local maximum are both examples of local extremums.
Find the function's local maximum and minimum points ?A point (x,y) on the function's graph at which the y coordinate is larger than all other y coordinates at positions "near to" it is known as a local maximum point (x,y).More specifically, if there is an interval (a,b) with axb and f(x)f(z) for every z in both (a,b) and the domain of f, then (x,f(x)) is a local maximum.Similar to this, if (x,y) has the smallest y coordinate locally, it is a local minimum point. If there is an interval (a,b) with axb and f(x)f(z) for every z in both (a,b) and the domain of f, then (x,f(x)) is a local minimum.A local minimum or a local maximum are both examples of local extremums.This is 0 at x=3-/3 and is defined everywhere.When we first consider x=3-/3, we can see that f(3-/3)=23-/9.Since 3-3, 3-/31, and we can use x=0 and x=1, we can test two points on either side of x=3-/3, making sure that neither is further away than the closest critical value.Given that f(0)=0>23-/9 and f(1)=0>23-/9, a local minimum at x=3-/3 is required. We observe that f(x=3-3/3)=23-/9 for x=3-/3.This time, we have the option of using x=0 and x=1, and we discover that f(x)=f(0)=023-/9, indicating that a local maximum exists at x=x-3/3.To learn more about Maxima and Minima refer to:
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Please help ASAP!!
100 Points + Brainliest if correct!
See Attachment!
The error step in the problem of finding an inverse is Step 4.
What is an inverse function?
In relation to the original function f, the inverse function is denoted by the symbol [tex]f^{-1}[/tex], and both the original function's domain and its range are transformed into the inverse function's domain and range, respectively.
Given, based on the inverse function
Step 1: y = 6x - 11 (Given equation)
Step 2: x = 6y - 11 (Exchange of variables x and y with each other respectively)
Step 3: x + 11 = 6y (Adding 11 on both sides)
Step 4: x/6 +11 = y Error step ( because dividing both sides by 6 will give x/6 + 11/6 = y)
Hence, the error step in the problem of finding an inverse is Step 4.
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What is the GCF of 4 and 8 and 12?; What is the greatest factor of 8?; What is the greatest common factor of 4xy2 and 20x2y4?; How do you find the GCF?; What is the GCF of greatest?; What is the greatest common factor of 12a and 9a2?
The greatest common factor of 4, 8 and 12 is 4
The first number = 4
The second number = 8
The third number = 12
The GCF is stands for greatest common factor.
To find the greatest common factor use the prime factorization method
Prime factorization
Factorize the number 4 = 2 × 2
Factorize the number 8 = 2 × 2 × 2
Factorize the number 12 = 2 × 2 × 3
Here we have to take the common terms from the prime factorization
The greatest common factor = 2 × 2
Multiply the number
= 4
Therefore, the greatest common factor is 4
I have solved the question in general, as the given question is incomplete
The complete question is:
What is the GCF of 4 and 8 and 12?
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Julia sets up a passcode on her tablet, which allows only six-digit codes. A spy sneaks a look at Julia's tablet and sees her fingerprints on the screen over six numbers. What is the probability the spy is able to unlock the tablet on his first try? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
The Probability of carcking the six digit code is 0.00139
What is Probability?
Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.
Solution:
We need to use Permutation to find total number of outcomes
6P6 = 6! = 6*5*4*3*2*1 = 720 outcomes
But only one outcome is correct
Probability is 1/720
Probability = 0.0013899 = 0.00139 (approx)
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2. A store offers a 20% discount if you buy a pair of pants, a shirt, and socks. You take advantage of the offer and get a pair of pants, a shirt for R$20 and socks for R$5. Sales tax is 7%. If the total cost was $47.08. What was the original price of the bike
Answer:
A topic sentence is used to bring
to a paragraph.
Step-by-step explanation:
A topic sentence is used to bring
to a paragraph.
a parallelogram has a heigh of x cm. the length of its base is 4 cm greater than it’s height. a triangle has the same height as the parallelogram. the length of the triangles base is 20 cm. write the system of two equations in two variables that can be used to tell me the values of X for which the parallelogram and a triangle have the same area
The value of x for which the parallelogram and a triangle have the same area is 6 cm.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know the area of a triangle is (1/2)×base×height.
We also know the area of a parallelogram is base×hright.
∴ The values of 'x' for which the parallelogram and a triangle have the same area is,
x×(x + 4) = (1/2)×x×20.
x² 4x = 10x.
x² = 6x.
x = 6.
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solve for x. answer must be simplified.
Answer:
x-24 > 9
x >33
it should be greater than or equal sign
Reminder: Assume all dimensions are feet.
Task: Surround the given figure with a fence. Estimate that you will need 5% more than the actual perimeter in case of mistakes.
Cost: $30 for 3 feet of fence
Cost of Task =
The cost of the task, given the perimeter of the figure, and the cost of feets of fence, is $ 5.17
How to find the cost of the task ?First, find the perimeter of the figure which is just the distance around the shape:
= 4 + 2 + 6 + 3
= 15 cm
The fence needs 5 % more :
= 15 x ( 1 + 5%)
= 15.75 cm
This distance in feet is :
= 15 . 75 / 30.48 cm per feet
= 0. 5167 feet
The cost of the task is therefore:
= 0. 5167 x 30 / 3 feet
= $ 5.17
In conclusion, the cost of the entire task after accounting for the various costs, is $ 5.17.
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A credit card account had a balance of $939 on May 5. A purchase of $216 was made on May 17, and a payment of $100 was made on May 20. The interest on the average daily balance is 1.4%
per month.
Find the average daily balance on the June 5 bill.
The average daily balance on the June 5 bill is $1,037.32, including the finance charge.
What is the average daily balance?The average daily balance is the total balance divided by the number of days in the billing cycle.
May has a 31-day billing cycle.
The average daily balance determines the finance charge, which is a product of the monthly interest rate (MPR) and the ending average daily balance.
Daily Balance
May 5 Credit card balance $939 $11,260 ($939 x 12)
May 17 Purchase 216 $4,620 ($1,155 x 4)
May 20 Payment -100 $15,825 ($1,055 x 15)
Total daily balances $31,705
Average daily balance $1,023 ($31,705 ÷ 31)
Interest rate per month = 1.4%
Finance charge for the month = $14.32 ($1,023 x 1.4%)
June 5 balance = $1,037.32 ($1,023 + $14.32)
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If the sample size is held constant, which of the following will produce the widest 90% confidence interval for the population mean difference for a repeated-measures study?Answer1. MD = 3 with s2 = 20 for the difference scores2. MD = 5 with s2 = 5 for the difference scores3. MD = 5 with s2 = 10 for the difference scores4. MD = 3 with s2 = 10 for the difference scores
The correct option is (d) i.e; MD = 3 with s2 = 20 for the difference scores because it generates a repeated-measures study's population mean difference with the widest 90% confidence interval.
Given that,
Which of the following will result in the widest 90% confidence interval for the population mean difference for a repeated-measures research, provided the sample size is kept constant?
MD = 3 with s2 = 20 for the difference scores.
Therefore, the correct choice is MD = 3 with s2 = 20 for the difference scores because it produces the widest 90% confidence interval for the population mean difference for a repeated-measures study.
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A college statistics professor has office hours from 9.00 AM: to 10.30 AM. daily sample of waiting times to see the professor (in minutes 10, 12,20, 15,17,10, 28,35, 28, 19,27, 25,22, 33, 37,14,21,20 Assuming & = 7.84, find the 99.74% confidence interval for the population mean. Round to two decima places_ a. 20.55 to 24.05 minutes b. 17.05 to 27.55 minutes c. 18.8 to 25.8 minutes d. 19.5 to 35. minutes
We are given the following data set:
10, 12,20, 15,17,10, 28,35, 28, 19,27, 25,22, 33, 37,14,21,20
Standard deviation = 8.043
Confidence level = 1 - Significance Level = 1 - 99.74% = 4.56% = 0.0456
2/5 added by 3/4 simplify it
The fraction 2/5 added by 3/4 will be 1 3/20.
How to calculate the fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers. On the other hand, a fraction appears in the numerator or the denominator of a complex fraction.
The fraction will be illustrated thus:
=✓2/5 + 3/4
= 8/20 + 15/20
= 23/20
= 1 3/20
The value is 1 3/20.
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After the amount due on a sale of $33,400, terms n/eom, is received from a customer, the seller consents to the return of the entire shipment for a cash refund. The cost of the merchandise returned is $20,040. a. What is the amount of the refund owed to the customer?
The total shipment amount of $ 33,066 must be paid back in order to receive a cash reimbursement for the $20,040 in goods that were returned.
what is amount ?When describing a singular noun that CANNOT be measured, you should use the word amount. – When discussing a singular, plural, or countable noun, the word number should be used. – Any single or plural noun that can be counted or measured should be referred to as having a certain quantity.
1/10 n (unclear) indicates that the consumer settled their debts within 10 days and was entitled to a 1% sales discount.
Therefore, the consumer should receive a refund equal to what they paid, which is 1% less than the total amount.
Using that as a basis, the calculation is,
Amount owed * (1-discount rate)
= $ 33,400 * ( 1 - 0.01)
= $ 33,066
$ 33,066 is is the sum that must be reimbursed.
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There are 1,295 students attending a small university. There are 714 women enrolled. What percentage of student are women?
Answer:
55.13 I'm sure is the answer
There are 714 women out of the total 1295 students:
[tex]\dfrac{714}{1295}\approx0.551351351351351[/tex]
About 55.14% of the students are women.
Solve the following equation if d = -2. If necessary, round to the nearest tenth. 2/3(6c+9d)+3/4(8c-16d)=-18
Answer:
c = - 3-----------------------------------
Simplify the equation by distribution, then substitute the value of d and solve for c:
2/3(6c + 9d) + 3/4(8c - 16d) = - 182/3(6c) + 2/3(9d) + 3/4(8c) - 3/4(16d) = - 184c + 6d + 6c - 12d = - 1810c - 6d = - 1810c - 6(-2) = - 1810c + 12 = - 1810c = - 12 - 1810c = - 30c = - 3If six granola bars contain 900 calories, write the equation to determine the calories for a single bar?
Answer:
[tex]6g=900[/tex]
Step-by-step explanation:
The number of calories in one bar multiplied by six is the number of calories in six bars. This is given to be equal to 900.
Determine the period.
Enter
The period is the time interval after curves repeat their behavior thus time period of the given curve will be 4.
What is a graph?The graph is a geometrical representation of a function and can be plotted by taking x's and y's corresponding values within the interval.
For example plot of y = x³ ,y = sinx.
As per the given graph of a function,
The time period is the time interval after curves repeat their behavior.
The given graph repeats after 1 + 1 + 1 + 1 = 4 thus period will be 4.
Hence "The period is the time interval after curves repeat their behavior thus time period of the given curve will be 4".
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the exponential model a=368.3e ^0.002t describes the population, a, of a country in millions, t years after 2003. use the model to determine the population of the country in 2003
The population of the country in 2003 is, 368.3 million.
What is population?
The term "population" refers to all citizens who are either permanently residing in a nation or are only temporarily absent from it. This indicator displays the population of a given area on a regular basis. Growth rates are the yearly changes in population brought on by births, deaths, and net migration.
Given:
The exponential model a = 368.3e^0.002t describes the population,
'a' is the population of a country in millions,
t years after 2003.
We have to find the population of country in 2003.
At 2003, t = 0.
So plug t = 0 in above exponential model.
a = 368.3e^0.002(0)
a = 368.3e^0
a = 368.3
Hence, the population of the country in 2003 is, 368.3 million.
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