Answer:
leaning at 3 degrees off of normal (to the nearest whole degree)
Step-by-step explanation:
To visualize, let's assume the tower is leaning to the right, (as viewed by us).
If the rope is dropped from the top to the ground, the tower, the rope and the ground (between the rope and the tower) form a right triangle.
The height and base of the triangle are given
Often we're looking for the angle near the ground, but here, we're looking for the angle between the rope and the tower because the angle is congruent to the angle that the tower forms with it's original vertical position (alternate interior angles). If the tower was standing straight up and hadn't been leaning at all, we wouldn't say that the tower was leaning 90°... we would say it was leaning 0°. Whereas if the tower fell over and was laying flat on the ground, we would say it was leaning at 90°. So, we're not measuring the angle between the tower and the ground, but rather the angle between the tower where it should be, and where it is... which is the same angle as the rope forms with the tower.
Recall that [tex]tan(\theta)=\dfrac {opp}{hyp}[/tex]
Since we know the two legs of the right triangle, one can setup a tangent relationship with the two legs, but remember that the "opposite" side is going to be the ground, and the "adjacent side" will be the rope.
[tex]tan(\theta)=\dfrac {ground}{rope}\\tan(\theta)=\dfrac {3ft}{57ft}\\tan(\theta)=\frac {3}{57}\\\theta=tan^{-1}(\frac {3}{57})\\\theta=3.012787504^o\\\theta \approx 3^o\\[/tex]
A farmer has decided to divide his land area in half in order to plant soy and corn. Calculate the area of the entire area so he knows how much soil is needed.
A parallelogram with a height of 6 yards and side length 9 yards. The height forms a triangle with the slanted side of the rhombus with a base of 2.5 yards. Rhombus is split into a soy half and a corn half.
Each bag of soil covers 20 square yards. How many bags should the farmer purchase?
The farmer should purchase 2 bags of soil for his farm.
What is Area of rectangle?Area of rectangle is the region occupied by a rectangle within its four sides or boundaries. The area of a rectangle depends on its sides.
The shape of the farm, according to the picture is a parallelogram. the total area can be calculated as follows:
Area = b X h
where
b = base
h = height
base = 6.5 + 2.5 = 9.0 yards
height = 6 yards
Area = 6 × 9 = 54 square yards.
40 square yards requires 1 bag of soil .
54 square yards will require ?
cross multiply
Bags required = 54 / 40 = 1.35 bag
Thus, the farmer will require 2 bags of soil for his farm.
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Solve for x:
5(1 – x) = 20
x = __
[tex]5(1-x)=20\\5-5x=20\\5x=-15\\x=-3[/tex]
Hii!
__________________________________________________________
[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Answer}}}\circ\leftharpoonup[/tex]
The value of x is -3! ^^
[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Explanation}}}\circ\leftharpoonup[/tex]
[tex]\bullet[/tex] First multiply 5 times 1 and -x
[tex]\twoheadrightarrow\sf 5(1-x)=20[/tex]
[tex]\twoheadrightarrow\sf 5-5x=20[/tex]
[tex]\bullet[/tex] Now subtract 5 from both sides
[tex]\twoheadrightarrow\sf -5x=15[/tex]
[tex]\bullet[/tex] Now divide both sides by -5
[tex]\twoheadrightarrow\sf x=-3[/tex]
--
Hope that this helped! Best wishes.
--
What is 4 third written in expanded form
4x+7-(x+6)=68
Solve.
[tex]4x + 7 - (x + 6) = 68 \\ \\ 4x + 7 - x - 6 = 68 \\ \\ 3x + 1 = 68 \\ \\ 3x = 68 - 1 \\ \\ 3x = 67 \\ \\ x = \frac{67}{3} \\ \\ x = 22.3[/tex]
The value of x is 67/3 or 22.3 .
Hi!
__________________________________________________________
[tex]\rightsquigarrow\circ\boldsymbol{Answer}\circ\leftharpoonup[/tex]
x=
[tex]\rightsquigarrow\circ\boldsymbol{Explanation}\circ\leftharpoonup[/tex]
First let's distribute the minus sign.
[tex]\twoheadrightarrow\sf 4x+7-x-6=68[/tex]
[tex]\bullet[/tex] Add 6 to both sides
[tex]\twoheadrightarrow\sf 4x+7-x=74[/tex]
[tex]\bullet[/tex] Subtract the x's
[tex]\twoheadrightarrow\sf 3x+7=74[/tex]
[tex]\bullet[/tex] Subtract 7 from both sides
[tex]\twoheadrightarrow\sf3x=67[/tex]
[tex]\bullet[/tex] Divide both sides by 3
[tex]\twoheadrightarrow\sf x=\cfrac{67}{3}[/tex]
[tex]\bullet[/tex] Great job! We solved for the variable
--
Hope that this helped! Best wishes.
[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]
--
What is the solution to this equation? 2ln4+lnx=3ln2+ln(x+1)
Answer:
[tex]x=1[/tex]
Step-by-step explanation:
Given equation:
[tex]2 \ln 4+\ln x=3 \ln 2+\ln(x+1)[/tex]
[tex]\textsf{Apply the power law}: \quad n \ln x = \ln x^n[/tex]
[tex]\implies \ln 4^2+\ln x=\ln 2^3+\ln(x+1)[/tex]
Simplify:
[tex]\implies \ln 16+\ln x=\ln 8+\ln(x+1)[/tex]
Subtract ln 8 from both sides:
[tex]\implies \ln 16+\ln x- \ln 8=\ln(x+1)[/tex]
Subtract ln x from both sides:
[tex]\implies \ln 16-\ln 8=\ln(x+1)-\ln x[/tex]
[tex]\textsf{Apply the quotient law}: \quad \ln x - \ln y = \ln \frac{x}{y}[/tex]
[tex]\implies \ln \left\dfrac{16}{8}\right = \ln \left(\dfrac{x+1}{x}\right)[/tex]
Simplify:
[tex]\implies \ln 2 = \ln \left(\dfrac{x+1}{x}\right)[/tex]
[tex]\textsf{Apply the equality law}: \quad \textsf{if }\: \ln x= \ln y\:\textsf{ then }\:x=y[/tex]
[tex]\implies 2=\dfrac{x+1}{x}[/tex]
Multiply both sides by x:
[tex]\implies 2x=x+1[/tex]
Subtract x from both sides:
[tex]\implies x=1[/tex]
If a and b are two distinct primes, the ab2 has ___ positive divisors.
The number ab², where a and b are prime numbers, has 6 divisors.
How many divisors are for the given expression?Remember that any number can be written as a product of primes, for example, 15 can be written as:
15 = 3*5
Where 3 and 5 are primes.
Such that the divisors of 15 are the factors made with the primes on the right side.
So for the number:
N = a*b^2 = a*b*b
The divisors are:
a, b, a*b, b*b
And trivially, itself and 1, so there are a total of 6 divisors.
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find the distance between the pair of points (7,6) and (4,10)
Answer:
5 units
Step-by-step explanation:
to find out the answer for this you must first find the distance between 7 and 4 and then 6 and 10
then you would square them and then add them
lastly you would take the square root of that and youd have your answer
so
7 - 4 = 3
6 - 10 = -4 (just use 4)
3^2 + 4^2 = 9 + 16 = 25
then you take the square root of this
sqrt(25) = 5
that is your answer
To solve this problem, you will use the Distance Formula to find the distance between two coordinate points.
Set Up the Distance FormulaThe Distance Formula is defined as follows:
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
We must title our points by the standard coordinate naming system:
[tex](x_1, y_1) \ \text{and} \ (x_2, y_2)[/tex]
Therefore, our points can be labeled:
[tex]x_1 = 7[/tex][tex]y_1 = 6[/tex][tex]x_2 = 4[/tex][tex]y_2 = 10[/tex]Substitute Known Values for VariablesNow, substitute the known values as the variables in the Distance Formula:
[tex]d=\sqrt{(4 - 7)^2 + (10 - 6)^2}[/tex]
You must know the BPEMDAS acronym, which stands for:
Brackets
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
Simplify the expression using BPEMDAS:
[tex]d=\sqrt{(-3)^2 + (4)^2}[/tex]
Remember that when a number is raised to the 2nd power, it is the same thing as multiplying the number by itself:
[tex]-3\times-3 = 9[/tex]
[tex]4\times4=16[/tex]
Simplify further by removing the parentheses:
[tex]d=\sqrt{9+16}[/tex]
Compute the additive operation:
[tex]d=\sqrt{25}[/tex]
Simplify the RadicandThe number that is placed inside of a square root symbol (or a radical symbol) is referred to as the radicand.
In this situation, the radicand is 25.
To simplify the radicand, you may either use a calculator to compute the result, or you can determine which number raised to the 2nd power will result in a final answer of 25.
In this case, we can determine that 5² will result in a final answer of 25.
[tex]5^{2} = 25[/tex]
The final answer is 5 units.
3 more than half a number
Answer:
3 + a/2
Step-by-step explanation:
3 + a/2
What is the rule for the reflection?
rx-axis (x, y) - (-x, y)
ry-axis (x, y) (-x, y)
rx-axis (x, y) - (x, y)
ry-axis (x, y) (x, −y)
When reflected over ry-axis (x, y) (-x, y) , rx-axis (x, y) (x,-y) , Option A and D is the correct answer.
What is rule for the reflection ?The rule for reflection is when an object or a coordinate point is reflected over x axis then the coordinate of the x axis remains the same while the y coordinate changes to be additive inverse.
Vice Versa happens when reflected over y axis.
So,
rx-axis (x, y) - (-x, y) --> (x,-y)
ry-axis (x, y) (-x, y)
Therefore Option A and D is the correct answer.
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Answer: its A not A & D
Step-by-step explanation:
3.
2. The diagram below is divided into equal parts. Which fraction of the parts is
white?
Mark only one oval.
Option 1
Option 3
37
314
I
Option 2
47
Option 4
4/3
Step-by-step explanation:
simply count them.
there are 7 little rectangles building the whole.
from these 7, 4 are gray and 3 are white.
so, 3 of 7 are white.
that means,
3/7 of all the parts are white.
Choose True or False, (T or F). Data are recorded observations used for explaining conditions of particular phenomenon
Answer:
true
Step-by-step explanation:
this is absolutely true
parallelogram
b=12 cm, h=10 cm, a=
Celia needs 75% of the marks in an exam to pass. She gets 4/5 of the marks. Does she pass the course? Show your working to justify your answer
Answer:
Yes, she passes with 80%
Step-by-step explanation:
4 divided by 5 = 0.8
0.8 multiplied by 100 = 80%
80% is greater than the required 75% needed to pass
Answer:
Yes
Step-by-step explanation:
First lets establish the key points
We know she needs 75% to pass and she gets 4/5 of the marks
Lets make 4/5 a decimal 4/5 X 2/2 is 8/10 better know as .8
.75 = 75%
.8 = 80%
80% > 75%
Meaning She PASSED!!!
A Store-It-All storage facility requires users to enter a four digit code, using numbers 0-9, to get through the
gate. You need to get a box of winter clothes from your storage container, but you forgot the code.
1. How many possible codes are there if the digits cannot be repeated?
There are
possible codes.
2. What is the probability that you will guess the correct code on your first try?
P(correct code) =
3. If the digits can be repeated, how many possible codes are there?
There are
different codes.
Answer:
Step-by-step explanation: 1. 5040 because 10x9x8x7
3. 10000 because 10^4=1000
1)There are 5040 possible codes are there if the digits cannot be repeated.
2)The probability that you will guess the correct code on your first try will be (1/5040).
3) Possible code = 10000 .
Given,
Numbers : 0 to 9
Here,
Total number of digit = 0,1,2,3,4,5,6,7,8,9
Given condition;
a)
Four digit card must be drawn;
The total possible ways there if the digits cannot be repeated will be;
⇒10×9×8×7
⇒5040
b)
The probability that you will guess the correct code on your first try is;
P(A) = n(A)/n(S)
Where,
n(A) is the event has the right code
n(S) is the total possible ways;
P(A) =1/5040
Hence the total possible ways there if the digits cannot be repeated and the probability that you will guess the correct code on your first try will be 5040 and (1/5040) respectively.
c)
If the gits can be repeated then we have 10 digits for each place :
Possible code = 10 * 10 * 10 *10
Possible code = 10000
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three-quarters of a pile of bricks were used for a certain project. when two thirds of the reminder had been used, 50 bricks were left. how many bricks were there in the original pile?
Answer:
600
Step-by-step explanation:
Let's consider this question using algebra.
Imagine the number of bricks in the original pile is [tex]x[/tex].
We are told that [tex]\frac{3}{4}[/tex] of the bricks are used for a project, meaning that [tex]\frac{3}{4} x[/tex] has been used, leaving us with [tex]\frac{1}{4}x[/tex] as our remainder.
Then, we are told that [tex]\frac{2}{3}[/tex] of the remainder are used to leave us with 50 bricks. This means that [tex]\frac{1}{3}[/tex] of the remainder is left, and this is equal to 50 bricks. This means that the remainder's original amount is equal to 150, because we are told that [tex]\frac{1}{3}[/tex] of the remainder is equal to 50.
So, we know that the remainder is 150, and we also know that the remainder is [tex]\frac{1}{4} x[/tex]. Let's now use these to form an equation.
[tex]\frac{1}{4} x = 150[/tex]
Because we know that a quarter of the original amount of bricks is equal to 150, we can multiply both sides of the equation by 4 to get the original amount of bricks in the pile.
[tex]x = 150 * 4 = 600[/tex]
So, there were 600 bricks in the original pile.
I also dont get this :(
An equation is formed of two equal expressions. If x is increased by 5 then the value of y is increased by 10.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given that y=2x+1, now if the value of x increased by 5. then the value of y will be,
[tex]y_1=2(x+5)+1\\y_1 = 2x + 11[/tex]
Now if we compare y and y₁, then it can be said that if x is increased by 5 then the value of y is increased by 10.
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7. Sapna travelled 48 km to meet her parents. She travelled the first 18 km by car and the remaining distance by train. Find the fraction of the journey sapna travelled by car and train
The fraction of the journey Sapna traveled by car and train is 3/8 and 5/8 respectively.
We know that fraction is an expression in mathematics used to denote the division of two whole numbers.
Given that the total distance = 48 km.
The distance Sapna traveled by car = 18 km.
So, the fraction is = distance traveled by car/total distance = 18/48 = 3/8
The distance Sapna traveled by train = 48 - 18 km = 30 km.
So, the fraction is = distance traveled by train/total distance = 30/48 = 5/8
Therefore the fraction of the journey Sapna traveled by car and train is 3/8 and 5/8 respectively.
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You have loaned a friend $100 and will charge him 5% annua simple interest when he pays it back.
The annual interest would be $5 if you have loaned a friend $100 and will charge him 5% annually and the total amount would be $105.
What is simple interest?It is defined as the interest based on the principal amount, it does not include the compounded amount. The interest calculates on the initial amount of borrowed amount.
We have:
You have loaned a friend $100 and will charge him 5% annually.
As we know:
A = P(1 + rt)
P = $100
r = 5% = 0.05
t = 1 years
A = 100(1 + 0.05×1)
A = $105
I = A - P = 105 - 100 = $5
Thus, the annual interest would be $5 if you have loaned a friend $100 and will charge him 5% annually and the total amount would be $105.
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A student wanted to find the sum of all the even numbers from 1 to 100. He said: The sum of all the even numbers from 1 to 100 is twice the sum of all the odd numbers from 1 to 100. The sum of all the odd numbers from 1 to 100 is 1002. Explain why each of these statements is incorrect. HELP ME ASAP
Statement 1
Twice the sum of the odd numbers would be:
[tex]2(1+3+5+\cdots+99)=2+6+10+\cdots+198[/tex], which is not equal to the sum of all the even numbers from 1 to 100.
Statement 2
The sum of all the odd numbers from 1 to 100 can be thought of as an arithmetic sequence containing 50 terms, with first term 1 and common difference 2. This means the sum of the series would be:
[tex]\frac{50}{2}[2(1)+(50-1)(2)]=2500[/tex]
which is not equal to 1002.
The statement 1 and the statement 2 are incorrect.
The sum of the arithmetic series of first term a₁ and common difference d will be s= n/2{2a₁+(n-1)d
Statement 1:
Given in statement 1, Twice the sum of the odd numbers would be:
2(1+3+5+7.......+99)=2+6+10+14+.....198
which is not equal to the sum of all the even numbers from 1 to 100.
Statement 2:
The sum of all the odd numbers from 1 to 100 can be calculated as follows where this is an arithmetic sequence of 50 terms, where the first term is 1 and the common difference is 2. This means the sum of the arithmetic series would be:
s= n/2{2a₁+(n-1)d}
putting the above formula
a₁=1
n=50
d=2
s= 50/2{2(1)+(50-1)2} = 25{2+98} =2500 ≠1002
which is not equal to 1002.
Therefore statement 1 and 2 are incorrect.
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If f(n)= n²-n, then f(-4) is
O-20
12
-12
20
Answer:
20
Step-by-step explanation:
Plug in -4 for n:
(-4)^2 - (-4) = 16 + 4 = 20
Determine whether each ordered pair is a solution to the inequality x+5y<2.
Select all that apply:
(−8,−1)
(−1,0)
(4,2)
(9,6)
(0,10)
Two points ( -8,-1) and ( -1,0) are the solutions and the other points are not the solution to the inequality.
What is inequality?The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than, or < ‘less than.
Given inequality is:-
x + 5y < 2.We will check all the points for the inequality:-
(−8,−1) → x + 5y < 2. → -8 +(5 x -1) < 2 → -13 < 2 It is inequality
(−1,0) → x + 5y < 2 → -1 < 2 It is inequality
(4,2) → x + 5y < 2 → 14 < 2 wrong
(9,6) → x + 5y < 2 → 39 < 2 wrong
(0,10) → x + 5y < 2 → 50 < 2 wrong
Therefore the two points ( -8,-1) and ( -1,0) are the solutions and the other points are not the solution to the inequality.
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Determine algebraically whether the function is even, odd, or neither: f(x)=3x ³ +5
If angle 1= 105°, angle 12= (3x + 15)°, and angle 7 = (8y-5)°, determine the values
of x and y?
The value of the variable x is 30° and the value of the variable y is 10°.
The missing diagram is attached below.
What is an angle?The angle is the distance between the intersecting lines or surfaces.
Corresponding angle – If two lines are parallel, then the third line. The corresponding angles are equal angles.
Vertically opposite angle – When two lines intersect, then their opposite angles are equal.
Linear angle – If the total of two angles is 180 degrees, they are said to be linear angles.
If angle ∠1 = 105°, angle ∠12 = (3x + 15)°, and angle ∠7 = (8y-5)°.
∠1 = ∠5 = ∠9 = 105° (corresponding angles)
∠1 = ∠4 = 105° (Vertical opposite angles)
∠1 + ∠2 = 180° (linear angle)
∠2 = 75°
∠2 = ∠3 = 75° (Vertical opposite angles)
∠3 = ∠8 = ∠12 = 75° (corresponding angles)
Then the value of x and y will be
∠9 = ∠12
∠1 = ∠12
105° = (3x + 15)°
3x = 90°
x = 30°
∠6 = ∠7
75° = (8y – 5)°
8y = 80°
y = 10°
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Frankie’s weekly budget includes a long-term goal of purchasing a car. He is saving $15 a week toward that goal. He is considering saving up his money to purchase his grandmother’s older car. Frankie knows his grandmother has maintained the car and it is in good condition. She is also giving him a greatly discounted price of $800. What should Frankie consider before buying the car? Check all that apply. what he will be giving up if he spends $800 on the car the cost to maintain (oil, tires, gas, brakes) and insure the car how many of his friends have cars his short- and long-term financial goals if an alternate mode of transportation, such as a bicycle or the bus, is sufficient for his needs
The decision of purchasing a car must be taken by Frankie after considering the following points:
1. what he will be giving up if he spends $800 on the car
2. The cost to maintain and ensure the car
3. his short- and long-term financial goals
4. if an alternate mode of transportation, such as a bicycle or the bus, is sufficient for his needs.
What is the point he must know about purchasing a car?Frankie is an individual person when he wants to purchase a car that is his long-term goal.
he must consider various things before making such a big expenditure.
The points to be noted before purchasing a car are:
what is the cost for Frankie for spending $800?
What will be the maintenance and insurance cost?
He must check his other short and long-term goals before purchasing a car.
Is the expense of the car a necessity for Frankie or he can use public transport.
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Answer:
Step-by-step explanation: thank me later
A,B,E
Students returning to a secondary school have to pass through a check point at the rate of 50 per though. The average time for checking is 35 seconds. The arrival rate and service rate follow a Poisson distribution. There is a delay and the principal is willing to include another check point to reduce the average time of checking to 28 seconds if the idle time is less than 10% and the average queue length is more than 10 students, check whether the introduction of an extra check point is justifiable.
The average queue length is greater than 10 students, the introduction of an extra checkpoint is justifiable.
How to explain the information?Since the arrival rate and service rate follow a Poisson distribution, we can use the Poisson arrival rate formula to calculate the average queue length.
Average queue length = (arrival rate * service time) / (1 - arrival rate * service time)
For the given problem, the average queue length is:
Average queue length = (50 * 35) / (1 - 50 * 35)
= 175
Since the average queue length is greater than 10 students, the introduction of an extra checkpoint is justifiable.
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If the hypotenuse of a 30-60-90 degree triangle is 14, what is the short leg?
Answer:
7 units
Step-by-step explanation:
The short leg is opposite the 30 degree angle
sin 30 = opposite side/ hypotenuse
Hypotenuse * sin 30 = opposite side = 14 * 1/2 = 7 units
Find two positive numbers such that their sum is 60 and their product is a maximum. Select one: O a. 30 and 30 O b. 25 and 35 O c. 1 and 59 O d. 20 and 40
Answer:
B: 25 and 35
Step-by-step explanation:
25 product 35 875
...............
................
Let the numbers be x and x/7
Now
sum=824x+x/7=8248x/7=8248x=824(7)8x=5768x=721The numbers are
721 and 721/7=103Answer:
7x+X=824
8X/8=834/8
x=108
Step-by-step explanation:
hope I helped
Determine whether each ordered pair is a solution to the inequality −7x−y>2.
Answer:
[tex]x < - \frac{2 + y}{7} [/tex]
Step-by-step explanation:
[tex] - 7x > 2 + y \\ x < - \frac{2 + y}{7} [/tex]
The percentage of automobile consumers who are under 50 years of age decreased approximately linearly from 58.8% in 1980 to 50.5% in 1995.
(A) Predict when the percentage will be 47%.
(B) Predict the percentage in 2005.
Using a linear function, we have that:
a) The percentage will be 47% during the year of 2001.
b) The predicted percentage in 2005 is of 44.97%.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The percentage in 1980 is considered as the initial amount, hence b = 58.8. In 15 years, the percentage decreased from 58.8% to 50.5%, hence the slope is given by:
m = (50.5 - 58.8)/15 = 0.5533.
Hence the percentage in t years after 1980 is given by:
P(t) = 58.8 - 0.5533t.
Item a:
This is t + 1980, for which P(t) = 47, hence:
P(t) = 58.8 - 0.5533t
47 = 58.8 - 0.5533t.
0.5533t = 11.8.
t = 11.8/0.5533
t = 21.3.
1980 + 21 = 2001, hence the percentage will be 47% during the year of 2001.
Item b:
2005 is 25 years after 1980, hence the percentage is P(25), given as follows:
P(25) = 58.8 - 0.5533x25 = 44.97%.
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