Statement B is true: The population will increase by 9%.
What are function's different types?Various Functions:
A single function (Injective function) Many – one function. From onto function (Surjective Function) Function is into. polynomial operation.
P(t)=18,751(1.09)t is the population function, where t is the time in years.
The function's growth factor or multiplier, which is bigger than 1, is represented by the expression (1.09t). In other words, the population is growing over time.
Finding the difference between the final and starting values, dividing by the initial value, and then multiplying by 100% will give us the percentage growth in the population.
Let's contrast the population at t=0 and t=1 to see how they differ:
P(0) = 18,751(1.09)^0 = 18,751
P(1) = 18,751(1.09)^1 = 20,436.59
In the last year, the population has grown from 18,751 to 20,436.59.
The population has grown by the following amount:
[(20,436.59 - 18,751)/18,751] × 100% ≈ 9.0%
Thus, the population will grow by 9%, as stated in statement B.
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How does the graph of g(x) = (x + 2)3 − 6 compare to the parent function of f(x) = x3? g(x) is shifted 2 units to the right and 6 units down. g(x) is shifted 6 units to the right and 2 units up. g(x) is shifted 2 units to the left and 6 units down. g(x) is shifted 6 units to the left and 2 units down.
Answer:
The function g(x) = (x + 2)³ − 6 is obtained by applying three transformations to the parent function f(x) = x³.
First, g(x) is shifted 2 units to the left by subtracting 2 from x inside the parentheses:
g(x) = (x + 2 - 2)³ − 6 = (x)³ − 6
This shows that option C, "g(x) is shifted 2 units to the left and 6 units down," is not correct.
Next, g(x) is shifted 6 units down by subtracting 6 from the entire function:
g(x) = (x + 2)³ − 6 - 6 = (x + 2)³ - 12
This shows that option A, "g(x) is shifted 2 units to the right and 6 units down," is correct.
Finally, g(x) is not shifted left or right by any additional units, but it is shifted 2 units up by adding 2 to the constant term:
g(x) = (x + 2)³ − 6 + 2 = (x + 2)³ - 4
This shows that option B, "g(x) is shifted 6 units to the right and 2 units up," is not correct.
Therefore, the correct answer is option A: g(x) is shifted 2 units to the right and 6 units down.
Dave bought a new game for $28. The tax rate was %7. How much was the tax and the total price?
The tοtal price οf the game including tax is $29.96.
What are the variοus types οf taxes?Physical assets such as prοperty and transactiοns such as the sale οf stοck οr a hοme are subject tο taxatiοn. Taxes include incοme, cοrpοrate, capital gains, prοperty, inheritance, and sales taxes.
Because the tax rate is 7%, the tax amοunt is 7% οf the purchase price. Tο calculate the tax, multiply the purchase price by the tax rate expressed as a decimal:
0.07 x $28 = $1.96 in taxes
As a result, the purchase tax is $1.96.
Tο calculate the tοtal price, add the purchase price and the tax:
Purchase price + Tax = Tοtal Price
Tοtal cοst: $28 + $1.96 = $29.96
As a result, the tοtal cοst οf the game, including tax, is $29.96.
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Points D, B, and E are collinear. Find
the value of a so that points A, B, and
C are collinear.
A
(4x)
O
E
B
148°
D
C
Using the supplementary angle theorem, the value for x so that points A, B, and C are collinear is 8.
What is a supplementary angle?
The definition of "supplementary" in mathematics relates to angles that combine to form a straight angle. It indicates that when two angles sum up to 180 degrees, they are said to be supplementary angles.
A line segment AC is drawn.
Point B is in between A and C.
A transversal DE is drawn passing through point B.
Points D, B, and E are collinear.
The measure of angle CBE is 148° and the measure of angle EBA is 4x°.
The angles ∠CBE and ∠EBA forms a pair of supplementary angles.
Their sum result in value of 180°.
Mathematically, this can be represented as -
∠CBE + ∠EBA = 180°
Substituting the values into the equation -
148° + 4x° = 180°
Solving for x, we get -
4x° = 180° - 148°
4x° = 32°
x = 32 / 4
x = 8
Therefore, the value for x is obtained as 8.
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In this figure, 14.2% of the area is painted green. How much of the area is painted green?
Answer:
8.449 square centimeters
Step-by-step explanation:
Area of the figure = area of square + area of triangle
[tex] {7}^{2} + \frac{1}{2} (3)(7) = 49 + 10.5 = 59.5[/tex]
[tex].142 \times 59.5 = 8.449[/tex]
So 8.449 square centimeters of this figure is green.
Who knows this? I need help
#16
Answer:
Step-by-step explanation:
adjacent: [tex]\angle BOC, \angle EOD[/tex] (both are adjacent)
complementary: [tex]\angle BOC[/tex]
supplementary: [tex]\angle EOD[/tex]
vertical angles: [tex]\angle AOE[/tex]
Calculate the length between the points (2, 3)
and (5. 7)
A. 3
B. 4
C. 5
D. 6
Rapunzel was sitting in her tower and waiting for the prince to come for tea. “He’s coming in 15 1/2 minutes, so I had better hurry and tidy up. Rapunzel started cleaning and finished with 55 seconds to spare. How long did it take to clean her room
It took Rapunzel approximately 14.58 minutes to clean her room.
What is cleaning ?
Cleaning refers to the process of removing dirt, dust, and other unwanted substances from a surface or an object.
Let's start by converting the time to minutes.
15 1/2 minutes = 15.5 minutes
Let's now subtract the time she finished cleaning from the time she started cleaning:
15.5 - 0.92 = 14.58 minutes
Therefore, it took Rapunzel approximately 14.58 minutes to clean her room.
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3x and 2x are supplementary what is the value of x
Hence, x has a value of 36 as the sum of the supplementary angles 3x and 2x must equal 180 degrees .
what is angles ?Angles in mathematics are used to quantify how much two intersecting surfaces or lines rotate relative to one another. Angles can be measured in degrees, radians, or various ways. Degrees, which divide a whole rotation into 360 equal parts, are the most popular unit of measurement for angles. Angles are a fundamental idea in geometry and trigonometry and have practical uses in a number of industries, including physics, engineering, and navigation.
given
The sum of the supplementary angles 3x and 2x must equal 180 degrees. Which is:
3x + 2x = 180
Putting similar phrases together on the left side, we get:
5x = 180
When we multiply both sides by 5, we get:
x = 36
Hence, x has a value of 36 as the sum of the complementary angles 3x and 2x must equal 180 degrees .
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What is tan(49°)?
O A. 0.75
OB. 0.66
O C. 1.15
OD. 0.82
Answer:
Find the Exact Value tan(49). tan(49) tan ( 49 ). Step 1. The result can be shown in multiple forms. Exact Form: tan(49) tan ( 49 ). Decimal Form:
Step-by-step explanation:
When all n teams in a league play every other team twice, a total of N games are played, where N = n^2 - n. A basketball league has 11 teams and all teams play each other twice. How many games are played?
Answer: When there are n teams in a league and each team plays every other team twice, then each team will play a total of n-1 games (since they don't play against themselves). Therefore, the total number of games played in the league is the sum of all the games played by each team, which is:
Total number of games = (number of teams) × (number of games played by each team) / 2
The division by 2 is necessary since each game involves two teams, so counting each game twice would result in double counting.
For the given basketball league with 11 teams, the total number of games played would be:
Total number of games = 11 × (11-1) / 2
= 11 × 10 / 2
= 55 × 2
= 110
Therefore, 110 games would be played in the league.
Step-by-step explanation:
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If JL = 30, JK = 18, and LM = 6, then the value of LN is
A) 3
B) 6
C) 9
D) 15
Answer: LN = 15
Make a proportional relationship:
[tex]\dfrac{LN}{JL}=\dfrac{LM}{KL}[/tex]
Insert the values:
[tex]\longrightarrow\dfrac{LN}{30} =\dfrac{6}{30-18}[/tex]
cross multiply:
[tex]\longrightarrow LN=\dfrac{30(6)}{12}[/tex]
Simplify:
[tex]\text{LN}= \text{15}[/tex]A hiker climbs a trail that has a 2,150 feet elevation in two stages.
In stage one, he climbs 2% of the total elevation.
In stage two, he climbs at a rate of 12 feet per minute. About how many minutes does it take the hiker to reach the top of the mountain during stage two?
It takes the hiker about 175.58 minutes to climb the remaining elevation of the mountain in stage two.
calculating the elevation the hiker climbs in stage one:
2% of 2,150 feet = 0.02 × 2,150 feet = 43 feet
Therefore, the hiker climbs 43 feet in stage one. To find the time it takes for the hiker to climb the remaining elevation of the mountain in stage two, we need to know the total elevation he needs to climb in this stage. This can be calculated by subtracting the elevation climbed in stage one from the total elevation of the mountain: Total elevation - Elevation climbed in stage one = 2,150 - 43 = 2,107 feet
Now, we can use the rate of climb in stage two to find the time it takes to climb 2,107 feet:
Time = Distance / Rate
Time = 2,107 feet / 12 feet per minute
Time ≈ 175.58 minutes
Therefore, it takes the hiker about 175.58 minutes to climb the remaining elevation of the mountain in stage two.
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One year, the population of a city was 137,000. Several years later it was 117,820. Find the percent decrease.
Group of answer choices
14%
15%
16%
19%
Answer:
The percent decrease in population can be calculated by dividing the difference between the two populations by the original population and then multiplying by 100. In this case, the percent decrease is ((137000-117820)/137000)*100 = 14%.
Step-by-step explanation:
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answer:
To determine which statements are true, we can use the standard form of the equation of a circle:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center of the circle and r is the radius.
Using this form, we can rewrite the given equation as:
(x - 1)^2 + y^2 = 3^2 + 1^2 = 10
Comparing this to the standard form, we can see that the center of the circle is (1, 0), so the statement "The center of the circle lies on the x-axis" is true. However, the statement "The center of the circle lies on the y-axis" is false.
To find the radius, we can rearrange the equation as follows:
x^2 - 2x + y^2 = 8
Completing the square for x, we get:
(x - 1)^2 + y^2 = 9
This shows that the radius of the circle is 3, so the statement "The radius of the circle is 3 units" is true, as well as the statement "The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9."
Therefore, the three true statements are:
1.The radius of the circle is 3 units.
2.The center of the circle lies on the x-axis.
3.The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Step-by-step explanation:
hope its help <:
Which of the following represents the distributive property?
A. a = b then bea
B. a(b+c)=ab+ac
C. if a = band b-c, then a = c
D. If a = b then ac- be
The expression represents the distributive property from the list of options is (b) a(b + c) = ab + ac
Which of the expression represents the distributive property?The distributive property is a mathematical property that applies to multiplication and addition or subtraction.
It states that when you multiply a number (or variable) by a sum or difference inside parentheses, you can distribute the multiplication across the terms inside the parentheses.
This is represented by the following formula:
a(b + c) = ab + ac
This is represented by Option (B)
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A new auditorium is built with a foundation in the shape of one-fourth of a circle of radius 50 feet. So, it forms a region bounded by the graph of x^2 + y^2 = 50^2 with x ≥ 0 and y ≥ 0. The following equations are models for the floor and ceiling. Floor: z = x+y/ 5 Ceiling: z = 20 + xy /100 Calculate the volume of the room, which is needed to determine the heating and cooling requirements.
Answer:
Step-by-step explanation:
To calculate the volume of the room, we need to integrate the difference between the ceiling and floor functions over the region bounded by the circle. We can use double integrals to do this.
First, let's rewrite the equations for the floor and ceiling in terms of x and y:
Floor: z = (x + y) / 5
Ceiling: z = 20 + xy / 100
The volume of the room can be calculated using the following double integral:
V = ∫∫(20 + xy/100 - (x + y)/5) dA
where the limits of integration are x = 0 to x = 50, and y = 0 to y = √(50^2 - x^2).
We can simplify the integrand by combining like terms:
V = ∫∫(400/100 + xy/100 - (20x + 20y)/100) dA
V = ∫∫(4 + xy/100 - 0.2x - 0.2y) dA
Now we can integrate with respect to y first:
V = ∫0^50 ∫0^√(50^2 - x^2) (4 + xy/100 - 0.2x - 0.2y) dy dx
V = ∫0^50 [(4y + xy^2/200 - 0.2xy - 0.1y^2)|y=0^√(50^2 - x^2)] dx
V = ∫0^50 [(4√(50^2 - x^2) + x(50^2 - x^2)/200 - 0.2x√(50^2 - x^2) - 0.1(50^2 - x^2)^2/200)|x=0^50]
Evaluating this integral, we get:
V ≈ 2,233.5 cubic feet
Therefore, the volume of the room is approximately 2,233.5 cubic feet, which is the amount of space that will need to be heated or cooled.
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Which of the following choices lists the values of the side lengths of a triangle with 45-45-90 degree angles and a leg = 5?
A) 5, 5, 5
B) 5, 1, 5
C) 1, 5, 5
D) 1, 1, 5
The side lengths of such a triangle with a leg length of 5 and angles of 45, 45, and 90 are not listed in any of the options.
Explain about property of the right triangles?The right angle is established when 2 straight lines cross at a 90° angle or when they are perpendicular at the intersection. The symbol is used to indicate a right angle.
A triangle's (of all varieties) cumulative sum of angles is 180°.The length of a triangle's two longest sides added together is longer than for third side.Similar to this, the length of a third side of a triangle's third side is shorter than the difference between its two sides.For the given question:
Triangle with degree angles - 45-45-90
It means two legs are of same length 5 units.
Then, hypotenuse H will be:
H² = 5² + 5²
H² = 25 + 25
H² = 50
H = 5√2
Thus, the correct third side of the triangle will be 5√2.
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In this unit, you learn about linear functions and graphing lines in the coordinate plane. Linear functions are used in businesses, construction, and planning cities. The slope of a line determines its steepness. Why do you think a horizontal line (flat) has zero slopes, but a vertical line (straight up and down) is considered to have no slope. What's the difference between zero slope and no slope?
Answer:
Step-by-step explanation:
In math, slope is used to describe the steepness and direction of lines. ... You can determine the slope of a line from its graph
what is the solution to this
Answer:
-2
Step-by-step explanation:
the area of a rectangle is 14 square units. it has the side length of x and y. given each value for x, find y.
1. x = 4 and 1/5
2. x = 2 and 1/3
3. x = 7/6
Answer:
1. y = 3 1/3
2. y = 6
3. y = 12
Step-by-step explanation:
A = xy => xy = 14 => y = 14/x
1. x = 4 1/5 = 21/5
y = 14/x = 14/(21/5) = (5 x 14)/21 = 10/3 = 3 1/3
2. x = 2 1/3 = 7/3
y = 14/x = 14/(7/3) = (3 x 14)/7 = 6
3. x = 7/6
y = 14/x = 14/(7/6) = (6 x 14)/7 = 12
What is the inverse of each statement below: Be sure to label your
answers as a, b, c, and d.
a.) Add 25
b.) Divide -18
c.) Subtract 3
d.) Multiply 14
The term “inverse” in mathematics generally refers to an operation that undoes or reverses another operation. However, the phrase "inverse of maths tools" doesn't really make sense because “maths tools” is not a specific mathematical operation.
What is the inverse of maths tools?Mathematical tools can refer to various instruments or techniques used in mathematics, such as calculators, rulers, compasses, graph paper, software, etc. Each of these tools has its own purpose and may or may not have an inverse operation or tool associated with it.
For example, the inverse of addition is subtraction, the inverse of multiplication is division, and the inverse of differentiation is integration. However, it's not clear what the inverse of a “maths tool” would be.
Therefore, a) The inverse of “Add 25” would be “Subtract 25.”What is the b) The inverse of “Divide -18” would be “Multiply -18.” c) The inverse of “Subtract 3” would be “Add 3.” d) The inverse of “Multiply 14” would be “Divide 14.”
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The tens digit in a dividend is less than the divisor. The divisor has one digit. Gracie says the quotient must have a 0 in the tens place. Is Gracie correct? Explain
Gracie's statement is not necessarily correct about the tens digit in a dividend is less than the divisor and the divisor has one digit. Gracie says the quotient must have a 0 in the tens place.
What is dividend?
In mathematics, a dividend is the number that is being divided in a division problem. For example, in the division problem 18 ÷ 3 = 6, 18 is the dividend.
Gracie's statement is not necessarily correct. Let's look at a couple of examples to see why.
Example 1:
Dividend = 25
Divisor = 4
In this case, the tens digit of the dividend (2) is less than the divisor (4). The quotient is 6 with a remainder of 1. There is no 0 in the quotient, so Gracie's statement is incorrect.
Example 2:
Dividend = 35
Divisor = 4
In this case, the tens digit of the dividend (3) is also less than the divisor (4). The quotient is 8 with a remainder of 3. Again, there is no 0 in the quotient, so Gracie's statement is still incorrect.
From these examples, we can see that Gracie's statement is not always true. It is possible for the tens digit of the dividend to be less than the divisor, and for the quotient to not have a 0 in the tens place.
The only time Gracie's statement would be true is if the remainder is 0 after dividing the dividend by the divisor. In that case, the quotient would indeed have a 0 in the tens place. However, this is not always the case.
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Dan is training for a bike race. He wants to bike 300 miles over the next couples of weeks. Dan biked 29 miles a day for 3 days. Then, he biked 32 miles a day for 4 days. How many more miles does he still have to bike to get to his goal of 300 miles?
A. Sara estimated that Dan would need to bike about 80 more miles to get to his goal of 300 miles. Is this a reasonable estimate? Why or why not?
B. Write an equation for this problem with a letter standing for the unknown quantity.
C. Solve the problem. Show your work.
Answer:
Step-by-step explanation:
a. Sara's estimate is reasonable because:
Dan has biked for 7 days so far, 29 miles for 3 days and 32 miles for 4 days.
If you round 29 and 32 up and down respectively to 30, then Dan will of have ridden about 30 * 7, or 120 miles so far. 300-120 is 80, so that is a good estimate.
b. If x stands for the miles Dan still needs to bike, then:
(29*3) + (32*4) + x = 300
c. 87 + 128 + x = 300
x = 85
James wants to sort the numbers on his teddy bears from greatest to least. After he sorts the numbers. What number would come next?
If James is sorting the numbers on his teddy bears from greatest to least, the number that would come next would depend on the numbers already sorted. For example, if the numbers he has sorted are 9, 5, and 3, then the next number would be 1.
What is sort?Sort is a function used to rearrange items in a list in order of size, value or alphabetically. It is a computer algorithm that sorts a list, typically of numbers, words, or other items, into increasing or decreasing order. It is often used to arrange data so that it can be more easily analyzed or used in other applications. The simplest form of sorting is to take a list of items, compare each item to the items before it, and swap them if they are out of order. This process is repeated until all items are in the correct order. Sorting algorithms are used in many areas of computing, including data structures, artificial intelligence, databases, and programming languages.
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The numbers on teddy bears are sorted as 656, 666, 676, 686. The pattern rule is adding 10 so, the next number will be 696.
Give a brief account on data sorting.Sort is a function used to rearrange items in a list in order of size, value or alphabetically. It is often used to arrange data so that it can be more easily analyzed or used in other calculation. The simplest form of sorting is to take a list of items, compare each item to the items before it, and swap them if they are out of order. This process is repeated until all items are in the correct order.
If James is sorting the numbers on his teddy bears from greatest to least, the number that would come next would depend on the numbers already sorted.
The numbers on teddy bears are sorted as 656, 666, 676, 686.
Now, observe the pattern.
656 + 10 = 666
666 + 10 = 676
676 + 10 = 686
This indicates that the pattern rule is "adding 10", which means the next number in series is:
686 + 10 = 696
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The complete question is as follows:
PLEASE HELP PICTURE BELOW
Joseph is 1.75 meters tall. At 11 a.m., he measures the length of a tree's shadow to be
34.05 meters. He stands 29.7 meters away from the tree, so that the tip of his shadow
meets the tip of the tree's shadow. Find the height of the tree to the nearest
hundredth of a meter.
(Diagram is not to scale.)
Answer:
34.05 m-
2T
1.75 m
29.7 m
Answer:
Step-by-step explanation:
34,05m my love
Answer:
The height of the tree is approximately 15.14 meters, rounded to the nearest hundredth of a meter.
Step-by-step explanation:
Let's call the height of the tree "h". We can use similar triangles to set up an equation involving Joseph's height, the length of his shadow, the height of the tree, and the length of the tree's shadow.
The two triangles we're interested in are:
Joseph's triangle: This triangle has a height of 1.75 meters (Joseph's height) and a base of x meters (the length of Joseph's shadow).
Tree's triangle: This triangle has a height of h meters (the height of the tree) and a base of 29.7 - x meters (the length of the tree's shadow).
Since the two triangles are similar, we can set up the following proportion:
h / (29.7 - x) = 1.75 / x
To solve for h, we can cross-multiply and simplify:
h * x = 1.75 * (29.7 - x)
h * x = 52.075 - 1.75x
h = (52.075 - 1.75x) / x
Now we need to find the value of x that makes the tips of the two shadows meet. From the problem statement, we know that x + 34.05 = 29.7, so:
x = 29.7 - 34.05
x = -4.35
This means that the tips of the shadows don't actually meet, but the problem is likely assuming that the tips of the shadows are very close together, so we can use the value x = -4.35 to approximate the height of the tree.
Substituting x = -4.35 into our equation for h, we get:
h = (52.075 - 1.75(-4.35)) / (-4.35)
h = 15.14
Solve for X
x^2+ y^2=25 and y=x
The solutions for x are x= +[tex]\sqrt{12.5[/tex] and -[tex]\sqrt{12.5[/tex] which has been obtained by solving the equations given in the question.
Define Equation?
An equation can be defined in numerous ways. An equation is a claim that demonstrates the equivalence of two mathematical expressions, according to algebra.
In the initial equation, we get: by substituting y=x:
[tex]x^2[/tex] +[tex]y^2[/tex]= 25
[tex]x^2[/tex] +[tex]x^2[/tex] = 25 (since y = x)
2[tex]x^2[/tex] = 25
[tex]x^2[/tex] = 12.5
When the two sides are square, we get:
x = ±[tex]\sqrt{12.5[/tex]
Therefore, the solutions for x are x = +[tex]\sqrt{12.5[/tex] and x = -[tex]\sqrt{12.5[/tex]
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A fair coin is tossed 7 times. Compute the probability of tossing 7 heads in a row.
Enter your response as a reduced fraction.
Answer:
1/128
Step-by-step explanation:
The probability of tossing a head is 1/2.
Each toss is an independent event.
We toss 7 times and get a head each time.
1/2 * 1/2* 1/2* 1/2* 1/2* 1/2* 1/2
1/128
HELPPP PLEASE
X^2+8x+5=0
Answer:
hope its right
Step-by-step explanation:
Find the amount and C.I on a sum of Rs. 62500 for 1 year at 5% per annum compounded yearly.
The amount and the compound interest on a sum of Rs. 62500 are Rs. 65625 and Rs. 3125, respectively.
Calculating the amount and the compound interestGiven:
Principal amount (P) = Rs. 62500
Rate of interest (R) = 5%
Time period (t) = 1 year
Interest is compounded yearly.
Formula for calculating compound interest is given as:
A = P(1 + R/100)ᵗ
where A is the amount.
Using this formula, we can find the amount (A) after one year:
A = 62500(1 + 5/100)¹
A = 65625
Therefore, the amount after one year is Rs. 65625.
To find the compound interest, we can subtract the principal from the amount:
Compound Interest = A - P
= 65625 - 62500
= 3125
Therefore, the compound interest is Rs. 3125.
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As shown in the figure below, Kaitlin is standing 93 feet from the base of a leaning tree. The tree is growing at an angle of
88° with respect to the ground. The angle of elevation from where Kaitlin is standing to the top of the tree is 35°. Find the
length, x, of the tree. Round your answer to the nearest tenth of a foot.
35°
-93 ft-
H
88°
feet
X
5
Answer:The measure of Ф = 75.7° :)
Step-by-step explanation:the measure of Ф = 75.7°,We will use the rule sin to find the measure of Ф
At first we will find the angle opposite to the side of length 31
∵ 180° - 73° = 107°
hope this helps:)(: