With a basic interest rate of 5%, a deposit earns $102 after 36 months. The duration and overall cost are 3 years and $782, respectively.
To resolve this issue, we can utilize the simple interest formula:
I = Prt
where I stands for interest, P for the principal (original deposit), r for interest rate, and t for the time in years.
We know that the interest earned is $102, the interest rate is 5%, and we want to find the time and total value. Let's call the principal "P" and the time "t". Then we have:
102 = P x 0.05 x 3
Simplifying this equation, we get:
102 = 0.15P
Dividing both sides by 0.15, we get:
P = 680
So the initial deposit was $680.
Now, we can calculate the time using the same formula:
102 = 680 x 0.05 x t
Simplifying this equation, we get:
102 = 34t
Dividing both sides by 34, we get:
t = 3
So the time was 3 years (or 36 months).
To find the total value, we simply add the interest earned to the initial deposit:
Total value = P + I = $680 + $102 = $782
Therefore, the time was 3 years and the total value after 36 months was $782.
The complete question is:-
A deposit earns $102 after 36 months at a simple interest rate of 5%
What is the time and total value
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1.1 Put the verb in brackets into the correct verb form (the Present Simple or the
Present Continuous) and then solve the problem.
(wait) at the bus stop for a friend to get off a bus from the
Imagine you .........
north. Three buses from the north and four buses from the south ......... (arrive) about
the same time. What .......... (be) the probability that your friend will get off the first
bus? Will the first bus come / be from the north?
...... I want the answer
Imagine you are waiting at the bus stop for a friend to get off a bus from the north. Three buses from the north and four buses from the south arrive about the same time. What is the probability that your friend will get off the first bus? Will the first bus come from the north?
What is verb?A "verb" is defined as "a word or group of words that express an action (such as eat), an event (such as happen), or a state (such as exist)" in the Oxford Learners' Dictionary. A verb is defined as "a word or phrase that describes an action, condition, or experience" by the Cambridge Dictionary.
Imagine you are waiting at the bus stop for a friend to get off a bus from the north. Three buses from the north and four buses from the south arrive about the same time. What is the probability that your friend will get off the first bus? Will the first bus come from the north?
Note: The verb "arrive" is in the Present Simple tense because it is a general statement about buses arriving at the same time. The verb "is" is in the Present Simple tense because it is a general question about the probability. The verb "come" is in the Present Simple tense because it is a general question about the first bus. The verb "is" could also be in the Present Continuous tense, i.e., "Will the first bus be from the north?" depending on the context and intended meaning. However, in this case, both Present Simple and Present Continuous are grammatically correct. The correct tense to use depends on the specific context and meaning intended. Please provide more context or clarify if you have a specific intended meaning or scenario in mind. I'll be happy to help you further.
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A side of a inner circle trapezium is a diameter of the circle. The non-parallel sides are equal to the radius of a circle. If the radius of the circle is 2 units, the area of the trapezium can be written as n√n. What is the value of n?
The value of n = 12, and the area of the trapezium can be written as 12√12.
How to determine the the value of nLet's call the diameter of the circle (and one of the parallel sides of the trapezium) "AB", and let's call the non-parallel sides "CD" and "EF". We know that CD and EF are both equal to the radius of the circle, which is 2 units.
We know that AB is a diameter of the circle, which means that its length is twice the radius, or 4 units.
We also know that CD and EF are each 2 units long.
To find the height of the trapezium, we can draw a perpendicular line from point C to line AB:
We can see that the height of the trapezium is the distance from point H to line AB. Since point H is directly above the center of the circle (point O), we can use the Pythagorean theorem to find its distance from point A (or point B, since AB is a diameter):
The length of the hypotenuse (OB) is 2 units (the radius of the circle), and the length of one of the legs (OA) is 2 units (half of AB). To find the length of the other leg (HB), we can use the Pythagorean theorem:
HB^2 + OA^2 = OB^2
HB^2 + 2^2 = 2^2
HB^2 = 0
This tells us that HB (and therefore the height of the trapezium) is 0 units.
Since the height is 0, the area of the trapezium is simply the average of the two parallel sides (AB and CD) multiplied by the distance between them (which is also AB).
Area = (AB + CD) / 2 * AB
= (4 + 2) / 2 * 4
= 3 * 4
= 12
Therefore, n = 12, and the area of the trapezium can be written as 12√12.
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Q10) use the accompanying graph of y = f(x)
1. What is the domain and range of f.
2. find f(-4) and f(-6).
3. find lim f(x)
x-4
4. find lim f(x)
5. Does lim f(x) exist? If it does, what is it?
6. Is f continuous at 0?
(-2,2)
(-4,1)
-6-4-2
(-6,2)
4
2
-2-
(3 marks)
The limits [tex]\lim_{x \to 0 } f(x)[/tex] exists and the function f(x) is continuous at x = 0
Other solutions are shown below
The domain and the range of the functionThe domain of a function is the set of all possible input values, while the range is the set of all possible output values.
From the graph, we have the domain and the range to be:
Domain: [-6, -4) ∪ (-4, -2) ∪ [-2, 0] ∪ (0, 2) ∪ (2, 5) ∪ (5, 6]Range: (-∝, ∝)The values of the functionFrom the graph, we have the values of the function to be
f(-4) = 1 and f(-6) = 2
The function limitsFrom the graph, we have the values of the limits to be
[tex]\lim_{x \to 4^{-} } f(x) = -2[/tex]
[tex]\lim_{x \to 4^{+} } f(x) = 2[/tex]
Checking if the limits exist at x = 0Yes, the limit [tex]\lim_{x \to 0 } f(x)[/tex]
Checking if the function is continuousTo check if a function is continuous at x=0, you need to check three conditions:
The function must be defined at x=0 i.e. f(0) = 4The limit of the function as x approaches 0 from the left must be equal to the limit of the function as x approaches 0 from the rightThese limits must be equal to the function's value at x=0. If all three conditions hold, the function is continuous at x=0.Hence, the function is continuous at x = 0
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the vertex of this parabola is at (-3,-2). Which of the equations below could be its equation
Hence, equation of parabola is option b, y = -2(x + 3)² - 2
What is parabola?A parabola is a U-shaped curve that is created by graphing a quadratic function.
It is a type of conic section, which is formed when a plane intersects a cone.
The general equation of a parabola is given by y = ax^2 + bx + c, where a, b, and c are constants.
The value of the parameter a determines the shape and orientation of the parabola. If a > 0, the parabola opens upwards and has a minimum point. If a < 0, the parabola opens downwards and has a maximum point.
The equation of parabola is:-
y = a(x - h)² + k
hence applying value in given equation-
y = -2(x - (-3))² - 2
y = -2(x + 3)² - 2
hence option b y = -2(x + 3)² - 2 is the correct answer.
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The complete question is :-
Hence, equation of parabola is option b, y = -2(x + 3)² - 2
What is a parabola?A quadratic function graphed as a U-shaped curve is called a parabola.
It is a particular kind of conic section that is created when a plane crosses a cone.
Y = ax² + bx + c is the general equation of a parabola, where a, b, and c are constants.
The parabola's shape and orientation depend on the value of the parameter a. The parabola has an upward opening and a minimum point if a > 0. The parabola has a maximum point and opens downward if a 0.
The equation of parabola is:-
y = a(x - h)² + k
hence applying value in given equation-
y = -2(x - (-3))² - 2
y = -2(x + 3)² - 2
hence option b y = -2(x + 3)² - 2 is the correct answer.
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complete question is:
Here is a pattern made from sticks with a triangle what is n
Solve 9+5x-x^2 by completing the square
A property is available for sale that could normally be financed with a fully amortizing $83,000 loan at a 10 percent rate with monthly payments over a 25-year term. Payments would be $754.22 per month. The builder is offering buyers a mortgage that reduces the payments by 50 percent for the first year and 25 percent for the second year. After the second year, regular monthly payments of $754.22 would be made for the remainder of the loan term.
The buyer were to opt for the builder's offer, the total payments over the life of the loan would be $248,110. This includes interest payments of $165,110. So, while the reduced payments may seem like a good deal in the short-term, buyers need to carefully consider the long-term implications before making a decision.
The builder's Mortgage offer seems attractive, as it significantly reduces the payments for the first two years. However, it's important to consider the long-term implications of this offer.
While the reduced payments may be helpful for buyers who are facing financial constraints in the short-term, they may end up paying more over the life of the loan.
Let's look at the numbers. With the builder's offer, the payments for the first year would be $377.11 per month, and $565.67 per month for the second year. This means that the total payments for the first two years would be $13,165.52. After that, the regular monthly payments of $754.22 would kick in, and the buyer would need to pay this amount for the remaining 23 years of the loan.
If the buyer were to opt for the fully amortizing loan with monthly payments of $754.22 for the entire 25-year term, the total payments over the life of the loan would be $226,266. This includes interest payments of $143,266.
On the other hand, if the buyer were to opt for the builder's offer, the total payments over the life of the loan would be $248,110. This includes interest payments of $165,110. So, while the reduced payments may seem like a good deal in the short-term, buyers need to carefully consider the long-term implications before making a decision.
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PLEASE HELP ILLL MAKE BRAINLY
By looking at the 0 and 1 column, 200 people own less than two smartphones
Which of the following similarity statements is correct?
Answer:
Two
Step-by-step explanation:
Trangles are labled n named alphabetically therefore on the bigger triangle D comes first than E and E comes forsr than R wich means that itvis triangle DER not any ather way around.
On the second triangle A comes first than N and N comes first then T thetefore it is triangle ANT
Answer:
Option A is the correct answer
Triangle RED IS SIMILAR TO TRIANGLE TAN
Please help!
Whoever answers right get brainliest!
Answer:
[tex]x = \frac{18}{ \sqrt{2} } = \frac{18 \sqrt{2} }{2} = 9 \sqrt{2} [/tex]
Each leg is 9√2 cm long.
Please help me I will give you 50 points.
The coordinate of the figure after translation and reflection is A"(-12, 2), B"(-8, 6) and C'(-7, 13)
What is the new image after translation and reflection?To translate the points A(12, -7), B(8, -3), and C(-7, 4) 9 units up, we simply add 9 to the y-coordinate of each point. The new coordinates of the translated points are:
A'(12, 2)
B'(8, 6)
C'(-7, 13)
To reflect the translated points across the y-axis, we simply negate the x-coordinate of each point. The final coordinates of the reflected and translated points are:
A"(-12, 2)
B"(-8, 6)
C'(-7, 13)
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Bella has 4 packs of spikes and 8 Beetlebots. The spikes come in pack
of 20. She puts the same number of spikes on each Beetlebot.
Complete the division sentence.
Operations - Tutorial - Level C
? spikes
80 spikes
Bella will put 10 spikes on each Beetlebot, since she has a total of 80 spikes and 8 Beetlebots.
What is division sentence?A division sentence is a mathematical sentence that expresses the relationships between numbers, when the operation of division is being applied.
Equation:The total number of spikes Bella has is 4 packs x 20 spikes per pack = 80 spikes. She wants to put the same number of spikes on each of the 8 Beetlebots. Let's call the number of spikes she puts on each Beetlebot "x".
The division sentence that represents this situation is:
80 spikes ÷ 8 Beetlebots = x spikes per Beetlebot
Simplifying this division sentence, we get:
10 spikes per Beetlebot = x spikes per Beetlebot
Therefore, Bella will put 10 spikes on each Beetlebot, since she has a total of 80 spikes and 8 Beetlebots and wants to distribute the spikes evenly.
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PLEASE HELP PLEASEEEEEEEEEEEEEE!!! SHOW WORK!
Answer:
C
Step-by-step explanation:
9x+2+4x+10+x=180
14x=180-2-10
14x=168
x=168/14=12
m∠Q=9x+2=9×12+2=108+2=110°
PLEASE SHOW WORK FOR BRAINLIST!!!
In circle A what is angle DAR?
Answer:
68°
Step-by-step explanation:
because the inscribed angle (at B) is half of the arc angle (at A).
angle B = 1/2 × angle A
34 = 1/2 × angle A
angle A = 34×2 = 68°
A quadratic function has zeros at x=3 and x=15. Which of the following must be the equation of its axis of symmetry?
The equation of its axis of symmetry is x = 4.
What is axis of symmetry?
The axis of symmetry is a line that divides a symmetrical object or shape into two mirror-image halves. In mathematics, the axis of symmetry is often used in the context of graphs of equations, particularly quadratic equations
The axis of symmetry of a quadratic function is a vertical line that passes through the vertex of the parabola.
If a quadratic equation has zeros at x = 3 and x = 5, then its factored form is:
(x - 3)(x - 5) = 0
Expanding this expression, we get:
x^{2} - 8x + 15 = 0
This is the standard form of a quadratic equation: ax^{2} + bx + c = 0, where a = 1, b = -8, and c = 15.
To find the x-coordinate of the vertex of the parabola, we can use the formula:
x = -b/2a
Substituting the values of a and b, we get:
x = -(-8)/(2*1) = 4
Therefore, the axis of symmetry is a vertical line passing through x = 4. The equation of this line is simply:
x = 4
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HELP I NEED THIS ASAP PLS HELP
Answer:
A
Step-by-step explanation:
I added a photo of my notes (the angles I've marked as equal are cross angles)
[tex]w = 180° - 30° - x°[/tex]
[tex]w = 150° - x°[/tex]
Find the product.
[675]
a.
b.
6
7
15
TYT
-1
TYT
6 7 5
-4 -4 -1
-24
-28
d. [-57]
Answer:
-57
Step-by-step explanation:
matrix multiplication
How do you solve this?
The approximate diameter of the sphere is 29.3 cm, the correct option is C.
To find the approximate diameter of the sphere, we can use the formula for the volume of a sphere and solve for the diameter.
The following equation determines a sphere's volume:
V = [tex]\frac{4}{3} \pi r^{3}[/tex]
where r is the sphere's radius and V is its volume.
We are given the volume of the sphere as 3600 cubic centimeters. If we use this value as a substitute in the formula, we get:
3600 = [tex]\frac{4}{3} \pi r^{3}[/tex]
Multiplying both sides by [tex]\frac{3}{4}\pi[/tex], we get:
r³ = ([tex]\frac{3}{4}\pi[/tex]) × 3600
r³ = 8100
If you take the cube-root of both sides, you get:
r = [tex]8100^{1/3}[/tex]
r ≈ 14.6 cm
So, the radius of the sphere is approximately 14.6 cm.
The sphere's diameter is twice its radius. Therefore, the approximate diameter of the sphere is:
d = 2r
d= = 2 × 14.6
d ≈ 29.3 cm
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The complete question is:
The volume of a sphere is 3600 cubic centimeters. What is the approximate diameter of this sphere?
Volume of the sphere = [tex]\frac{4}{3} \pi r^{3}[/tex]
A) 9.5 cm
B) 19 cm
C) 29.3 cm
D) 14.6 cm
An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 22 feet up. The ladder makes an angle of 77
∘
∘
with the ground. Find the length of the ladder.
The length of the extension ladder that is against the outside wall of the house is 22.58 feet.
What is the length of the ladder?
The ladder forms a right triangle when it is placed up against a home. The hypotenuse of a ladder is its length. The base of the ladder is where the distance from the house to the base begins. The length is the distance from the home.
Here, we have
Given: An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 22 feet up. The ladder makes an angle of 77
To find the length of the ladder, Sin would be used:
Sin = opposite / hypotenuse
Sin77 = 22 / h
h = 22 / 0.9743 = 22.58 feet
Hence, the length of the extension ladder that is against the outside wall of the house is 22.58 feet.
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Find the area <<<<<<
Answer:
Area = 100 units^2
Step-by-step explanation:
This shape is a trapezoid. The area of a trapezoid is:
A = 1/2(Base+Base)•h
What you do is average the bases and times by the height. The only thing is in your picture the bases are the 12 and 8. And the height is the 10.
Area = 1/2(12+8)•10
= 1/2(20)•10
= 10•10
= 100
The area is 100 square units.
Is 5x^2 - 2x a polynomial?
Answer:
yES
Step-by-step explanation:
Veronica's meal cost $11.92. She pays 8% tax. She then adds a 15 % tip to the total. What is the total cost of the meal to the nearest cent?
The cost of Veronica's supper was $11.92, plus an additional 8% tax of $0.954 and a 15% gratuity on top of tax of $2.0681, for a total price of $14.94.
We first need to figure out the tax and tip amounts and add them to the initial cost to get the final price of Veronica's dinner.
Let's first figure out the tax amount. The cost of the meal is multiplied by the 8% tax rate to determine the tax:
Tax = 11.92 * 0.08 = 0.954
Hence, the meal's tax is $0.954.
Next, let's figure out how much to tip. We multiply the price of the meal plus the tax by the 15% tip percentage to determine the tip:
Tip = (11.92 + 0.954) x 0.15 = 2.0681
Thus, $2.0681 is the total tip for the lunch, tax included.
The original price of the meal, the tax, and the tip can now be added to determine the final price:
Total Cost: 11.92 plus 0.9544 plus 2.0681
Veronica's total bill, rounded to the nearest cent, is therefore $14.94.
In conclusion, Veronica's dinner cost $11.92, plus an additional 8% tax of $0.954 and a 15% tip on top of the meal plus tax of $2.0681, for a total of $14.94.
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SOEMEONE AWNSEER BRU.Reggie wants to conduct a survey of the opinions of the customers in the pizzeria. Which survey sample would give the most accurate results?
Ask every third child in the restaurant Ask each server in the pizzeria.
Ask the manager every shift.
Ask Random customers as they enter the pizzeria.
Ask each server in the pizzeria.
We can conclude by answering the provided question that We get a equation sample size of 579 people by rounding up to the closest whole number. To be 90% sure that the sample percentage is within 1.5
What is equation?An equation in mathematics is a declaration that states the equivalence of two expressions. An equation is made up of two parts that are separated by a mathematical equation (=). For example, the argument "2x + 3 = 9" asserts that the sentence "2x + 3" equals the number "9." The objective of equation solution is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more variables. The variable x is elevated to the second degree in the equation "x2 + 2x - 3 = 0." Lines are used in many different areas of mathematics, such as algebra, calculus, and geometry.
To calculate the sample number required for this poll, use the following formula:
[tex]n=(Z^{2} *P*Q/E^{2}[/tex]
[tex]n=(1.645^{2} *0.5*0.5)/0.015^{2} a578.98[/tex]
We get a sample size of 579 people by rounding up to the closest whole number. To be 90% sure that the sample percentage is within 1.5 percentage points of the actual population percentage, we would need to poll at least 579 randomly chosen air passengers.
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find the area and perimeter of the figure. show your work. (start by finding the missing side lengths) PLEASE HELP ASAP
From the calculation, we have the total area of the figure as shown to be 86 cm^2.
What is area of a triangle?The area of a triangle is the amount of space that is enclosed within the three sides of a triangle. It can be calculated using the formula:
A = 1/2 * b * h
where A is the area of the triangle, b is the length of the base of the triangle, and h is the height of the triangle, which is the perpendicular distance from the base to the opposite vertex.
We know that;
Tan 45 = h/10
h = 10 cm
Then;
Tan 30 = 10/10 + x
0.58 = 10/10 + x
0.58(10 + x) = 10
5.8 + 0.58x = 10
x = 7.2 cm
Thus;
The area of the first triangle = 1/2 * 10 * 10
= 50 cm^2
The area of the second triangle = 1/2 * 7.2 * 10
= 36cm^2
Total area = 86 cm^2
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At age 20, someone sets up an IRA (individual retirement account) with an APR of 6%. At the end of each month he deposits $50 in the account. How much will the IRA contain when he retires at age 65?
Compare that amount to the total deposits made over the time period.
After retirement the IRA will contain S
(Do not round until the final answer. Then round to the nearest cent as needed.)
The total deposits made over the time period is $
(Type a whole number.)
Answer:
To calculate the amount in the IRA at retirement, we can use the formula for the future value of an annuity:
S = PMT * (((1 + r)^n - 1) / r)
Where:
PMT = the monthly payment (in dollars)
r = the monthly interest rate (APR/12)
n = the number of months (45 years * 12 months/year)
Substituting the given values, we get:
PMT = $50
r = 0.06/12 = 0.005
n = 45 * 12 = 540
S = $50 * (((1 + 0.005)^540 - 1) / 0.005) = $204,055.57
So the IRA will contain $204,055.57 at retirement.
The total deposits made over the time period is:
Total deposits = 540 * $50 = $27,000
Therefore, the amount in the IRA at retirement ($204,055.57) is significantly higher than the total deposits made over the time period ($27,000). This demonstrates the power of compound interest over a long time horizon
Step-by-step explanation:
If u have other qstns too, feel free to ask me on my sn ap
A group of students stand at the door of the school and asked every 10th student who they would vote for in the upcoming class elections and why?
This is an example of a survey or sampling technique called systematic sampling. The students are selecting every 10th student from the population (in this case, the population is the entire student body) to survey.
This technique can be useful when the population is too large to survey everyone or when a random sample is difficult to obtain. By using systematic sampling, the students can obtain a representative sample of the student body without having to survey every single student.
However, it's important to note that systematic sampling can introduce bias if there is a pattern or structure in the population that is related to the sampling interval. For example, if every 10th student is in a particular grade level or section of the school, this could skew the results of the survey. To mitigate this potential bias, researchers should ensure that the sampling interval is random and that they are not selecting every nth person based on any identifiable characteristics.
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Triangle DEF with D(-4, 6), E(2,6),
F(0,8): k = 1/2
Triangle DEF as shown ion figure D(-4, 6), E(2,6), F(0,8) translate by a factor of 1/2, So the new vertex are: D' (-2, 3), E' (1, 3), F' (0, 4)
Describe the term triangle?Triangle is commonly represented by a graph in which the three points are labeled as A, B, and C, and the three line segments are labeled as AB, AC, and BC. The graph of a triangle typically looks like below figure.
The new coordinates of each vertex of the triangle after scaling by 1/2.
For vertex D:
x-coordinate = -4, y-coordinate = 6
New x-coordinate = (1/2) × (-4) = -2
New y-coordinate = (1/2) × 6 = 3
So the new coordinates for D' are (-2, 3)
For vertex E:
E (2, 6) ⇒ 1/2 × (2, 6) ⇒ (1, 3)
So the new coordinates for E' are (1, 3)
For vertex F:
F (0, 8) ⇒ 1/2 × (0, 8) ⇒ (0, 4)
So the new coordinates for F' are (0, 4)
D(-4, 6), E(2,6), F(0,8) ⇒ D' (-2, 3), E' (1, 3), F' (0, 4)
Finally, plot the new points on the same coordinate plane and connect them to form the new triangle. You should see that the new triangle is a smaller version of the original triangle, with all sides and angles scaled down by a factor of 1/2.
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What is the combined weight of their pieces of leaf?
Total weight of piece of leaf which both ant carries can be calculated by summing both the weight of leaf is 1.48×10⁻².
what is weight?
In the context of physics and engineering, weight refers to the force with which an object is attracted towards the Earth or any other celestial body due to gravity. The weight of an object is equal to the product of its mass and the acceleration due to gravity.
In the given question,
we need to just add both weight of leaf to get total weight
total weight= weight₁ of leaf +weight₂ of leaf
=1.25×10⁻² +2.3×10⁻³
=1.25×10⁻² +0.23×10⁻²
=1.48×10⁻²
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what is 1/7 divided by 2/5
Step-by-step explanation:
[tex] \frac{ \frac{1}{7} }{ \frac{2}{5} } = \frac{1}{7} \times \frac{5}{2 } = \frac{5}{14} \\ [/tex]
Answer: 5/14
Step-by-step explanation:
It would help if you used the KCF (Keep, Change, Flip) method. First, you write 1/7 as a fraction, then change the division sign to a multiplication sign, and flip the fraction 2/5 to 5/2. Then multiply 1/7 by 5/2 to get 5/14.
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The triangle proportionality theorem indicates that Maria and Juan properly divides the plot of land
What is the triangle proportionality theorem?The triangle proportionality theorem which is known as Thales Theorem states that the segment drawn joining two of the sides of a triangle and parallel to the third side divides the other two sides proportionately.
The parallel lines with which Maria and Juan uses to divide the 300 feet long side into six sides of the same length, indicates that length of each division on the Shady Lane is 50 feet, therefore, the length of each division on the Oak Creek will also be the same.
The slope of the the divisions on Maria's Plan is steeper than the slopes on the division on Juan's Plan such that the length of each division on Oak Lane is longer for Juan, than for Maria.
However, the triangle proportionality theorem, and the width of each division on Shady Lane indicates that the width of each division is 50 feet.
Learn more on the triangle proportionality theorem here: https://brainly.com/question/27887351
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