The equation that best represents the depth of the pond each week is,
[tex]y=10(1.03)^{x}[/tex]
What is an equation?
A mathematical statement that has two expressions with equal values separated by the symbol "equal to" is called an equation.
Given:
The given equation is,
[tex]y=P(1+r)^{x} \;\;\;\;\;-------equation(1)[/tex]
Depth of the pond, P = 10 feet deep
Rate of pond increase, r = 3% = 0.03
Substitute the value of P and r in the equation (1),
[tex]y=10(1+0.03)^{x}[/tex]
Therefore, The equation that best represents the depth of the pond each week is,
[tex]y=10(1.03)^{x}[/tex]
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Write a method called listlength() that takes in a list of strings and returns a list of their lengths as integers. you must create a new list for your answer.
Following are examples of the listlength() methods -
listLength(list("Guava" "apple", "orange", "pineapple")) -> list(0, 1, 2, 3)listLength(list("HI")) -> list(2)listLength(list()) -> list()What is the function of listlength() method?It counts the string characters.
What are the different methods to get string length in python?Len(), a built-in method in Python, may be used to determine a list's size or length. The iterable that is accepted as an input by the len() function counts and returns the number of elements that are present in the list.Using a for loop in a Python program to determine the length of the list is seen as an antiquated or simple approach.The length hint() method in the Python operator module may be used to determine the total number of entries in a list.To learn more about string methods from given link
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Each year, Jennifer's school hosts a student vs. teacher basketball tournament to raise money for charity. This year, there are eight teams participating in the tournament. During the first round, each team plays all of the other teams.
(c) Find a numerical method that you could use regardless of the number of the teams in the tournament to calculate the number of games in the first round.
A numerical method that you could use regardless of the number of the teams in the tournament to calculate the number of games in the first round is; (n − 1) + (n − 2) +…+ 1.
What is the Numerical Method used?
The first team will play with the other 7 teams.
Then the second team will play with the 6 other teams, as the game between the first and the second team has already been counted.
Similarly, the third team will play with 5 other teams, and so on. Thus, the
total number of games will be 7 + 6 + 5 + 4 + 3 + 2 + 1 = 28.
Therefore, in the first round there will be 28 games.
If there are 8 teams in the tournament, the number of games in the first round is (8 − 1) + (8 − 2) +…+ 1. Therefore, if there are n teams in the
tournament, the number of games in the first round is given by the sequence; (n − 1) + (n − 2) +…+ 1.
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how do you factor x^6-27x^9 completely
Answer: -x^6(3x-1)(9x^2+3x+1)
Step-by-step explanation:
x^6-27x^9=
x^6(1-27x^(9-6))=
x^6(1-27x^3)=
-x^6(27x^3-1)=-x^6(3x-1)(9x^2+3x+1)
18÷ 3 2/3
Can someone help me with this q
the 45
Step-by-step explanation:
679
Answer:
54/11 (or) 4 10/11
Step-by-step explanation:
Let's solve the problem,
→ 18 ÷ 3 2/3
→ 18 ÷ (11/3)
→ 18 × (3/11)
→ 54/11 = 4 10/11
Hence, the answer is 54/11.
if two groups of numbers have the same mean, then group of answer choices their standard deviations must also be equal. their medians must also be equal. their modes must also be equal. other measures of location need not be the same.
If two groups of numbers have the same mean, then (D) none of these alternatives is correct.
What is mean?In mathematics, particularly statistics, there are several types of means. Each mean is used to summarize a specific set of data, often in order to better understand the overall value (magnitude and sign) of a given data set.The arithmetic mean, also known as "arithmetic average," of a data set is a measure of the central tendency of a finite set of numbers: specifically, the sum of the set divided by the number of values. If two sets of numbers have the same mean, their standard deviations, medians, and modes must also be different.Therefore, if two groups of numbers have the same mean, then (D) none of these alternatives is correct.
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The correct question is given below:
If two groups of numbers have the same mean, then
a. their standard deviations must also be equal
b. their medians must also be equal
c. their modes must also be equal
d. None of these alternatives is correct.
why do i have a limit that's weird i shouldn't have a limit to something i've signed up for
Answer:
A limit on what? And what website
Step-by-step explanation:
1 and 4 are supplementary and 2 and 3 are supplementary because they are corresponding angles.
Proved that angle 2 is congruent to angle 4 (∠2 ≅ ∠4).
What are supplementary angles?Supplementary angles are those that total 180 degrees. Angles 130° and 50°, for example, are supplementary angles because the sum of 130° and 50° equals 180°.To proof:
Given:
Angles 1 and 2 are supplementary.Angles 3 and 4 are supplemental.Angle 1 is parallel to angle 3.Show that angle 2 and angle 4 are congruent.This proof includes definitions of congruence and supplementary angles, as well as some equality properties.
∠1 and ∠2 are supplementary (given)∠3 and ∠4 are supplementary (given)∠1 ≅ ∠3 (given)m∠1 + m∠2 = 180°m∠3 + m∠4 = 180° m∠1 + m∠2 = m∠3 + m∠4 (transitive property of equality)m∠1 = m∠3 9congruent angles)m∠1 + m∠2 = m∠1 + m∠4 (substitution property of equality) (replaced m∠3 with m∠1)m∠2 = m∠4 (subtraction property of equality) (subtracted m∠1 from both sides)∠2 ≅ ∠4 (congruent angles)Therefore, the proving is shown.
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The correct question is given below;
Angle 1 and angle 2 are supplementary. Angle 3 and angle 4 are supplementary. Angle 1 is congruent to angle 3. Prove: Angle 2 is congruent to angle 4.
M is the midpoint of RT. RS=6x+7 and ST=9x-8. find the length of RS and RT
Applying the definition of a midpoint of a segment, the lengths are:
RT = 74 units
RS = 37 units
What is the Midpoint of a Segment?The midpoint is defined as the point that bisects a line segment into two equal halves.
If M is the midpoint of RT, therefore:
RS = ST
RS = 6x + 7
ST = 9x - 8
Substitute
6x + 7 = 9x - 8
6x - 9x = -7 - 8
-3x = -15
x = -15/-3
x = 5
RT = RS + ST [segment addition postulate]
RT = 6x + 7 + 9x - 8 [substitution]
RT = 15x - 1
Plug in the value of x
RT = 15(5) - 1
RT = 74 units
RS = 6x + 7 = 6(5) + 7
RS = 37 units.
Thus, applying the definition of a midpoint of a segment, the lengths are:
RT = 74 units
RS = 37 units
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X. Y
-5 -4
-2 -11
1 -18
4 -25
We get the graph for the given points.
We are given the points:
X. Y
- 5 - 4
- 2 - 11
1 - 18
4 - 25
We will plot them on the graph.
In geometry, a coordinate system is a system that makes use of one or extra numbers, or coordinates, to uniquely decide the placement of the factors or different geometric factors on a manifold which include Euclidean space.
In mathematics, the graph of a function f is the set of ordered pairs, where f(x)=y.
A plane is the two-dimensional analogue of a point, a line and three-dimensional space.
Therefore, we get the graph for the given points.
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Which property would be the best to help simplify the expression? (-2.7 x 5) x 2 commutative commutative associative associative transitive transitive distributive
Associative property would be the best to help simplify the given expression.
It's given that (-2.7 x 5) x 2 and using associative property we can write it as , (-2.7 x 5) x 2 = -2.7 x ( 5 x 2 ) = -2.7 × 10 = - 27
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1. A group of 12 students goes on a
school field trip. Of all the students
on the trip, 6 are in third grade.
Which fraction is equivalent to?
A. 1/3
B. 1/4
C. 1/6
D. 1/2
3/4x-4=5/6 rewrite without a fraction or decimal
The solution to the given fractional equation for the unknown value of x, is 6 4/9
Fraction3/4x - 4 = 5/6
Add 4 to both sides3/4x = 5/6 + 4
3/4x = (5+24) / 6
3/4x = 29/6
Divide both sides by 3/4x = 29/6 ÷ 3/4
= 29/6 × 4/3
= (29 × 4) / (6 × 3)
= 116 / 18
x = 6 8/18
x = 6 4/9
Therefore, the solution to the given fractional equation for the unknown value of x, is 6 4/9
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Directions: Translate equation DO NOT SOLVE!
(8) "two times the sum of number and 5 is 20"
Answer: 2(n +5) = 20
Step-by-step explanation:
Answer:
2(n+5)=20
Step-by-step explanation:
n+5 is the sum. Two times of the sum is 2*(n+5) which is 2(n+5). This is set to equal 20.
The table shows the cost of 4 movie tickets at two theaters. Theater Cost ($) Movies Galore 30 Star Cinema 31 What equation can be used to model the total cost y for x tickets at Star Cinema? Write the equation in the form
The cost of x tickets for Star Cinema is; y = 7.5x
How to create equation word problems?
From the given table, we see that;
Cost of 4 tickets at Movie Galore = $31
Cost of 4 tickets at star Cinema = $30
Thus, we can find the cost of one ticket for each of the cinema's as;
Cost per ticket for Movie Galore = 31/4 = $7.75
Cost per ticket for Star Cinema = 30/4 = $7.5
Thus, cost of x tickets for Star Cinema is;
y = 7.5x
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Answer:
Step-by-step explanation:
List all pairs of congruent angles, and write a proportion that relates the corresponding sides for each pair of similar polygons.
\triangle D F G \sim \triangle K M J
All pairs of congruent angles, and proportion that relates the corresponding sides for each pair of similar polygons are;
∠A ≅ ∠Z, ∠B ≅ ∠Y and ∠C ≅ ∠X
AC/ZX = BC/YX = AB/ZY
What are the congruent angles?
From the attached image, we see that Triangle ABC is similar to Triangle ZYX.
Now, the order of vertices in a similarity statement identifies the corresponding angles and sides. Since we know that ΔABC is similar to ΔZYX, we can take the corresponding angles of this statement and set them congruent to each other.
Now, since the corresponding sides of similar triangles are proportional to each other, we can write a proportion that relates the corresponding sides to each other as;
∠A ≅ ∠Z, ∠B ≅ ∠Y and ∠C ≅ ∠X
AC/ZX = BC/YX = AB/ZY
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42. (a) find the unit vectors that are parallel to the tangent line to the curve y − 2 sin x at the point sy6, 1d. (b) find the unit vectors that are perpendicular to the tangent line. (c) sketch the curve y − 2 sin x and the vectors in parts (a) and (b), all starting at sy6, 1d.
Vectors is a quantity that has both magnitude and direction as well. A vector that has 1 magnitude is called unit vector. Unit vector is represented by the symbol '^'.
To find a Unit vector we divide the vector by its magnitude.
First find the slope of the tangent line, slope of a tangent line for a point f(x) is given by f'(x). Hence at point (π/6,1) where x = π/6, the slope of the tangent line is :
[tex]f(x)=2sinx\\f'(x)=2cosx\\f'(\pi /6)=2cos(\pi /6)=2.\frac{\sqrt{3} }{2}=\sqrt{3}[/tex]
The slope of the tangent line at this point is [tex]m=\sqrt{3}[/tex]
Finding a unit vector parallel to the tangent line. since slope is the ratio y and x then we can set an arbitrary vector with slope 4 by letting x=1 and y = √3 or v=[1,√3]. this vector has slope √3 and this is parallel to the tangent line, However this is not unit vector because its magnitude is not equal to 1 so we can divide this vector by its magnitude to find the unit vector.
[tex]u_v=\frac{v}{|v|} =\frac{1 \sqrt{3} }{\sqrt{1^{2}+(\sqrt{3})^2 } } \\=\frac{1}{\sqrt{4} } ,\frac{\sqrt{3} }{\sqrt{4} } =\frac{1}{2}, \frac{\sqrt{3} }{2} =[\frac{1}{2},\frac{\sqrt{3} }{2} ][/tex]
If a line has slope of m then all lines perpendicular of it will have a slope of -1/m
So we are looking for a unit vector of slope of -1/√3
Using the same logic we have unit vector that are perpendicular to the tangent line are [tex][\frac{\sqrt{3} }{2},-\frac{1}{2} ][/tex]
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Which table represents a linear function?
Rewrite 19/4 as a mixed number. A 9 1/4 B 5 1/4 C 4 3/4 D 4 1/4
Answer:
C) 4 3/4
Step-by-step explanation:
19 divided by 4 doesn't divide equally.
4*5=20 X
4*4=16 YEP
19-16=3
So...
19 can be divided 4 whole times and you're left over with 3.
Thus, it's 4 3/4.
Hope this helps.
It cost Fawzia $12.00 to send 80 text messages. How many text messages did she send if she spent $19.95?
Answer: she would have sent 133 text messages
hope this helps
Add.
7/4 + 2/3
help pls!!
Answer: 2 5/12
Step-by-step explanation: you multiply each number to 12 as the bottom number it’s hard to explain
HELP ME RN PLS IF YK MATH arithmetic operations and function
lol maybe like 8 or something yeah
need help with homework quick!
Answer:
it is the second one(that what I learned in school)
Determine the correct METRIC length of the cockroach in this image.
A 1.0 in
B 2.5 cm
C 7.5 cm
D 3.0 in
Answer:
B
Step-by-step explanation:
7.5cm - 5cm = 2.5cm
So it is B :)
a couple decides to have 4 children. if they succeed in having 4 children and each child is equally likely to be a boy or a girl, what is the probability that they will have exactly 2 girls and 2 boys?
3/8 is the probability that they will have exactly 2 girls and 2 boys.
What does a probability mean?
The probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the formula for probability.Got to have 4 children
Boy and Girl are equally likely
Hence, P( boy) = P( girl) = 1/2
This is like performing binomial distribution.
P( excatly 2 boys and 2 girls)
=4C2(1/2)^2 (1/2)^2
=6/16
=3/8
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Complete the following table
Answer:
a)30
b) 5 to 2
c)25
what three numbers are next in the sequence 2,3,6,11,18? and how do you get these numbers?(answer needed as soon as possible)
The next three numbers in the sequence are 27, 38, and 51
SequenceFrom the question, we are to determine the next three numbers in the given sequence
The given sequence is
2,3,6,11,18
The difference between the 1st and 2nd terms is 3 -2 = 1
The difference between the 2nd and 3rd terms is 6 -3 = 3
The difference between the 3rd and 4th terms is 11 - 6= 5
The difference between the 4th and 5th terms is 18 - 11= 7
We can observe that the successive odd numbers are being added to the terms
Thus,
The sixth term will be 18 + 9 = 27
The seventh term will be 27 + 11 = 38
The eight term will be 38 + 13 = 51
Hence, the next three numbers in the sequence are 27, 38, and 51
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☆*: .｡. o(≧▽≦)o .｡.:*☆ wasting my points
Answer:
Step-by-step explanation:
Totally rad!
5a/b+c=10, solve for a
Answer:
a = b(10-c)/5
Step-by-step explanation:
5a/b + c = 10
5a/b = 10-c
5a = b(10-c)
a = b(10-c)/5
How should this model be completed to represent 642/11 ??
Enter the answer in the box.
Model be completed to represent 642/11 is 29.1818181818
[tex]\frac{642}{11}[/tex] = 58.3636363636
58.3636363636 = 583.636363636 to the nearest tenth
58.3636363636 = 58.36 to the nearest hundredth
58.3636363636 = 58.364 to the nearest thousandth
= 0 to the nearest tenth
= 0 to the nearest hundredth
= 0 to the nearest thousandth
Other Divisions Math homework are
642 divide by half plus 20
([tex]\frac{642}{2}[/tex]) + 20 = 341
642 divide by half plus 40
([tex]\frac{642}{2}[/tex]) + 40 = 361
[tex]\frac{642}{11}[/tex] divided by 2
([tex]\frac{642}{11}[/tex]) ÷ 2 = 29.1818181818
Division is one among the four basic operations of arithmetic, the ways in which numbers are combined to make new numbers. the opposite operations are addition, subtraction, and multiplication.
At an elementary level the division of two natural numbers is, among other possible interpretations, the method of calculating the number of times one number is contained within another.7 This number of times needn't be an integer. for instance , if 20 apples are divided evenly between 4 people, everyone receives 5 apples (see picture).
The division with remainder or Euclidean division of two natural numbers provides an integer quotient, which is that the number of times the second number is completely contained in the first number, and a remainder, which is that the part of the first number that remains, when within the course of computing the quotient, no further full chunk of the dimensions of the second number can be allocated. for instance , if 21 apples are divided between 4 people, everyone receives 5 apples again, and 1 apple remains.
For division to always yield one number instead of a quotient plus a remainder, the natural numbers must be extended to rational numbers or real numbers.
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Mary used 10 2/3 yards of fabric to make 4 identical curtain panels.
What equation can be used to model the total number of yards of fabric, y. needed to make x curtain panels? Write the equation in the form
The equation that can be used to model the total number of yards of fabric, y. needed to make x curtain panels is y = (10 2/4 ÷ 4) × x
How to compute the expression?It should be noted that Mary used 10 2/3 yards of fabric to make 4 identical curtain panels.
Therefore, the equation that can be used to model the total number of yards of fabric, y. needed to make x curtain panels will be:
y = (10 2/4 ÷ 4) × x
where
y = number of yards
x = number of panels
Therefore, the equation is y = (10 2/4 ÷ 4) × x
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