If a box turtle Marcos found is 0.115m long, then the length in expanded form is (0.1 + 0.01 + 0.005).
As per the question statement, a box turtle Marcos found is 0.115m long.
We are required to find out the expanded form of the length.
To solve this question, we need to know the procedure to convert a decimal into a fraction:
First, we will have to eliminate the decimal point and then, consider the digits in the same order as a complete number which will be our numerator. Secondly, we will use (10ⁿ) as our denominator where "n" is the number of digits on the right side of the decimal point in the original decimal number. Thus, 0.115 can be written as [tex]\frac{115}{1000}[/tex], since there are three digits after decimal point.
Now [tex]\frac{115}{1000}[/tex] can be written in the following manner as shown below.
[tex]\frac{115}{1000}=\frac{100+10+5}{1000}\\ or, \frac{115}{1000}=\frac{100}{1000}+\frac{10}{1000}+\frac{5}{1000}\\ or, \frac{115}{1000}=\frac{1}{10}+\frac{1}{100}+\frac{5}{1000}\\ or, \frac{115}{1000}=0.1+0.01+0.005[/tex]
Therefore, 0.115 can be written as (0.1 + 0.01 + 0.005) in its expanded form.
Expanded Form (of a number or decimal): This is a format of writing a number as a summation of its individual digits multiplied by their place values.
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Find two numbers that have a sum of -10 and a product of -56.
Choose an equivalent expression for two thirds to the fourth power times two thirds raised to the third power comma all raised to the second power.
A. four ninths raised to the fourteenth power
B. four ninths raised to the twenty fourth power
C. two thirds raised to the fourteenth power
D. two thirds raised to the twenty fourth power
Answer:
C. two-thirds raised to the fourteenth
Step-by-step explanation:
What is the quotient of (−56) ÷ (−4) ÷ 7?What is the quotient of (−56) ÷ (−4) ÷ 7?
Answer:
98
Step-by-step explanation:
What is 31/50 as a percent
Answer:
62%
Step-by-step explanation:
31/50 can be multiplied by 2 to get 62/100. 62/100 is equal to 62%. to get percents, attempt to get the demoninator (bottom number in fraction) to be 100, then the top number is the percent (because its basically saying 62 out of 100 pieces, which is 62 percent)
A control tower observes the flight of an aircraft. At 09:23 the aircraft is 580 km away on a bearing of 043º. At 09:25 the aircraft is 360 km away on a bearing of 016º. What is the speed and the course of the aircraft? (Use a scale of 1 cm to 50 km.)
The speed and the course of the aircraft is 27465 km/h.
What is an aircraft?A machine or vehicle can fly by obtaining support from the air, and this is how an airplane works. It uses either static lift, dynamic lift provided by an airfoil, or, in certain rare situations, the downward thrust from jet engines to counteract the pull of gravity.
From the figure, let us use cosine formula to calculate the resultant displacement.
B^2 = C^2 + A^2 - 2(A)(C) cosØ
Where C = 580km
A = 360 km
Ø = 153 degree
Substitute all the parameters into the formula
B^2 = 580^2 + 360^2 - 2(360)(580)cos153
B^2 = 466000 - ( - 372084.32 )
B^2 = 466000 + 372084.32
B^2 = 838084.32
Square root both sides
B = 915.5 km
You are told to use a scale of 1 cm to 50 km.
Therefore, B = 915.5/50 = 18.3 cm
The time given are: 09:23 and 09:25.
The time difference = 25 - 23 = 2 minute
Convert minutes to hours
2 minute = 2/60 = 1/30 hours
Speed = distance/time
Speed = 915.5 ÷ 1/30
Speed = 915.5 × 30
Speed = 27465 km/h
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Need help with number 6
Applying the definition of bisection, PR = RQ = 28.5 cm.
What is the Definition of Bisection?When a line segment bisects another line segment, it divides the line into two equal segments. This means the two resultant line segments formed have the same length.
The image below shows the bisection of segment PQ by segment ST at point R, which forms two equal segments, PR and RQ.
This means that the length of segments PR and RQ will be equal to each other.
Given that, PQ = 57 centimeters, therefore:
PR = RQ = 1/2(PQ)
PR = RQ = 1/2(57)
PR = RQ = 28.5 cm
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Given the points A (-4,-2) and B (4, 10), find the
coordinates of point P on directed line segment AB that is 3/4 is of the way from A to B.
Answer:
P = (2, 7)
Step-by-step explanation:
You want to find coordinates of P on segment AB such that P is 3/4 is of the way from A to B.
Equation for PFor some fraction q of the distance from A to B, the point P that lies at that fraction of the distance is given by ...
P = A +q(B -A) = (1 -q)A +qB
ApplicationFor q = 3/4, the location of P is ...
P = (1 -3/4)A + 3/4B = (A +3B)/4
Using the given point coordinates, we have ...
P = ((-4, -2) +3(4, 10))/4 = (-4 +12, -2 +30)/4 = (8, 28)/4
P = (2, 7)
Approximate square root 80 by using perfect squares. 80 is between which two perfect squares? What are the square roots of those two perfect squares? What is the approximate value of square root 80?
By finding square numbers, we will get:
8 < √80 < 9
And we can assume that √80 is closer to 9 than to 8, so a good estimation can be 8.95
How to approximate the square root of 80?
We want to approximate √80, now we need to find two consecutive square numbers such that one is smaller and the other is larger than 80.
We know that:
9*9 = 81
8*8 = 64
Then:
√81 = 9
√64 = 8
So we can see that:
√64 < √80 < √81
Then:
8 < √80 < 9
And we can assume that √80 is closer to 9 than to 8, so a good estimation can be 8.95
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Find the circumference.
Use 3.14 for T.
r = 4 cm
C = ? cm
C =
Answer:
25.12 cm
Step-by-step explanation:
The circumference of a circle can also be understood as the perimeter of the circle.
Circumference of circle= 2πr= πd
r refers to radius while d refers to diameter
Given that r= 4,
circumference of circle
= 2(π)(4)
= 8π
≈ 8(3.14)
= 25.12 cm
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The function f(x) = |x| is graphed over the interval [−6, 3].
Which translation of the graph has the domain [−3, 6]?
A. g(x) = |x| + 3
B. g(x) = |x + 3|
C. g(x) = |x| − 3
D. g(x) = |x − 3|
The translation of the graph that has the domain [−3, 6] is:
B. g(x) = |x + 3|.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
In this problem, the parent function is given by:
f(x) = |x|.
The domain changed by [−6, 3] to [-3,6], meaning that 3 units was added to each bound of the domain, hence x -> x + 3 and:
g(x) = |x + 3|.
Which means that option B is correct.
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Mr jacobs backyard mesures 150 ft. he wants to fence it to secure his garden, how many meters of fence would he need?
The number of meters of fence he would need is 45.72 meters
How to determine how many meters of fence would he need?The given parameters are
Length of backyard = 150 ft
As a general rule, we have the following conversion equation
1 foot = 0.3048 meters
So, we have
Length of backyard = 150 * 0.3048 meters
Evaluate the product
So, we have
Length of backyard = 45.72 meters
Hence, the number of meters of fence he would need is 45.72 meters
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how do i solve for 6+3+11/4=5
Answer:
6+3+11/4[tex]\neq[/tex]5
Step-by-step explanation:
Answer:
The answer to the question is 0
I'm looking for a full positive integer for K as my answers.
The value of full positive integer k such that [tex]O(n^k)[/tex] is the most restrictive polynomial-time upper bound of f(n) are as follows : (A) 9 (B) no integer exists (C)5/3(not an integer) (D)no integer exists (E) [tex]3e^{99}[/tex]
Using the Lower and Upper Bound Theory, it is possible to identify the algorithm with the lowest level of complexity. Let's quickly review what Lower and Upper bounds are before we can understand the theory.
If there are two constants C and N such that U(n) = C*g(n) for n > N, then g(n) is the Upper Bound of A. Let U(n) be the running time of an algorithm A(say). An algorithm's upper bound is displayed using the asymptotic notation Big Oh(O).If there are two constants C and N such that L(n) >= C*g(n) for n > N, then g(n) is the Lower Bound of A. Let L(n) be the running time of an algorithm A(say). The asymptotic notation known as Big Omega displays an algorithm's lower bound.A)[tex]2^{lg(3n+4n+5)}+lg {\spaceh} n \inO(n^k)[/tex]
or, [tex]O(2^{lgn^9}+lgn)\inO(n^k)[/tex] since [tex]3n^9+4n+5=O(n^9)[/tex]
or, [tex]O(2^{lgn^9})\in O(n^k)[/tex] as [tex]2^m+lg m=O(2^m)[/tex]
Applying lg 2 on both sides we get:
[tex]lg_22^{lgn^9}=lg_2n^k[/tex]
solving we get:
k=9 × lg2 × lg n
At n=1/2
k=9
Hence the minimum integer for K is 9.
B) [tex]7lgn+13lg^5n\in O(n^k)[/tex]
Solving for k we get:
k=lgₙ(lg⁵n)
C) [tex]\sqrt[3]{7n^5+2n^3-4}\in O(n^k)[/tex]
Solving by exponent rule we get:
[tex]O(n^{5/3})\in O(n^k)[/tex]
k=5/3
D)[tex]13lg2^{3^n\inO(n^k)}[/tex]
or, [tex]k=lg_n(lg2^{3^n})[/tex]
E)[tex]7^{20!+1} \inO(n^k)[/tex]
As we don't have any term of n on the Left Hand Side, therefore no most restrictive polynomial-time upper bound exist for [tex]O(n^k)[/tex]
[tex]k=e^{99}[/tex]
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The sum of 8 and three times a number is 41
Answer:
x=11
Step-by-step explanation:
let number =x
(8+3x)=41
group like terms
3x=41-8
3x=33
divide both side by the coefficient of x
3x/3=33/3
x=11
Translate and solve: 82 less than a is at least −82.
Give your answer in interval notation.
The interval representing the expression "82 less than a is at least −82." is given by ( -82, 82).
We are given an expression that:
82 is less than a which is at least - 82.
This expression can also be written as:
- 82 < a and a > 82
where a is any variable that can take any value according to the expression.
This can also be written as:
- 82 < a < 82
In interval form, it will be written as:
( -82, 82)
"()" brackets are used as -82 and 82 are not included in the interval.
Therefore, we get that, the interval representing the expression "82 less than a is at least −82." is given by ( -82, 82).
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Translate the English phrase into an algebraic expression: the quotient of the sum of a and b and the product of a and b.
The algebraic expression from the given statement is (a+b)/ab.
Given the statement is the quotient of the sum of a and b and the product of a and b.
In mathematics, an expression is defined as a set of numbers, variables, and operations that are formed according to context-dependent rules.
In the given statement the sum of a and b means a+b.
And the product of a and b means ab.
Now, as it is given in the statement that the quotient of the sum of a and b and the product of a and b can be written as
(a+b)/ab.
Hence, the algebraic expression from the given statement "the quotient of the sum of a and b and the product of a and b" is (a+b)/ab.
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Write an equation in point-slope form of the line
(-7,2); m=2
Answer: y - 2 = 2(x + 7)
Step-by-step explanation:
Point-slope form is written as y - [tex]y_{1}[/tex] = m(x - [tex]x_{1}[/tex]) where m is the slope and ( [tex]x_{1}[/tex], [tex]y_{1}[/tex]) are points on the line.
y - [tex]y_{1}[/tex] = m(x - [tex]x_{1}[/tex])
y - 2 = 2(x + 7)
Out of 350 racers who started the marathon, 310 completed the race, 30 gave up, and 10 were disqualified. What percentage did not complete the marathon?
Answer:
The answer is %11.42 I think
Step-by-step explanation:
30+10=40
40/350= 0.1142
0.1142x100= %11.42
First divide the total of people who didn't complete the race by the total of racers which is 350 total racers.
Then u multiply ur answer by 100 to get ur percentage which is 11.42.
The tables below show some inputs and outputs of functions f and h.
Evaluate
Oh
The value of the composite functions, (h ° f)(1) = 0.5.
How to Solve Composition of Functions?Given the function, (h ° f)(1), this means h(f(1)) as a composition of functions.
Using the table given for the function, f(x), f(1) = -1.
This means that, to find (h ° f)(1) = h(f(1)), we would find the value of h(x) in the table where x = -1.
Thus, from the table for h(x), when x = -1, h(-1) = 0.5.
Therefore, the value of the composite functions, (h ° f)(1) = 0.5.
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Ty was making a map of his neighborhood and decided to use the scale of 1 inch : 2 miles. He measured that the distance from his garage to the entrance of the skatepark was 3,520 feet. How far should he make this distance on his map? (note 1 mile = 5,280 feet). Write your answer as a fraction.
The distance on the map is 3/4 inch
Given data
scale of the map = 1 inch : 2 miles
measurement from garage to the entrance of the skatepark = 3,520 feet
1 mile = 5,280 feet
How to solve for the distance on his mapThe required measurement to convert to map measurement = 3520 feet
we solve for number of miles in 3520 feet knowing that 1 mile = 5,280 feet. we solve this by:
5280 / 3520= 3 / 2 miles
so if scale of the map is 1 inch : 2 miles
x : 3 / 2 miles
we cross multiply to find x as
x = 3/2 / 2
x = 3/4
The distance on the map is 3/4 inch
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3x divided by -8 = -21 divided by 4. The answer is 14. I'm trying =g to figure out why it was not a negative 14
Answer:
See explanation
Step-by-step explanation:
3x/(-8)=-21/4
-3x/8=-21*8/4
-3x*8/8=-21*8/4 ==> multiply 8 on both sides to get rid of denominator
-3x=-21*2
-3x=-42
3x=42 ==> Multiply by -1 on both sides to get positive values on both sides
x=14
Find the area of the figure.
Answer:
10 x 12 x 9 cm^2
= 1080 cm^2
Answer:
105
Step-by-step explanation:
a = 1/2(bh) + 1/2(bh)
a = 1/2(12)(10) + 1/2 (9)(10)
a= 1/2 (120) + 1/2(90)
a = 60 + 45
a = 105
Find the value of x. Then find the missing angle measures of the polygon.
x = ?
5x degrees = ?
2x degrees = ?
Answer:
x = 22.5
2x = 45
5x = 112.5
Step-by-step explanation:
The sum of all internal angles in a triangle is 180 degrees. This can be expressed as the following:
x + 5x + 2x = 180
Combine the like terms:
8x = 180
Divide both sides by 8 to find the value of x:
x = 180/8
Simplify:
x = 22.5
Multiply by 2 to get 2x:
2x = 22.5 * 2
2x = 45
Multiply by 5 to get 5x:
5x = 22.5 * 5
5x = 112.5
Verify the answer is correct by taking all the obtained values and ensuring they sum to 180:
22.5 + 45 + 112.5 = 180
Lines a & m are parallel. Using the diagram below, what is the degree measure of angle 2?
Enter the numerical answer only. Example, if the answer is 12 degrees, only enter 12.
Answer:
27
Step-by-step explanation:
just subtract 153 from 180
7/39
in lowest terms.
Answer: 7/39
Step-by-step explanation:
Find the GCD (or HCF) of numerator and denominator GCD of 7 and 39 is 1
Divide both the numerator and denominator by the GCD 7 ÷ 1 39 ÷ 1
Reduced fraction: 7 39 Therefore, 7/39 simplified to lowest terms is 7/39.
Daslyn has a piece of rope 2.085 meters long and another piece
2.63 meters long. Which piece can she cut to make a piece that is
2.5 meters long? Explain.
Answer:
the second piece of rope
Step-by-step explanation:
2.63 ≥ 2.5
2.085≤2.5
The mean height of American women in their late twenties is about 64.5 inches and the standard deviation is about 2.5 inches. The mean height of men the same age is about 68.5 inches, with a standard deviation of about 2.7 inches. If the correlation between the heights of married heterosexual men and their wives is about r=0.5, what is the equation of the regression line of the the husbands height on the wife’s height in young couples?
Answer:
For married couples in their early 20s, the regression equation and the prediction of a husband's heightEquation: Y'=33.67+0.54*X'
Step-by-step explanation:
Given that
r=0.5x'=64.5Sx=2.5y'=68.5Sy=2.7General regression line equation is:
Y'=a+b*X'
Therefore, the slope of the regression line is equal to the linear correlation coefficient times the difference between the standard deviations of y' and x'.
[tex]b = r\times\frac{S_y}{S_x}[/tex]
[tex]b = 0.5\times\frac{2.7}{2.5}[/tex]
b = 0.54
The mean of the lowered by the slope and mean of x is the intercept with axis y.
[tex]a = y'-b\times x'[/tex]
[tex]a = 68.5-0.54\times 64.5[/tex]
[tex]a = 33.67[/tex]
Now, putting the values of a and b in regression equation
So, we get
Y'=a+b*X'
Equation: Y'=33.67+0.54*X'
Answer:
For married couples in their early 20s, the regression equation and the prediction of a husband's heightEquation: Y'=33.67+0.54*X'
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Algebra Question Help
Answer:
[tex]y=\dfrac{7}{3}\left(\dfrac{1}{3}\right)^x[/tex]
Step-by-step explanation:
Given table:
[tex]\begin{array}{|c|c|}\cline{1-2} \phantom{\dfrac{1}{1}} x & y \\\cline{1-2} \phantom{\dfrac{1}{1}} -1 & 7 \\\cline{1-2} \phantom{\dfrac{1}{1}} 0 & \frac{7}{3}\\\cline{1-2} \phantom{\dfrac{1}{1}} 1 & \frac{7}{9}\\\cline{1-2} \phantom{\dfrac{1}{1}} 2 & \frac{7}{27}\\\cline{1-2} \phantom{\dfrac{1}{1}} 3 & \frac{7}{81}\\\cline{1-2}\end{array}[/tex]
Linear function: As x increases by one, y always increases by a constant value. Therefore, the first differences between y-values are the same.Quadratic function: The second differences between y-values are the same.Exponential function: The y-value either increases or decreases by a constant factor.Work out the first differences between the y-values:
[tex]7 \underset{-\frac{14}{3}}{\longrightarrow} \dfrac{7}{3} \underset{-\frac{14}{9}}{\longrightarrow} \dfrac{7}{9} \underset{-\frac{14}{27}}{\longrightarrow} \dfrac{7}{27} \underset{-\frac{14}{81}}{\longrightarrow} \dfrac{7}{81}[/tex]
As the first differences are not the same, it is not a linear function.
Work out the second differences:
[tex]-\dfrac{14}{3} \underset{+\frac{28}{9}}{\longrightarrow} -\dfrac{14}{9} \underset{+\frac{28}{27}}{\longrightarrow} -\dfrac{14}{27} \underset{+\frac{28}{81}}{\longrightarrow} -\dfrac{14}{81}[/tex]
As the second differences are not the same, it is not a quadratic function.
Work out if the second differences have a common ratio:
[tex]\implies \sf \dfrac{28}{27} \div \dfrac{28}{9}=\dfrac{1}{3}[/tex]
[tex]\implies \sf \dfrac{28}{81} \div \dfrac{28}{27}=\dfrac{1}{3}[/tex]
As the second differences have a common ratio of ¹/₃, the function is exponential with base ¹/₃.
General form of an exponential function:
[tex]y=a(b)^x[/tex]
where:
a is the y-intercept.b is the base (growth/decay factor) in decimal form.The y-intercept is the value of y when x = 0.
From inspection of the table, the y-intercept is ⁷/₃.
Therefore:
[tex]a = \dfrac{7}{3}[/tex]
[tex]b = \dfrac{1}{3}[/tex]
Substitute the found values of a and b into the formula to create an exponential function that models the given data:
[tex]\implies y=\dfrac{7}{3}\left(\dfrac{1}{3}\right)^x[/tex]
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Question 8 of 10
What
transformation was not done to the linear parent function, f(x) = x, to
get the function g(x) = -1/(x+5)+7?
A. Shifted up 7 units
B. Shifted right 5 units
C. Vertically compressed by a factor of 2
D. Reflected over the x-axis
The transformation was not done is Shifted right 5 units and vertically compressed by a factor of 2.
If the function f(x) reflected across the x-axis, then the newfunction g(x) = - f(x)
If the function f(x) reflected across the y-axis, then the newfunction g(x) = f(-x)
If the function f(x) translated horizontally to the rightby h units, then the new function g(x) = f(x - h)
If the function f(x) translated horizontally to the leftby h units, then the new function g(x) = f(x + h)
If the function f(x) translated vertically upby k units, then the new function g(x) = f(x) + k
If the function f(x) translated vertically downby k units, then the new function g(x) = f(x) – k
A vertical stretching is the stretching of the graph away from
the x-axis
A vertical compression is the squeezing of the graph towardthe x-axis.
If k > 1, the graph of y = k*f(x) is the graph of f(x) verticallystretched by multiplying each of its y-coordinates by k.
If 0 < k < 1 (a fraction), the graph is f(x) vertically compressedby multiplying each of its y-coordinates by k.
If k should be negative, the vertical stretch or compress isfollowed by a reflection across the x-axis.
So, we can write,
f(x) = x
g(x) = -1/(x+5)+7
-1 means the graph is vertically compressed by a factor of 1and reflected over the x-axis
x + 5 means the graph shifted to the left 5 units + 7 means the graph shifted up 7 unitsReflected over the x-axisTherefore,
The transformation was not done is Shifted right 5 units and vertically compressed by a factor of 2.
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What is the quotient for 81/-9, -123 divided by -4, -94/-9, and 65 divided by (-5)
The final answer is -9, -30.75, -13
What is Quotient?
The number resulting from the division of one number by another.
In the given statement is:
What is the quotient for 81/-9
If we divide 81 by -9
The Quotient will be -9
And, come to the next :
-123 divide by -4
The quotient will be -30.75
And, 65 divided by (-5)
The Quotient will be -13
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