[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{13}~,~\stackrel{y_1}{2})\qquad B(\stackrel{x_2}{7}~,~\stackrel{y_2}{10})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AB=\sqrt{(~~7 - 13~~)^2 + (~~10 - 2~~)^2} \implies AB=\sqrt{( -6 )^2 + ( 8 )^2} \\\\\\ AB=\sqrt{ 36 + 64 } \implies AB=\sqrt{ 100 }\implies AB=10[/tex]
How many digits long could the repeating cycle of a repeating decimal be if the denominator of the rational number is 7?
A up to seven digits long
B up to six digits long
C any finite length
D infinitely long
Answer: a
Step-by-step explanation:
Every six powers of ten, the cycle repeats. In other words, a repeating decimal with a denominator of 7 can have a repeating cycle that is up to six digits long.
The repeating cycle of a repeating decimal for the rational number with a denominator of 7 can be determined by considering the factors of the denominator.
In this case, the denominator is 7, which is a prime number. The length of the repeating cycle can be determined by examining the powers of 10 modulo 7.
To find the length of the repeating cycle, we need to find the smallest positive integer "n" for which 10ⁿ - 1 is divisible by 7. In other words, we are looking for the smallest "n" such that 10ⁿ ≡ 1 (mod 7).
Let's calculate the powers of 10 modulo 7:
10¹ ≡ 3 (mod 7)
10² ≡ 2 (mod 7)
10³ ≡ 6 (mod 7)
10⁴ ≡ 4 (mod 7)
10⁵ ≡ 5 (mod 7)
10⁶ ≡ 1 (mod 7)
As you can see, the cycle repeats every 6 powers of 10. This means that the repeating cycle of a repeating decimal with a denominator of 7 can be up to six digits long.
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Triangle xyz x’y’z’ What scale factor was used in dialation xz=4 x’z’=5
The scale factor used to dilate triangle XYZ so as to form X'Y'Z' is a scale factor of 5/4.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, rotation, translation and dilation.
Triangle X'Y'Z' is the image of triangle XYZ after a dilation by a scale factor.
Given that XZ = 4; X'Z' = 5
Hence:
Scale factor = X'Z'/XZ = 5/4
The scale factor used to dilate triangle XYZ so as to form X'Y'Z' is a scale factor of 5/4.
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A bag contains 10 red, 5 yellow, and 6 blue marbles. What is the probability of pulling out one blue marble and then one red marble without replacing the first blue marble?
The probability of pulling out one blue marble and then one red marble without replacing the first blue marble is 1/7
How to determine the probability?The given parameters are
Red = 10
Yellow = 5
Blue = 6
The probability of pulling out one blue marble and then one red marble without replacing the first blue marble is
P = P(Blue) * P(Red Having selected Blue)
So, we have
P = 6/21 * 10/20
Evaluate
P = 1/7
Hence, the probability of pulling out one blue marble and then one red marble without replacing the first blue marble is 1/7
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Lisa wants to buy some new shirts at her favorite store. Each shirt costs $15 and she wants to buy a pair of shoes that are $35. Lisa only has $137 to spend.
Let S represent the number of shirts that Lisa buys.
Which inequality describes this scenario?
(A) 137> 15s +35
(B) 137< 15s +35
(C) 137≥ 15s +35
(D) 137≤ 15s +35
Considering the definition of an inequality, the correct answer is option (C): the inequality 15×S + 35≤ 137 describes the scenario.
Definition of inequalityAn inequality is the existing inequality between two algebraic expressions, connected through the signs:
greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.An inequality contains one or more unknown values called unknowns.
Solving an inequality consists of finding all the values of the unknown for which the inequality relation holds.
Inequality in this caseIn this case, you know that
Each shirt costs $15.Lisa wants to buy a pair of shoes that are $35.Lisa only has $137 to spend.Being "S" the number of shirts that Lisa buys, the inequality that expresses the previous relationship is
15×S + 35≤ 137
Finally, the correct answer is option (C): the inequality 15×S + 35≤ 137 describes the scenario.
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Can someone please help me of solving this and show answer
By solving inequality [tex]x[/tex] ∈ [tex][-2,3)[/tex]
What is inequality?
A declaration of the relation in terms of greater, greater than or equal to, smaller, or less than or equal to between two numbers or algebraic expressions is known as inequality.
[tex]4\leq 3x+10 < 19[/tex]
Rearranging the above equation
[tex]\left \{ {{4\leq 3x+10} \atop {3x+10} < 19} \right.[/tex]
Subtracting 10 from the above equation
[tex]\left \{ {{4-10\leq 3x+10-10} \atop {3x+10-10 < 19-10}} \right[/tex]
[tex]\left \{ {{-6\leq 3x} \atop {3x < 9}} \right.[/tex]
Dividing the above equation by 3
[tex]\left \{ {{\frac{-6}{3}\leq \frac{3x}{3} } \atop {\frac{3x}{3} < \frac{3}{3} }} \right.[/tex]
[tex]\left \{ {{-2\leq x} \atop {x < 3}} \right[/tex]
[tex]-2\leq x < 3[/tex]
Therefore, by solving inequality we get [tex]x[/tex] ∈ [tex][-2,3)[/tex]
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how are decimal .009 and .09 related
Answer-
-They are related because they are numbers that are less than 1 that can be converted into a fraction.
-They also both contain the number nine.
-They are not repeating decimals.
-They are positive numbers.
Those are just a few examples of how they are related. I hope this helps, good luck!
Shep Company’s records show the following information for the current year:
Beginning of year End of year
Total assets $ 53,200 $ 84,000
Total liabilities $ 23,600 $ 36,600
Determine net income (loss) for each of the following separate situations. (For all requirements, losses should be entered with a minus sign.)
a. Additional common stock of $4,600 was issued, and dividends of $8,600 were paid during the current year.
b. Additional common stock of $15,400 was issued, and no dividends were paid during the current year.
c. No additional common stock was issued, and dividends of $13,600 were paid during the current year.
.
The determination of the net income for each of the following separate situations is as follows:
Situation A Situation B Situation C
Net income $21,800 $2,400 $31,400
How is the net income determined?The formula for determining the net income (loss) for the year is:
Net Income (loss) = Ending Equity - Beginning Equity - Additional stock + Dividend Paid).
Data and Calculations:Beginning of year End of year
Total assets $ 53,200 $ 84,000
Total liabilities $ 23,600 $ 36,600
Situation A:
Common Stock issued = $4,600
Dividend paid = $8,600
Situation A:Beginning of year End of year
Total assets $ 53,200 $ 84,000
Total liabilities $ 23,600 $ 36,600
Equity $29,600 $47,400
Common Stock issued 4,600
Dividend paid (8,600)
Net Income = Ending Equity - Beginning Equity - Additional stock + Dividend Paid)
$21,800 ($47,400 - $29,600 - 4,600 + 8,600)
Situation B:Common Stock issued = $15,400
Beginning of year End of year
Total assets $ 53,200 $ 84,000
Total liabilities $ 23,600 $ 36,600
Equity $29,600 $47,400
Common Stock issued 15,400
Dividend paid
Net Income = Ending Equity - Beginning Equity - Additional stock + Dividend Paid)
$2,400 ($47,400 - $29,600 - 15,400)
Situation C:Dividends paid = $13,600
Beginning of year End of year
Total assets $ 53,200 $ 84,000
Total liabilities $ 23,600 $ 36,600
Equity $29,600 $47,400
Common Stock issued
Dividend paid $13,600
Net Income = Ending Equity - Beginning Equity - Additional stock + Dividend Paid)
$31,400 ($47,400 - $29,600 + 13,600)
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14. Kristin is using paper for an art project that
is 0.025 mm thick. If she glues a layer of the
paper onto a construction board with a
thickness of 7 x 10-2 mm, what will the total
thickness of the paper and the construction
board be? Write your answer in scientific
notation.
The thickness of the paper and the construction board will be 9.5 x [tex]10^{-2}[/tex] mm.
What will the thickness be?The thickness of the paper is written in standard form while the thickness of the construction board is written in scientific notation.
Scientific notation is used to compress large numbers into smaller number. In order to write a digit that is less than zero in scientific notation, count the numbers after the decimal point to the first non-zero digit, the numbers counted would be the power of the notation. he power would have a negative number.
Thus, 0.025 becomes 2.5 x [tex]10^{-2}[/tex]
(2.5 x [tex]10^{-2}[/tex]) + (7 x [tex]10^{-2}[/tex]) = 9.5 x [tex]10^{-2}[/tex] mm
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Sam and Bethan share £54 in the ratio 5:4 how much does each person get
Answer:add 5 and 4, you get 9. divide 54 by 9, and you get 6. this is because for every 5 sam gets bethan will get 4. if you add, that, you will get the total amount for 1 share.
Step-by-step explanation:
Answer:
Sam gets £30
Bethan gets £24
Step-by-step explanation:
Since they split the money in a ratio of 5:4, that means for every 5 parts of the money that Sam gets, Bethan gets 4 parts. The total of 5 parts and 4 parts is 9 parts.
To find how much each part is, we divide £54 by 9.
£54/9 = £6
Each part is £6.
Sam gets 5 parts: 5 × £6 = £30
Bethan gets 4 parts: 4 × £6 = £24
y=3x2 + 2 translated down three units
The output of the equation after transformation is y=3x^2 - 1.
According to the statement
We have to find that the mathematical transformation.
So, For this purpose, we know that the
A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.
From the given information:
The details are:
y=3x^2 + 2 translated down three units
According to this it is clear that the there is decrease of the 3 numbers.
Then the equation become:
y=3x^2 + 2
After transformation of the 3 units then:
y=3x^2 + 2 -3
y=3x^2 - 1
Then the output gets the y=3x^2 - 1.
So, The output of the equation after transformation is y=3x^2 - 1.
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puzzle one find the values of the unknown variables a b c d e and f substitude the values of the unknown numbers
The values of the unknown variables a,b,c,d,e and f is 8, 7, -3, 6, 1, and 2 respectively.
The code is 2 ( 7 + 6 ) + 8 ( 1 - ( - 3 ) ).
How to find the values of a,b,c,d,e and f?1.given that
[tex] x^4 . x^a = {x}^{12}[/tex]
we know the formula
[tex] a^m . a^n = {a}^{m+n}[/tex]
so, [tex] {x}^{(4+a)} = {x}^{12}[/tex]
if bases are equal then Powers will be equals.
then 4 + a = 12
a = 12 - 4
a = 8.
2. given that.
[tex] (y^b)/(y^5)= y^2[/tex]
we know the formula
[tex] a^m/a^n = {a}^{(m-n)}[/tex]
so, [tex] {y}^{(b-5)} = y^2[/tex]
when bases are equal then Powers will be equal.
b - 5 = 2
b = 2 + 5
b = 7
3.given that
[tex] 3^c = (1)/(27)[/tex]
so, [tex] 3^c = ( 1/3)^3 [/tex]
[tex] 3^c = {( 3/1)}^{-3} [/tex]
if bases are equal then Powers will be equals.
then c = -3.
4.given that
[tex] (m^3)^2 = m^d[/tex]
we know the formula
[tex] (a^m)^n = {a}^{m.n}[/tex]
[tex] m^6 = m^d[/tex]
if bases are equal then Powers will be equals.
then d = 6
5. given that
[tex] 7^0 = e[/tex]
e = 1
6. given that
[tex] {4}^{(-2) }. {4}^{9}. {4}^{(-5)} = 4^f[/tex]
we know the formula
[tex] a^m . a^n = {a}^{(m+n)}[/tex]
so, [tex] {4}^{(-2+9-5)} = 4^f[/tex]
if bases are equal then Powers will be equals.
then -7+9 = f
f = 2.
Hence, the values of the unknown variables a,b,c,d,e and f is 8, 7, -3, 6, 1, and 2 respectively.
The code is
f ( b + d ) + a ( e - c )
2 ( 7 + 6 ) + 8 ( 1 - ( - 3 ) ).
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Let X be the number of students who show up for a professor's office hour on a particular day, pmf of X is p(0) = 0.10, p(1) = 0.20, p(2) = 0.25, p(3) = 0.30 and p(4) = 0.15, what is the probability at least 2 students show up? I tried doing P(p(1) u p(2)) = P(p(1)) + P(p(2)) - (P(p(1) n p(2))) what would be the correct formula?
The probability of at least 2 students showing up is .70 or 70%
Let X be the number of students who show up for a professor's office hour on a particular day, probability of X is p(0) = 0.10, p(1) = 0.20, p(2) = 0.25, p(3) = 0.30 and p(4) = 0.15
If we add the probability of 1 student showing up, 2 students to show up, 3 students to show up, and 4 students showing up
We get 0.10+ 0.20+ 0.25+ 0.15 =1
As the sum of these individual 4 possibilities is 1 that means these are the only possibilities to exit
Now we need to find out the probability of at least 2 students showing up which means the probability of two or more students showing up
Which can be written as
p(≥2) = p(2) + p(3) + p(4)
p(≥ 2) = 0.25+0.30+0.15
p(≥2) = 0.70
Hence, the probability of at least 2 students showing up is .70 or 70%
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The probability density of a random variable X is given in the figure below. The random variable is uniformly distributed between 0 and 2. From this density, find the probability that X is at least 0.48.
The probability that X is at least 0.48 given the information about the density of a random variable X is 0.76.
How to calculate the probability?Given that x is uniformly distributed between 0 and 2.
Therefore, the probability density function:
f(x)= 1 / (b-a) = 1 / (2-0)
= 0.5
This will be illustrated as:
P(X<=x)=(x-a)/(b-a)=(x-0)/(2-0)=x/2
Now, we have to find:
P(x >= 0.48)
= 1 - P(x<=1.68)
= 1-(0.48 / 2)
= 1 -0.24
= 0.76
Therefore, the probability that X is at least 0.48 given the information about the density of a random variable X is 0.76.
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What question is correct? A-B-C-D?
Answer:
b is the answer
Step-by-step explanation:
b is the answer
How are translations along the vectors ⟨a,b⟩ and ⟨-a,-b⟩ similar and how are they different ?
The similarity of two vectors ⟨a,b⟩, and ⟨-a,-b⟩ is that they can both be placed on the same graph; the difference is that they belong to different quadrants.
What are vectors?A vector is a two-dimensional object with a magnitude and a direction. A vector can be visualized geometrically as a directed line segment with an arrow indicating the direction and a length equal to the magnitude of the vector. The vector's direction is from its tail to its head.So, the similarity between two vectors ⟨a,b⟩, and ⟨-a,-b⟩ is that they can be placed on the same graph and the difference between the two is that they belong to different quadrants.
⟨a,b⟩ belongs to the 1st quadrant, and ⟨-a,-b⟩ belongs to the 3rd quadrant.Therefore, the similarity of two vectors ⟨a,b⟩, and ⟨-a,-b⟩ is that they can both be placed on the same graph; the difference is that they belong to different quadrants.
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help please i need help
Answer:
100
Step-by-step explanation:
first let's convert 240 mins to hours
240/60 = 4
now let's find approximately how many pages per hour
200/4 = 50
so, in one hour she approximately read 50 pages
let's say she reads 25 pages per hour
25(4)= 100
Evaluate.
18-2³ 0
I don’t understand it and I need help
The sum of the squares of three consecutive positive integers is 2030. What is the middle integers?
The value of the middle integer is 26
Solving Linear equationsFrom the question, we are to determine the middle integer
From the given information,
"The sum of the squares of three consecutive positive integers is 2030"
Let the first integer be x,
Then the middle integer will be x + 1
and the third integer will be x + 2
Thus,
x² + (x +1)² + (x +2)² = 2030
x² + x² + 2x + 1 + x² + 4x + 4 = 2030
3x² + 6x + 5 = 2030
3x² + 6x + 5 - 2030 = 0
3x² + 6x - 2025 = 0
x² + 2x - 675= 0
Solve quadratically
x² + 27x - 25x - 675 = 0
x(x + 27) -25(x + 27) = 0
(x - 25)(x + 27) = 0
x - 25 = 0 and x + 27 = 0
x = 25 and x = -27
Since x is a positive integer,
x = 25
Thus,
The middle integer,
x + 1
= 25 + 1
= 26
Hence, the value of the middle integer is 26
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Which of the following values is greater than −2.5?
Answer:
-2,-1.5,-1,-0.5 etc
Step-by-step explanation:
The smaller the negative value the greater the value compared to other negative value carrying a negative sign.
Ryan downloaded a video game to his computer. The size of the file was 3.1 times 10E4 kilobytes. After the game, Ryan installed a patch that is 40000 kilobytes. What is the size of the game file written in standard form?
The size of the game file written in standard form is 350000 kilobytes
What is the size of the game file written in standard form?The given parameters are:
Size of the file = 3.1 x 10E4 kilobytes
Patch = 40000 kilobytes
The size of the game file written in standard form is then calculated as
Size = Size of the file + Patch
This gives
Size = 3.1 x 10E4 kilobytes + 40000 kilobytes
Rewrite as
Size = 310000 kilobytes + 40000 kilobytes
Evaluate the sum
Size = 350000 kilobytes
Hence, the size of the game file written in standard form is 350000 kilobytes
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Duration (amount of time) is what type of data in the scenario? A study was done to determine the age, the number of times per week, and the duration (amount of time) of residents using a local gym in San Antonio, Texas. The first car in the parking lot was selected randomly, and then the resident of every eighth car in the lot around the gym was interviewed.
The sampling method used to get the sample is Systematic sampling.
The variable type of color of cars around the gym is qualitative.
Sampling is the process of choosing a subset of people (a statistical sample) from a statistical population in order to estimate characteristics of the entire population. It is used in statistics, quality control, and survey technique. Statisticians try to get samples that are typical of the population under consideration.
The different sampling methods used are:
Simple random sampling: Every member of the population has an equal probability of getting chosen.Systematic sampling : Members are chosen after a fixed interval every time.Stratified sampling: The entire population is divided into sub populations and then the sample is chosen from each sub population. Cluster sampling: The population is also divided into smaller groups for cluster sampling, although each smaller group should share traits with the larger sample. You choose complete subgroups at random rather than picking a representative sample of each subgroup.Now the given sample of the residents that were selected was every eighth car . Hence Systematic sampling is used.
Disclaimer: Missing question stem: Identify the sampling method(simple , stratified, cluster, systemic).
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How many different 4 card hands can be dealt from a deck of 52 cards
Answer:
There are thirteen 4 card hands are possible with a 52 card deck.
Answer:
Thirteen 4 card hands are possible with a 52 card deck
Convert 3.5% to a decimal.
Question 2 options:
0.0035
0.35
0.035
3.5
Answer:
0.035
Step-by-step explanation:
hope this helps :)
A student wants to find out if LMC students prefer eating out or eating in
the cafeteria. She talks to 25 of her friends in the Transfer Academy and
finds that they prefer eating in the cafeteria. She then concludes that LMC
students prefer eating in the cafeteria.
What is the intended population?
What is the actual population?
What is the sample?
The intended population based on the information given is LMC students.
The actual population based on the information illustrated is Transfer Academy.
The sample is the 25 friends that the student talked to.
How to illustrate the information?Using the data, the student decides to interview 25 of her acquaintances from the Transfer Academy to learn whether LMC students prefer eating in or eating outside of the cafeteria.
According to the data shown, Transfer Academy is the actual population in this circumstance. It is important to remember that the sample represents the population.
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given then functions: f(x)=4x+9 and g(x)=7x-5
Part 1
[tex](f+g)(x)=f(x)+g(x) \\ \\ =4x+9+7x-5 \\ \\ =11x+4[/tex]
Part 2
[tex](f-g)(x)=f(x)-g(x) \\ \\ =(4x+9)-(7x-5) \\ \\ =4x+9-7x+5 \\ \\ =-3x+14[/tex]
Part 3
[tex](f \cdot g)(x)=f(x) \cdot g(x) \\ \\ =(4x+9)(7x-5) \\ \\ =28x^2-20x+63x-45 \\ \\ =28x^2+43x-45[/tex]
Part 4
[tex]\left(\frac{f}{g} \right)(x)=\frac{f(x)}{g(x)} \\ \\ =\frac{4x+9}{7x-5}[/tex]
2.75 divided by (2.2)
Answer:
1.25
Step-by-step explanation:
=2.75/2.2
=1.25
it is answer .it think answer give some help
which is an algebraic expresson for 5 more than z
Answer:
z+5
Step-by-step explanation:
the word more indicates addition
7+1/X (1/x) multiply
The value of the linear equation after multiplying is 8/xX.
According to the statement
We have to find that the value of the statement.
So, For this purpose, we know that the
The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.
From the given information:
The equation is a:
7+1/X (1/x)
Here we know that the X and x are the different variables.
Then
7+1/X (1/x)
Now add the terms which are possible then
8/X (1/x)
Now, multiply the terms which are possible to multiply
Then the equation become
8/xX.
So, The value of the linear equation after multiplying is 8/xX.
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The length of a rectangular pool is three times its width. If the perimeter of the pool is one hundred and sixty meters, find the length and width of the pool.
Answer:
w = 20m
l = 60m
Step-by-step explanation:
P = 2l + 2w
We know the perimeter = 160 and we know that l = 3w, so write what we know and solve for w.
P = 2l x 2w
160 = 2(3w) + 2w
160 = 6w + 2w
160 = 8w
Divide both sides by 8
20 = w
Now we can figure out the length, which is 3(w) or 3 x 20 = 60
Answer:
w = 20m, l = 60m
Step-by-step explanation:
What are the common factors of 70 and 110
Answer:
Do you mean GCF? If so, it is 10.
If you mean factors that they have in common it is: 1,2,5 and 10.
Step-by-step explanation:
Factors of 70: 1,2,5,7,10,14,35,70
Factors of 110: 1,2,5,10,11,22,55,110
GCF is 10
Answer:
10
Step-by-step explanation:
