The difference of the fraction is 2/3 or two-thirds
Difference of fractionsFractions are written as a ratio of two integers. They are written in the form a/b
Given the following expression
Negative 2 and one-half minus (negative 1 and three-fourths)
This can also be written as;
-2 1/2 - (-1 3/4)
Convert mixed to improper to have;
-5/2 + 7/4
Swap to have;
7/4 - 5/3
Find the LCM
3(7)-4(5)/12
21-20/12
8/12
Write in its simplest form
8/12 = 2/3
Hence the difference of the fraction is 2/3 or two-thirds
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Answer:
2
Step-by-step explanation:
because -3/4 + 2 3/4= 2
my car uses 8.5L of pertrol per 100km travelled. If I travel 400km, how many litres of petrol will my car use?
Answer:
34 L
Step-by-step explanation:
there are four 100 km(s) in 400 km
so
8.5 * 4 is what you need to do to find your answer
8.5 * 4 = 34
34 L is your answer
A plan for a baseball diamond is drawn in a coordinate plane. The baseball diamond is in the shape of a square with vertices at approximately (0, 64), (64, 0), (0, -64), and (-64, 0). One unit in the coordinate plane represents 1 ft. What is the approximate area of the baseball diamond?
The area of the baseball diamond is 8192 sq. units.
We assume the square-shaped, baseball diamond to be ABCD with A = (0, 64), B = (64, 0), C = (0, -64), and D = (-64, 0).
The side of the square can be computed using the distance formula,
D = √((x₂ - x₁)² + (y₂ - y₁)²), when the endpoints of a line are (x₁, y₁) and (x₂, y₂).
Thus, the side of the square,
a = √((x₂ - x₁)² + (y₂ - y₁)²),
or, a = √((64 - 0)² + (0 - 64)²) {Considering A(0,64) and B(64, 0) as the endpoints,
or, a = √(64² + (-64)²),
or, a = √(4096 + 4096),
or, a = 64√2 units.
Now, the area of the square can be calculated using the formula, A = a², where A is the area and a is the side of the square.
Thus, the area of the square = (64√2)² = 4096*2 = 8192 sq. units.
Thus, the area of the baseball diamond is 8192 sq. units.
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Quick algebra 1 assignment for some points and brainliest!
(EASIER THAN IT LOOKS)
Only help if you know the answer PLEASE HELP EXPERTS AND GENIUSES ITS DUE TOMMAROW
(ANSWER ALL 4 PARTS OF THE ASSIGNMENT PLEASE :p )
1. The 100 prisoner experiment: 100 prisoners are about to be executed (you can use paper stick figures to model 100 prisoners, or you can do about 10), but the warden has agreed to allow all prisoners to be commuted to a 6-month sentence if they can pass one game. The game states that 100 pieces of paper with each of the prisoner's numbers are to be randomly shuffled into boxes that have random prisoner's numbers (where the number on the paper does not match the number on the boxes.) Each prisoner is allowed to open 50 boxes to find their number such that they have a [tex]\frac{1}{2}[/tex] chance of finding their number. If you find your number, you are cleared to another room to wait. If you don't, then you've messed up huge. If even one prisoner does not find their number, all the prisoners die. If all of the prisoners find their numbers, they all get 6-month sentences instead. The chance of all the prisoners randomly finding their numbers is [tex](\frac{1}{2})^{100}[/tex], which is about a 0.0000000000000000000000000000008% chance. 30 zeros after the decimal placement. For reference, two people have a better chance of picking up the same grain of sand from any of the beaches in the world than finding their numbers randomly.
The Vickrey Auction can be modeled into an experiment by testing people's psychological thinking. You can do this with any of your friends. In a Vickrey auction, you put your bids into a closed letter. For an item, the highest bidder wins the auction, but does not pay what he or she put their bid under in the auction, but rather pays what the second bidder had bidded. It teaches people to be more honest, because if you bid the highest and win, you pay the second-highest bidder's payment, which could also be almost equally as high and could cost you a fortune for an undervalued item.
Another great experiment you can do is to measure the different unsynchronizations of analog clocks that are not close together. Scientists have measured atomic clocks that are just a millimeter apart that start ticking in different measures.
2. I select the 100-prisoner experiment.
3. A curved graph like -x^2 would fit perfectly.
4. A quadratic function would fit my experiment the best. The best graph to use would be [tex]y = -x^2[/tex]. An equation with a large curve would be the best for this type of experiment to graph success and failure. More than three quarters of my graph wouls be full of failure and maybe a little more than 10% would be full of success if repeated over 100,000 times. I am not too sure though.
On the interval [0, 2π), which points are intersections of r = 5 4 sin(θ) and r = −6 sin(θ)? check all that apply.
Correct option is D) and E)
(3,7π/6),(3,11π/6)
What is Point of intersection?Point of intersection is the point where two lines or two curves meet each other.
The point of intersection of two lines of two curves is a point.
If two planes meet each other then the point of intersection is a line.
The term "point of intersection" refers to the intersection of two lines. The equations a1x+b1y+c1=0 and a2x+b2y+c2=0, respectively, are used to represent these two lines. The two lines' intersection point is shown in the following figure. The intersection of three or more lines can also be located.
According to the given information:let
5 + 4 sin(θ) = −6 sin(θ)
Then get
θ= -1/2
Then you can make it
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I understand that the question you are looking for is:
On the interval [0, 2π), which points are intersections of r = 5 4 sin(θ) and r = −6 sin(θ)? check all that apply.
A) -3,7/6
B) (-3,11/6)
C) (3,7/6)
D) (3,11/6)
johns first three test scores out of 100 are 84,78,82. what did he score on his fourth test if the average for all four tests is 80 out of 100
Answer:
76
Step-by-step explanation:
In order for John's average to be 80, the sum of all of his test scores must be 4*80 = 320. We can add 84, 78, and 82 to get 244, and then we subtract 244 from 320 to obtain the answer 76.
Answer:
Step-by-step explanation:
80 * 4 = 320
84 + 78 + 82 + x = 244
244 + x = 320
x = 320 - 244
x = 76
If the population standard deviation σ=25. What is the required minimum sample size to construct a 95 confidence level for the population mean with an allowable error of ±3?
The required minimum sample size to construct a 95% confidence level for the population mean is 267.
In this question,
In the probability and statistics theory, the confidence interval of the population parameter is the estimated range of values we are sure with a certainty that our parameter will lie within, the range being calculated from the sample obtained. The smaller is the margin of error, the more confidence we have in our results.
The population standard deviation, σ = 25
Confidence level for the population mean = 95%
Margin of error = ±3
Let n be the sample size of the population
The z-score for the confidence level of 95% for the population mean is 1.96.
The formula of margin of error is
[tex]E=\frac{z \sigma}{\sqrt{n} }[/tex]
Now, the sample size of the population can be calculated as
[tex]n=(\frac{z\sigma}{E} )^{2}[/tex]
On substituting the above values,
⇒ [tex]n=(\frac{(1.96)(25)}{3} )^{2}[/tex]
⇒ [tex]n=(\frac{49}{3}) ^{2}[/tex]
⇒ [tex]n=(16.33)^{2}[/tex]
⇒ n = 266.77 ≈ 267
Hence we can conclude that the required minimum sample size to construct a 95% confidence level for the population mean is 267.
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Researchers surveyed recent graduates of two different universities about their income. the following two-way table displays data for the sample of graduates who responded to the survey. how many graduates in the sample had an income of \$40\text{,}000$40,000dollar sign, 40, start text, comma, end text, 000 and over?
Universities A had an income under $20,000 25% graduates.
What is a two-way table?A two way table is a way to display frequencies or relative frequencies for two categorical variables. One category is represented by rows and a second category is represented by columns.
Researchers surveyed recent graduates of two different universities about their income. The following two-way table displays data for the sample of graduates who responded to the survey.
A had an income under $40,000 25% graduates.
We have to add 30 45 together and get 75 because those are the students that have income under $40,000 dollars in both Universities
Then u convert have to convert it to a percentage and get 25%.
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The above question is not complete:
Researchers surveyed recent graduates of two different universities about their income. The following two-way table displays data for the sample of graduates who responded to the survey.
How many graduates from University A had an income under $40,000?
________graduates.
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The answer is 25%
its what khan says :>
A system of linear equations is shown below, where A and B are real numbers.
3x + 4y = A
Bx – 6y = 15
What values could A and B be for this system to have no solutions?
Answer:
A = 0; B = -9/2
Step-by-step explanation:
To have no solutions, you need parallel lines with equal slopes and different y-intercepts.
3x + 4y = A Eq. 1
Bx - 6y = 15 Eq. 2
In Eq. 1, notice that the coefficient of x is 3/4 of the coefficient of y.
We must have the same ratio for the coefficients in Eq. 2.
B/(-6) = 3/4
4B = -6(3)
4B = -18
B = -9/2
Now we have
3x + 4y = A Eq. 1
-9/2 x - 6y = 15 Eq. 2
How do we change the left side of the second equation into the left side of the first equation? -6/4 = -3/2 and also -9/2 ÷ 3 = -3/2
To change the left side of the second equation into the left side of the first equation, divide the left side by -3/2.
If we divide 15 by -3/2 we get -10.
The equation -9/2 x - 6y = -10 is the same as Eq. 1, so that would create a system of equations with only one equation and an infinite number of answers.
To have no equations, the y-intercepts must be different, so A can be any number other that -10.
Answer: A = 0; B = -9/2
2x-1, x < 2 12. Show that f(x) = { 3x 2 x ≥ 2 is continuous.
Using the continuity concept, since the lateral limits and the numeric value of the function are equal at the point in which the definition changes, the function is continuous.
What is the continuity concept?A function f(x) is continuous at x = a if it is defined at x = a, and:
[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]
The definition of the piecewise function is given by:
f(x) = 2x - 1, x < 2.f(x) = 3x/2, x >= 2.Since the definition of the function changes at x = 2, and the domain of the function has no restrictions, this is the only point in which there may be a discontinuity.
The lateral limits are:
[tex]\lim_{x \rightarrow 2^-} f(x) = \lim_{x \rightarrow 2} 2x - 1 = 2(2) - 1 = 3[/tex].[tex]\lim_{x \rightarrow 2^+} f(x) = \lim_{x \rightarrow 2} 1.5x = 1.5(2) = 3[/tex].The numeric value is:
f(2) = 1.5 x 2 = 3.
Since the lateral limits and the numeric value of the function are equal at the point in which the definition changes, the function is continuous.
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10. The product of -2 and a number n is increased by 15. The result is greater than 3. Choose the inequality that represents the solution set to the problem. A. n>6/ B. n-6 D. n
Answer:
-2n+15>3
Step-by-step explanation:
What is the euclidean distance between x(3,2,5) and y(2,3,3) in three dimensional space?
a) 4
b) 2. 45
c) 3
d) 1. 5
Answer:
b) 2.45
Step-by-step explanation:
The Euclidean distance in 3-space is the root of the sum of the squares of the x-, y-, and z-differences between the points.
ApplicationFor the given points ...
[tex]x(3,2,5)=(x_1,y_1,z_1)\quad\textsf{and}\quad y(2,3,3)=(x_2,y_2,z_2)[/tex]
The distance between x and y is ...
[tex]d=\sqrt{(x_2-x_1)^2+(y_2=y_1)^2+(z_2-z_1)^2}\\\\d=\sqrt{(2-3)^2+(3-2)^2+(3-5)^2}=\sqrt{1+1+4}\\\\d=\sqrt{6}\approx2.45[/tex]
On a coordinate plane, a parabola opens to the left. It has a vertex at (0, 0), a focus at (negative 2, 0), and a directrix at x = 2.
Which equation represents the parabola shown on the graph?
y2 = –2x
y2 = –8x
x2 = –2y
x2 = –8y
The equation represents the parabola shown on the graph is x^2 = - 8y . Option D
How to determine the equationWe were given the following parameters;
Vertex ( 0, 0 )Focus ( -2, 0)Directrix , at x = 2The standard for a parabola is given as;
y² = 4ax
It can also be written as;
x² = 4ay
Given the focus as ( -2, 0), we have the value of 'a' to be -2
Now, let's substitute the value into the standard equation of a parabola
x^2 = 4ay
x^2= 4 × -2 × y
Multiply through
x^2 = - 8y
The equation of the parabola is x^2 = - 8y
Thus, the equation represents the parabola shown on the graph is x^2 = - 8y . Option D
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Answer:
b
Step-by-step explanation:
trust
Please solve the attachment which is given, and give me the answer. Thank you for your lovely time! <3
Answer:
1. 36 liters
2. 3 kg
Step-by-step explanation:
because 12 liters is 4kg if you multiply both by 3 you’ll get that 12 kg is equal to 36 liters
also, if you divide both by 4, you’ll see that 1kg is equal to 3 liters. Then with this knowledge, yiucc be an see that if you multiply both by 3; 3 kg will be 9 liters! :)
Answer:
1.) 36 litres
2.) 3 kg
Step-by-step explanation:
In this case there is a ratio of 1:3 of mass to volume. If we know the mass, the volume is 3 times that. If we know the volume, the mass is that divided by 3.
Explain the steps for moving three disks from one peg to another. start with moving the small disk to the right peg.
There are some ways by which move the steps from sequence and series method like
Move the medium desk to the left peg. Move the small desk to the left peg. Move the large desk to the right peg. With the small disc to the middle peg. Move the middle desk to the right peg. With the small desk to the right peg.
According to the statement
we have to explain the moving steps to change the position of the given three disk from one peg to another.
So, for the solution of this problem
Firstly we know that the sequence and series
An itemized collection of elements in which repetitions of any sort are allowed is known as a sequence, whereas series is the sum of all elements.
we have to use the sequence and series method.
So, according to this method
Move the medium desk to the left peg. Move the small desk to the left peg. Move the large desk to the right peg. With the small disc to the middle peg. Move the middle desk to the right peg. With the small desk to the right peg.
So, there are some ways by which move the steps from sequence and series method like
Move the medium desk to the left peg. Move the small desk to the left peg. Move the large desk to the right peg. With the small disc to the middle peg. Move the middle desk to the right peg. With the small desk to the right peg.
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25. A chocolate bar which weighs of a pound is 9/16 cut into seven equal parts. How much do three parts weigh? (A) pound 21/112 (B) pound/27/112 (C) pound 16/63 (D) pound 47/63
The three parts weigh 27/112 pound ( letter B).
Rules for Multiplication and Division of FractionsFor Multiplication - First, you should multiply both numerators after that you should multiply both denominators. Finally, you can simplify if it is necessary.For Division- First, you should repeat the numerator and after that you should multiply the numerator by the reciprocal of denominators. Finally, you can simplify if it is necessary.The question gives:
A chocolate bar that weighs = 9/16A chocolate bar cut into seven equal parts.Therefore, each part will be [tex]\frac{\frac{9}{16} }{7} =\frac{9}{16} *\frac{1}{7} =\frac{9}{112}[/tex].
For knowing the three parts weigh, you should mulitiply the previous value for 3. Thus,
[tex]\frac{9}{112}*3=\frac{27}{112}[/tex].
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The weight of three parts is 27/112 pounds
How to determine the weight of three parts?The weight of the chocolate bar is given as:
Weight = 9/16
When it is cut into 7 equal parts, the weight of each part is
Each = Weight/7
This gives
Each = 9/16 * 1/7
Evaluate the product
Each = 9/112
The weight of three parts is then calculated as:
Three parts = Each * 3
This gives
Three parts = 9/112 * 3
Evaluate the product
Three parts = 27/112
Hence, the weight of three parts is 27/112 pounds
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Is anyone really good at math?
Answer: 12 cm
Step-by-step explanation:
[tex]\mathtt{Using\ the \ pythagorean \ theorem: \\}[/tex]
[tex]a^2+b^2=c^2, \\\ we\ can\ plug\ in\ values\ for\ a,\ b,\ and\ c[/tex]
[tex]L=a\ and\ M=b\ and\ N=c[/tex]
Therefore,
[tex]L^2+35^2=37^2\\L^2+1225=1369\\L^2=144\\\sqrt{L^2} =\sqrt{144} \\L=\pm12\\Taking\ only\ the\ positive\ answer,\ we\ get:\\\large\boxed{L = 12cm}[/tex]
We have: L² + M² = N²
=> L² = N² - M² = 37² - 35² = 144 = 12²
=> L = 12
ANSWER: B.12
OK done. Thank to me :3
GEOMETRY STUFF!! PLSS HELPP, NEED ANSWERS AND SOLUTIONS RN!!
Applying the angle bisector and triangle proportionality theorem, the solutions are:
16. x = 1/2 or x = 4
17. x = 5
18. x = −1 or x = 6.
What is the Angle Bisector Theorem?The angle bisector theorem states that when a line segment divides one of the angles of a triangle into two halves, it also divides the triangle to form segments that are proportional to each other.
16. 3x/(x - 1) = (x + 4)/(x - 2) [triangle proportionality theorem]
Cross multiply
(x - 1)(x + 4) = 3x(x - 2)
x² + 3x - 4 = 3x² - 6x
x² - 3x² + 3x - 4 + 6x = 0
-2x² + 9x - 4 = 0
Factorize -2x² + 9x - 4
(−2x + 1)(x − 4)
-2x = -1
x = 1/2
or
x = 4
17. (2x + 2)/(x + 3) = (4x - 2)/(2x + 2)
(2x + 2)(2x + 2) = (4x - 2)(x + 3)
4x² + 8x + 4 = 4x² + 10x - 6
Combine like terms
4x² - 4x² + 8x - 10x = -4 - 6
-2x = -10
x = -10/-2
x = 5
18. (2x + 3)/(x + 4) = x/(x - 2) [angle bisector theorem]
Cross multiply
(2x + 3)(x - 2) = x(x + 4)
Expand
2x² - x - 6 = x² + 4x
2x² - x - 6 - x² - 4x = 0
x² - 5x - 6 = 0
Factorize x² - 5x - 6 = 0
(x+1)(x−6) = 0
x = −1 or x = 6
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When we use the Distributive
Property, we multiply the number in
front of the parenthesis with each
term inside the parenthesis.
Enter the number that belongs in the green box.
3(4x + 2) = [?]x + [ ]
Answer:
12x+6
Step-by-step explanation:
Can i have brainliest
Answer: 12x + 6
Step-by-step explanation:
In Distributive property, you multiply each of the numbers in the parentheses by the outside number.
The percentage of the battery's capacity that is charged as a function of time (in minutes) is graphed.
A first quadrant coordinate plane. The horizontal axis is from zero to thirty-two-point-five with a scale of two point five and is titled Time in minutes. The vertical axis is from zero to one hundred with a scale of five and is titled Capacity, percent charged. The graph of the line is y equals two x plus forty. The graph ends at thirty minutes.
A first quadrant coordinate plane. The horizontal axis is from zero to thirty-two-point-five with a scale of two point five and is titled Time in minutes. The vertical axis is from zero to one hundred with a scale of five and is titled Capacity, percent charged. The graph of the line is y equals two x plus forty. The graph ends at thirty minutes.
At what rate is the battery charged?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
111 percent per minute
(Choice B)
B
202020 percent per minute
(Choice C)
C
101010 percent per minute
(Choice D)
D
222 percent per minute
The rate at which battery charges is 10 percent per minute.
According to the statement
we have given that the charging capacity of battery in the graphical representation.
And we from this we have to find the percentage by which battery charges.
And the graphical representation given is :
The horizontal axis is from zero to thirty-two-point-five with a scale of two point five and is titled Time in minutes. The vertical axis is from zero to one hundred with a scale of five and is titled Capacity, percent charged. The graph of the line is y equals two x plus forty. The graph ends at thirty minutes.
A first quadrant coordinate plane. The horizontal axis is from zero to thirty-two-point-five with a scale of two point five and is titled Time in minutes.
And according to this representation it is clear that the percentage by which battery charges is 10 percentage per minute.
So, The rate at which battery charges is 10 percent per minute.
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which graph below shows the solutions for the linear inequality y>- 1/3x + 1
The graph that shows the solutions for the inequality, y > -1/3x + 1 is: C. Graph A.
How to Find the Graph of a Linear Inequality?The inequality sign, ">" means that the graph of the inequality has a dashed line where the shaded part is above the boundary line and the boundary line is dashed or dotted. If "≥" is used, the boundary line would not be dashed or dotted and the shaded area would be above it.
On the other hand, "<" is used when the shaded area is below the boundary line and the boundary line is a dashed line. If "≤" was used, the boundary line won't be dashed or dotted, while the shaded area would be below the boundary line that is not dotted.
Given y > -1/3x + 1, the slope (m) = change in y / change in x is -1/3.
Graph A has a slope of -1/3 and the shaded part is above the boundary line.
Therefore, the graph that shows the solutions for y > -1/3x + 1 is: C. Graph A.
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1/2.x + 3 ( x-1 ) - 5 = 30
Answer:
1/2.x+3(x-1)-5=30
1/2.x+3x-3-5=30
(1/2+3)x-8=30
7/2.x-8=30
7/2.x=38
7x=76
x=76/7
CMIIW
Consider this quadratic equation.
2x²2²-1=3x+4
Which equation correctly applies the quadratic formula?
COA
OB.
OC.
OD.
2=
H=
H=
-(-3) ± √(-3)²-4(2)(-5)
-(-3);
2
-(-3) ± √(-3)²-4(-5)
(2)
-(-3) ± √(-3)²(2)(-5)
(2)
-(-3) ± √(-3)²-4(2)(-5)
2(2)
Answer:
-(-3) ± √(-3)^2 - 4(2)(-5) / 2(2) (the last choice).
Step-by-step explanation:
Im ignoring the 2^2 in the equation
The equation transforms to
2x^2 - 3x - 5 = 0 (standard form)
So x = -(-3) ± √(-3)^2 - 4(2)(-5) / 2(2)
$10- (5.80+28 cents)
Can someone pls help me get the anwser for this question
Answer: [tex]\Large\boxed{x=6.5}[/tex]
Step-by-step explanation:
Given equation
-9 - (x + 1) = -2 - (3x - 5)
Expand the parenthesis
-9 - x - 1 = -2 - 3x + 5
Combine like terms
-9 - 1 - x = -2 + 5 - 3x
-10 - x = 3 - 3x
Add 3x on both sides
-10 - x + 3x = 3 - 3x + 3x
-10 + 2x = 3
Add 10 on both sides
-10 + 2x + 10 = 3 + 10
2x = 13
Divide 2 on both sides
2x / 2 = 13 / 2
[tex]\Large\boxed{x=6.5}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Find a power series for the function, centered at c. g(x) = 4x x2 2x − 3 , c = 0
The power series for given function [tex]g(x)=\frac{4x}{(x-1)(x+3)}[/tex] is [tex]g(x)=\sum{_{n=0}^\infty}~x^n(-1+(-\frac{x}{3} )^n)[/tex]
For given question,
We have been given a function g(x) = 4x / (x² + 2x - 3)
We need to find a power series for the function, centered at c, for c = 0.
First we factorize the denominator of function g(x), we have:
[tex]\Rightarrow g(x)=\frac{4x}{(x-1)(x+3)}[/tex]
We can write g(x) as,
[tex]\Rightarrow g(x)=\frac{1}{x-1}+\frac{3}{x+3}\\\\\Rightarrow g(x)=\frac{-1}{1-x}+\frac{1}{1+\frac{x}{3} }\\\\\Rightarrow g(x)=\frac{-1}{1-x}+\frac{1}{1-(-\frac{x}{3} )}\\[/tex]
We know that, [tex]\frac{1}{1-x}=\sum{_{n=0}^\infty}~{x^n}[/tex] if |x| < 1
and [tex]\frac{1}{1-(-\frac{x}{3} )}=\sum{_{n=0}^\infty}~x^n(-\frac{x}{3} )^n[/tex] if [tex]|\frac{x}{6}| < 1[/tex]
[tex]\Rightarrow g(x)=-\sum{_{n=0}^\infty}~x^n+\sum{_{n=0}^\infty}~x^n(-\frac{x}{3} )^n\\[/tex] if |x| < 1 and if [tex]|\frac{x}{6}| < 1[/tex]
[tex]\Rightarrow g(x)=\sum{_{n=0}^\infty}~x^n(-1+(-\frac{x}{3} )^n)[/tex] if |x| < 1
Therefore, the power series for given function [tex]g(x)=\frac{4x}{(x-1)(x+3)}[/tex] is [tex]g(x)=\sum{_{n=0}^\infty}~x^n(-1+(-\frac{x}{3} )^n)[/tex]
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20 points please help
The data set below has 7 values. Find the mean absolute deviation for the data set. If necessary, round your answer to the nearest hundredth. 14, 13, 16, 12, 17, 21, 26
Answer:
3.71
Step-by-step explanation:
The mean absolute deviation(MAD) of a data set is given by the formula
[tex]$ MAD =\frac{1}{n} \sum_{i=1}^n |x_i-\bar{x}|$[/tex]
[tex]n[/tex] = number of data set values. Here [tex]n = 7[/tex]
[tex]\bar{x}=[/tex] mean of the data set values; [tex]\bar{x}=[/tex] [tex](14+13+16+12+17+21+26)/7[/tex] = [tex]119/7=17[/tex]
[tex]x_{i}[/tex] are the n individual values
[tex]\frac{1}{7} |14-17| + |13-17| + |16-17| + |12-17| + |17-17| + |21-17| + |26-17|\\= (3 + 4 + 5 + 1+ 0 + 4 + 9)/7\\= 26/7 = 3.71428 \\[/tex]
= [tex]3.71 \textrm{ rounded to the nearest hundredth}[/tex] Answer
pls helpp
1. There are 3 1/2 groups of students ready to load buses for a field trip. Each group will fill one bus 2/5 of the students on each bus are boys. How many buses would it take to carry only the boys.
2. Mark is going to a pool party. It is 2 3/4 miles from his house. Mark decides to ride his bicycle, but he has a flat tire 2/3 if the way there. How far is Mark from his house?
We know that there are (3 + 1/2) groups, such that each group fill one bus.
2/5 of the students are boys, then the number of groups that we can make only with boys is:
(2/5)*(3 + 1/2) = 6/5 + 1/5 = 7/5 = 5/5 + 2/5 = 1 + 2/5
Then you can make one and a little less than a half of a group, which means that you need 1 and 2/5 of a buss to transport the boys, rounding that to the a whole number, you will need 2 busses to only transport the boys.
How far is Mark from his house?The original distance is:
D = (2 + 3/4) miles.
But Mark only covers 2/3 of that distance, then we have:
d = (2/3)*D = (2/3)*(2 + 3/4) miles = (4/3 + 2/4) miles
d = (4/3 + 1/2) miles = (8/6 + 3/6) miles = (1 + 5/6) miles
Mark is at (1 + 5/6) miles of his house.
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A graph of a line goes through the points (zero, four) and (negative six, zero).
Find the equation of the line using exact numbers.
The equation of the line is y = 2/3x + 4
How to find the equation of the line using exact numbers?The points on the line are given as:
(zero, four) and (negative six, zero).
Rewrite the points properly as
(0, 4) and (-6, 0)
The slope of the line is calculated using:
m =(y2 - y1)/(x2 - x1)
Substitute the known values in the above equation
m = (0 - 4)/(-6 - 0)
Evaluate
m = 2/3
The equation of the line is then calculated as:
y = mx + b
This gives
y = 2/3x + b
So, we have:
4 = 2/3 * 0 + b
Evaluate
b = 4
Substitute b = 4 in y = 2/3x + b
y = 2/3x + 4
Hence, the equation of the line is y = 2/3x + 4
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which expression is equivalent to (60x^(20)y^(24))/(30x^(10)y^(12)
a. 2x^(2)y^(2)
b. 2x^(10)y^(12)
c. 30x^(2)y^(2)
d.30x^(10)y^(12)
Answer:
b. 2x^10y^12.
Step-by-step explanation:
(60x^(20)y^(24))/(30x^(10)y^(12)
60 / 30 = 2
x^20 / x^10 = x^(20-10) = x^10
y^(24) / y^(12) = y^(24-12) = y^12.
Thus, the answer is:
2x^10y^12.
Answer:
b. 2x^(10)y^(12)
Step-by-step explanation:
(60x^(20)y^(24))/(30x^(10)y^(12)
when there is division we simplify that by subtracting the power
by using rules of indices
[tex] \frac{x^a}{x^b}=x^{a-b}[/tex]
and number can be divided easily
[tex] \frac{60}{30}*\frac{x^{20}}{x^{10}}*\frac{y^{24}}{y^{12}}[/tex]
[tex] 2*x^{20-10}y^{24-12}[/tex]
[tex] 2x^{10}y^{12}[/tex]
so answer is b. 2x^(10)y^(12)
(08.01 mc) sue wants to know how many families in her small neighborhood of 50 homes would volunteer to help at a neighborhood animal shelter. she put all the addresses in a bag and drew a random sample of 25 addresses. she then asked those families if they would volunteer to help at the shelter. she found that 18% of the families would volunteer to help at the shelter. she claims that 18% of the neighborhood families would be expected to help at the animal shelter. is this a valid inference?
Answer:
Yes, this is a valid inference because she took a random sample of the neighborhood.
Step-by-step explanation:
As we can see, Sue's survey was perfectly random and without any prejudice.
18% of the families, according to her research, would volunteer at the shelter. According to her, 18% of the local households should be required to volunteer at the animal shelter.
Therefore, given that she chose a representative sample of the area, her conclusion is valid.
