Therefore exact coordinates of Centroid = (0,3/2)
Define Centroid.The centroid of a flat figure or solid figure, also known as the geometric center or center of figure, in mathematics and physics, is the arithmetic mean position of all the points on the figure's surface. Any n-dimensional Euclidean object is included by the same definition.
What is Triangle?A polygon having three edges and three vertices is called a triangle. It is one of the fundamental geometric forms. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
This region is a parabola opening downward, with vertex at (0, 49) and a range of y values from 0 to 49. The region is symmetric about the y-axis, This means that the x-coordinate of the centroid is at 0.
To find the y-coordinate:
Integral from -√(49) to √(49) of (49-x²) x dx = [x²(49-x²)/3] from -√(49) to √(49) = (492√(49))/3 = (98√(49))/3
The area is integral from -√(49) to √(49) of (49-x²) dx = [x(49-x²)/2] from -√(49) to √(49) = (49*(2√(49)) - (2/3)(49^(3/2)))/2 = (49*(2*√(49)) - (98√(49))/3)/2
Therefore Centroid = (0, (98√(49))/(49*(2*√(49)) - (98√(49))/3)) = (0,3/2)
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Mr Paul has 4 bars of chocolate. He distributes 1/3
of each bar to 4 children.
a) Write the fraction of chocolate distributed.
b) Write the fraction of cholates left with Mr. Paul
a) The fraction of chocolate distributed is given as follows: 4/3.
b) The fraction of chocolates left with Paul is given as follows: 8/3.
How to obtain the fractions?The fractions are obtained applying the proportions used in the context of this problem.
He distributes 1/3 of each bar to 4 children, hence the total number of bars distributed is given as follows:
4 x 1/3 = 4/3.
(multiplication of fractions, multiply the numerators and the denominators, keeping the quotient).
The total number of bars that Paul had initially is given as follows:
4 bars.
Then the fraction of chocolate remaining with Paul is given by the subtraction of the total amount of bars by the amount given to the children, as follows:
4 - 4/3 = 12/3 - 4/3 = 8/3 bars.
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Suppose that R, S and T are digits and that N is the four-digit positive integer
8RST. That is, N has thousands digit 8, hundreds digit R, tens digits S, and ones
(units) digit T, which means that N = 8000 + 100R + 10S + T. Suppose that the
following conditions are all true:
• The two-digit integer 8R is divisible by 3.
• The three-digit integer 8RS is divisible by 4.
The four-digit integer 8RST is divisible by 5.
The digits of N are not necessarily all different.
The number of possible values for the integer N is
(A) 8
(B) 16
(C) 12
(D) 10
87
(E) 14
Answer:
8RST. That is, N has thousands digit 8, hundreds digit R, tens digits S, and ones
(units) digit T, which means that N = 8000 + 100R + 10S + T. Suppose that the
following conditions are all true:
• The two-digit integer 8R is divisible by 3.
• The three-digit integer 8RS is divisible by 4.
The four-digit integer 8RST is divisible by 5.
The digits of N are not necessarily all different.
The number of possible values for the integer N is
(A) 8
(B) 16
(C) 12
(D) 10
87
(E) 14
Since 8R is divisible by 3, R must be a multiple of 3. The possible values for R are 3, 6, and 9.
Since 8RS is divisible by 4, S must be a multiple of 2. The possible values for S are 0, 2, 4, 6, and 8.
Since 8RST is divisible by 5, T must be 0 or 5.
The possible values for N are therefore:
8000 + 300 + 00 + 0 = 8300
8000 + 600 + 00 + 0 = 8600
8000 + 900 + 00 + 0 = 8900
8000 + 300 + 20 + 0 = 8320
8000 + 600 + 20 + 0 = 8620
8000 + 900 + 20 + 0 = 8920
8000 + 300 + 40 + 0 = 8340
8000 + 600 + 40 + 0 = 8640
8000 + 900 + 40 + 0 = 8940
8000 + 300 + 60 + 0 = 8360
8000 + 600 + 60 + 0 = 8660
8000 + 900 + 60 + 0 = 8960
8000 + 300 + 80 + 0 = 8380
8000 + 600 + 80 + 0 = 8680
8000 + 900 + 80 + 0 = 8980
8000 + 300 + 00 + 5 = 8305
8000 + 600 + 00 + 5 = 8605
8000 + 900 + 00 + 5 = 8905
8000 + 300 + 20 + 5 = 8325
8000 + 600 + 20 + 5 = 8625
8000 + 900 + 20 + 5 = 8925
8000 + 300 + 40 + 5 = 8345
8000 + 600 + 40 + 5 = 8645
8000 + 900 + 40 + 5 = 8945
8000 + 300 + 60 + 5 = 8365
8000 + 600 + 60 + 5 = 8665
8000 + 900 + 60 + 5 = 8965
8000 + 300 + 80 + 5 = 8385
8000 + 600 + 80 + 5 = 8685
8000 + 900 + 80 + 5 = 8985
There are a total of 30 possible values for N. The answer is therefore (E) 14.
Step-by-step explanation:
y 10- 9 8 6 5 4 2 1 2 3 4 5 6 7 8 9 10 What is the equation of the blue line? X
Therefore , the solution of this is the required system of equation is,
y=-x+6 and y=x+10.
Explain the equation.A mathematical equation is a formula that links two statements by indicating their equivalence with the equal sign (=). A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the components 3x + 5 and 14 in the equation 3x + 5 = 14 are separated by an equal sign. The relationship between two sentences on either side of a letter is expressed mathematically. There is frequently only one variable, which doubles as the symbol. say that 2x - 4 Equals 2.
Here,
(0,6) and the blue line pass through them (-2,8). You may figure out the equation for the blue line as,
=> y-6/x-0 = 8-6 /-2-0
=>y-6/x = 2/-2
=> y-6=-1(x)
y=-x+6
(-2, 8) and the red line pass through them (-3,7). The red line's equation can be calculated as,
y-8/x- (-2) = 8-7 /-2-(-3)
y-8 /x+2 = 1
y-8=x+2
y = x + 10
Thus, the required system of equations is,
y=-x+6 and y=x+10.
Therefore , the solution of this is the required system of equations is,
y=-x+6 and y=x+10.
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A person draws a card from a hat. Each card is one color, with the following probabilities of being drawn: 1/10 for pink, 1/15 for white, 1/20 for blue, and 1/5 for black. What is the probability of pulling a black or pink card, written as a reduced fraction?
Answer:
wouldn't it be 1/25 black??
What is the value of the expression below?
−2
1
3
− 3
5
6
+ 1
1
3
?
Answer:
Step-by-step explanation:
The expression you've provided is a combination of several fractions, but it's not clear how they are supposed to be combined. Without more information, it's impossible to know what the value of the expression is.
It would be helpful if you could provide more context or clarify how you want the fractions to be combined.
I can only tell you how the fraction works in mathematics and how you can evaluate the value of it if you have the complete information.
Reduce 17/5 to It lowest term
Answer:
17/5
It is already simplified to lowest terms.
This number, as a mixed fraction, would look like this:
3 2/5.
Simplify the expression
-4|2.5-6|
Answer: -14
Step-by-step explanation:
S Janine is considering buying a water filter and a reusable water bottle rather than buying bottled water. Will doing so save her money? First, determine what information you need to answer this question, then click here to display that info (along with other info). • How much water does Janine drink in a day? She normally drinks 6 bottles a day, each 16.9 ounces. How much does a bottle of water cost? She buys 24-packs of 16.9 ounce bottles for $3.99. • How much does a reusable water bottle cost? About $10. • How long does a reusable water bottle last? Basically forever (or until you lose it). . • How much does a water filter cost? How much water will they filter? o A faucet-mounted filter costs about $28 and includes one filter cartridge. Refill filters cost about $33 for a 3-pack. The box says each filter will filter up to 100 gallons (378 liters) o A water filter pitcher costs about $22 and includes one filter cartridge. Refill filters cost about $20 for a 4-pack. The box says each filter lasts for 40 gallons or 4 months • An under-sink filter costs $130 and includes one filter cartridge. Refill filters cost about $60 each. The filter lasts for 500 gallons. Which option is cheapest over one year (365 days)? faucet-mount filter The cheapest option saves her $ Give your answer to the nearest cent. Pro-rate the costs of additional filters (so if you only use part of a filter, only count the corresponding fraction of the filter cost) and pro-rate the cost of the bottled water (so if you only use part of a case, only count the cost for the portion of the case used). over a year.
Janine currently spends about $150.11 on bottled water every year.The total sum of the cost for the pitcher filter is $42. The sink filter costs $130
The first step in finding how much money Janine will save is to calculate how much water Janine drinks and how much bottled water costs her in one year.
To find how much money Janine currently spends on water, calculate the number of cases of water she buys each year (365 days / (24 bottles in a case/ 3 bottle per day) and multiply this number by the price per case ($3.29) to find that Janine currently spends about $150.11 on bottled water every year.To calculate the amount of water Janine drinks each year we multiply the amount she drinks in one day (3 bottles x 16.9oz per bottle) by 365 and then since there are 128 ounces in a gallon, we divide this number by 128 to find that she drinks 144.6 gallons of water each yearThe next step in this problem is to calculate the cost of each water filter in the first year. To find this, add the cost of the reusable water bottle, the cost of the filter, and the cost of any additional filters needed.
The faucet filter costs $28 dollars and includes a filter, plus each additional filter costs $11. Since the filter will last for 100 gallons, we can subtract that amount from the total water she drinks in a year to find the cost of filtering the remainder of the water in the year (144.6 gallons- 100gallons /$11). The total sum of the cost of the faucet filter and reusable water bottle in the first year is $42.91.The pitcher filter costs $22 and each additional filter costs $5. Since the included filter lasts 4 months, Janine will need two additional replacement filters for the other 8 months of the first year. The total sum of the cost for the pitcher filter is $42.The sink filter costs $130 and since the included filter will work for 500 gallons of water, Janine will not need to purchase additional filters in the first year. The total cost of the sink filter is $140.From these calculations, you can see that the pitcher filter is the cheapest option and will save Janine $108.11 in her first year of using this filter.Lastly the question asks you to pro-rate the cost of each filter
Since the faucet filters cost $11 each and filter 100 gallons of water, this filter costs 11 cents per gallon and $15.91 per year. She will have to begin replacing these filters approximately 8 months after the initial purchase of the filter.Filtering 40 gallons and costing $5 each the pitcher filter costs 12.5 cents per gallon and $18.08 per year. She will have to replace these filters every 4 months.The sink filter filters 500 gallons of water and costs $60, so it costs 12 cents per gallon and $17.35 per year. She will not have to replace this filter for about 3 and half years after the initial purchase.Learn more about cost at:
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what is the area of 12 1/2 feet long and 11 3/4 feet wide
now, we're assuming this is some rectangular area, and thus is simply the product of both quantities, let's change all mixed fractions to improper fractions firstly.
[tex]\stackrel{mixed}{12\frac{1}{2}}\implies \cfrac{12\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{25}{2}} ~\hfill \stackrel{mixed}{11\frac{3}{4}} \implies \cfrac{11\cdot 4+3}{4} \implies \stackrel{improper}{\cfrac{47}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{25}{2}\cdot \cfrac{47}{4}\implies \cfrac{1175}{8}\implies 146\frac{7}{8}~ft^2[/tex]
Photo attached. Someone please help
Thanks
By using the graph, a solution the given system of equations include the following:
x = 0, y = 3
x = 3, y = 6
What are quadratic functions?In Mathematics, the graph of every quadratic functions (equations) is either an upward or downward parabola, which is typically a u-shaped curve. This ultimately implies that, the graph of a quadratic function (equation) would always form a parabolic curve.
In this scenario, we would use an online graphing calculator to plot the graph of the given system of equations and then determine the point of intersection.
y = x + 3
y = x² - 2x + 3
By critically observing the graph of the given system of equations, the solutions are as follows;
x = 0, y = 3.
x = 3, y = 6.
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What is 10/83 simplified
Answer:
5/19
Step-by-step explanation:
Need it ASAP, please!!!
Answer:
27y - 45 + 7z
(5 x 7) + (n x 4) = 5 x (7+ 4) write each missing number
The missing number in the expression (5 x 7) + (n x 4) = 5 x (7+ 4) is 5.
What are GCF and distributive property?The GCF of two or more than two numbers is the highest number that divides the given two numbers completely.
We also know that distributive property states a(b + c) = ab + ac.
Given, An expression (5 × 7) + (n × 4) = 5 × (7 + 4).
Now, If we expand the RHS we have,
5×(7 + 4).
= (5 × 7) + (5 × 4).
Now, Writing the obtained RHS with LHS we have,
(5 × 7) + (n × 4) = (5 × 7) + (5 × 4).
So, The missing number is 5.
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Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
Suppose a researcher compiled a data set of the following variables fora sample of 100 retired men
Answer:
The researcher compiled a data set consisting of variables such as age, income, and marital status for a sample of 100 retired men
Step-by-step explanation:
A discrete variable is a type of variable that can only take on specific, distinct values that can be counted. Examples of discrete variables include the number of countries visited, shoe size, and number of pets living in a household.
On the other hand, a continuous variable is a type of variable that can take on any value within a certain range through measurement. Examples of continuous variables include pounds of chocolate consumed in the past and height in inches.
How many real solutions does this system of equations have? x²+y²=36
3x-y+1=0
A.0
B. 2
C. 3
D. 1
This system of equations have 2 real solution.
Do fractions actually solve problems?As a result, all of these numbers—rational and otherwise—as well as fractions are regarded as real numbers. Due to the decimal's ability to float within the numbers, real numbers with decimal points are known as floating point numbers. No whole number or integer can be a floating point number.
y = 3x + 1 is a solution to 3x - y + 1 = 0.
This line's y-intercept is represented by (0, 1). Plot this point inside the circle with radius 6 that was previously mentioned, and then draw a straight line through it with a slope of 3.
Two points where this line crosses the circle denote actual solutions.
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Keshia goes to the post office to mail a package and a few letters. Stamps cost 49 cents each. It will cost $7.65 to mail the package. Keshila has 10.00. a. Write an inequality to represent this situation, where x is the number of stamps.
The inequality to represent the number of stamps Keshia can buy with $10.00, considering that each stamp costs 49 cents, can be written as:
0.49x + 7.65 <= 10.00
Define Inequality.An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.
Define expression.Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
The inequality to represent the number of stamps Keshia can buy with $10.00, considering that each stamp costs 49 cents, can be written as:
0.49x + 7.65 <= 10.00
This inequality can be read as "the cost of x number of stamps plus the cost of the package is less than or equal to Keshia's budget of $10.00."
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What is the value of sin(7pi/4)? See attached.
Answer:
-sqrt(2)/2 , the last option of your document.
Step-by-step explanation:
sin(7pi/4) = -sin(7pi/4 - pi)
= -sin(7pi/4 - 4pi/4)
= - sin(3pi/4)
sin(3pi/4) is a special angle , which is sqrt(2)/2
Hence, sin(7pi/4) = -sin(3pi/4)
= -sqrt(2)/2
Answer:
-sqrt(2)/2
Step-by-step explanation:
did the test
Calculate the sample mean and sample variance for the following distribution of heights in centimeters for an 8 year old boy
Answer: To calculate the sample mean of a distribution, you add up all the values and divide by the number of values in the sample. The sample mean is also known as the average.
The formula for the sample mean is:
X-bar = (X1 + X2 + ... + Xn) / n
To calculate the sample variance of a distribution, you first need to calculate the sample mean. Then, for each value, you subtract the sample mean and square the result. You add up all these squared differences, and divide the sum by the number of values in the sample.
The formula for the sample variance is:
s^2 = ( (X1 - X-bar)^2 + (X2 - X-bar)^2 + ... + (Xn - X-bar)^2 ) / (n - 1)
It would be helpful to have the sample data, however I cannot complete this task without it.
Please provide me with the data.
Step-by-step explanation:
there are no good answers on brainily can someone pls answer this
Answer:
D
Step-by-step explanation:
first simplify everything
2/9v + 1/3v - 5/9
A and B is wrong because it is - 5/9 not + 5/9
C is wrong because it is -1/3v not 1/3, it is supposed to be - 5/9
You can solve this problem without much solving
hope this helps :)
-20 POINTS- only answer If you know dont guess again.
Using the Pythagoras theorem, the value of y is [tex]6\sqrt{7}[/tex], and the value that goes in the green box is 6.
What is Pythagoras Theorem?
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.
Mark the intersections as A, B, C, and D.
It is given that BC=12 and CD=9.
The relationship between the height on the hypotenuse of a right triangle and the two line segments it generates on the hypotenuse is described by the right triangle altitude theorem, also known as the geometric mean theorem. It claims that the altitude is equal to the geometric mean of the two segments.
Apply the geometric mean theorem -
(AC)^2 = BC x CD
(AC)^2 = 12 x 9
(AC)^2 = 108
AC = [tex]\sqrt{108}[/tex]
AC = [tex]6\sqrt{3}[/tex]
Triangle ABC is a right-angled triangle, so apply Pythagoras theorem -
(AB)^2=(BC)^2+(AC)^2
(AB)^2=(12)^2+([tex]6\sqrt{3}[/tex])^2
(AB)^2=144+108
(AB)^2=252
AB=[tex]\sqrt{252}[/tex]
AB=[tex]6\sqrt{7}[/tex]
Therefore, the value of y is obtained as [tex]6\sqrt{7}[/tex].
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6+√-18 simplified for edmentum
Answer:
= 18√2
decimal =25.45584412
8. If you got 27 questions correct on
a test that has 32 questions, what
percent of the questions did you
correct on the test?
Malcom wrote the equivalent ratios shown below. Find the scale factor he used to write the equivalent ratios
9/40 and 54/240
In this question, we're looking for the number Malcom used to scale the two numbers. We can see there's a pattern, 9 is 1/6 of 54 and 40 is 1/6 of 240!
(54 divided by 9 is 6 and 240 divided by 40 is 6!)
therefore, the scale factor must be 6
An algebraic expression 2x² + 2xy is trinomial algebraic expression true or false
Answer:
False
Step-by-step explanation:
right!!
Write an equation and solve for x using the diagram
below. Also give the angle measure. YOU MUST
WRITE THE EQUATION IN ORDER TO GET
Answer:
x = 45
Step-by-step explanation:
2x + 6 and 96 are vertically opposite angles and are congruent , then equation is
2x + 6 = 96 ( subtract 6 from both sides )
2x = 90 ( divide both sides by 2 )
x = 45
Which problem situation matches the
equation $95.25 = 15p?
A Cassie is paid $95.25 for 15 hours
of work. Find p, the amount she
was paid per hour.
B Kris is paid $6.35 per hour for
mowing the lawn. Find p, the
amount he is paid for 15 hours of
mowing.
CA iPad was on sale for $95.25. Find
p, the amount Noah needs to buy
the iPad if he already has $15.
D Fifteen friends spend $95.25 each
for tickets to a Cowboy's game.
Find p, the amount they paid total.
Answer:
Step-by-step explanation:
Which problem situation matches the
equation $95.25 = 15p?
So We Can Just Cross B Cause $6.35 Wasnt Even In The equation
Lets look at A.
So Im pretty sure its A, But Lets look at the rest.
.
D Wouldnt Work Cause It Says The Spend $95.25 EACH
C dont work so its A.
Please help me with this question
Answer:
cos(x -π/3) = (1/2)cos(x) +(√3/2)sin(x)
Step-by-step explanation:
You want cos(x -π/3) written in terms of sine and cosine.
Angle differenceThe formula for the cosine of the difference between two angles is ...
cos(a -b) = cos(a)cos(b) +sin(a)sin(b)
ApplicationWe have a=x, b=π/3, so the desired function is ...
cos(x -π/3) = cos(x)cos(π/3) +sin(x)sin(π/3)
We know that ...
cos(π/3) = 1/2sin(π/3) = √3/2so the rewrite is ...
cos(x -π/3) = (1/2)cos(x) +(√3/2)sin(x)
Here is a graph of the function h.
Use the graph to find the following
If there is more than one answer, separate them with commas
(a)
All local minimum values of
h
(b) All values at which h has a local minimum:
The graph also shows two other local maxima, at x=0.5 and x=1.5.
The local minimum(a) -4, -2, 0, 2 (b) The local minimum values of h occur at x = -4, -2, 0, and 2.These values can be seen on the graph as points at which the graph of h changes from decreasing to increasing.At each of these points, the value of h is at a minimum compared to the values of h on either side of the point.All values at which h has a local maximum: 0.5, 1.5All local maximum values of h: 2.5, 4.5.The graph of the function h is a parabola that opens upwards, with a turning point at x=1.This indicates that the function has a local maximum at this point.The local maximum values of h at these points can be determined by looking at the y-values at these points, which are 2.5 and 4.5 respectively.To learn more about All local minimum values refer to:
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g(x) = (2 (x+3))^3 + 4
.....................................