Answers
Check the picture below.
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ S(\stackrel{x_1}{-2}~,~\stackrel{y_1}{7})\qquad R(\stackrel{x_2}{-1}~,~\stackrel{y_2}{3}) ~\hfill SR=\sqrt{(~~ -1- (-2)~~)^2 + (~~ 3- 7~~)^2} \\\\\\ ~\hfill SR=\sqrt{( 1 )^2 + ( -4)^2} \implies \boxed{SR=\sqrt{ 17}}[/tex]
[tex]R(\stackrel{x_1}{-1}~,~\stackrel{y_1}{3})\qquad U(\stackrel{x_2}{-1}~,~\stackrel{y_2}{5}) ~\hfill RU=\sqrt{(~~ -1- (-1)~~)^2 + (~~ 5- 3 ~~)^2} \\\\\\ ~\hfill RU=\sqrt{( 0)^2 + ( 2)^2} \implies RU=\sqrt{ 4}\implies \boxed{RU=2} \\\\\\ U(\stackrel{x_1}{-1}~,~\stackrel{y_1}{5})\qquad T(\stackrel{x_2}{2}~,~\stackrel{y_2}{5}) ~\hfill UT=\sqrt{(~~ 2- (-1)~~)^2 + (~~ 5- 5~~)^2} \\\\\\ ~\hfill UT=\sqrt{( 3)^2 + ( 0)^2} \implies UT=\sqrt{ 9}\implies \boxed{UT=3}[/tex]
[tex]T(\stackrel{x_1}{2}~,~\stackrel{y_1}{5})\qquad S(\stackrel{x_2}{-2}~,~\stackrel{y_2}{7}) ~\hfill TS=\sqrt{(~~ -2- 2~~)^2 + (~~ 7- 5~~)^2} \\\\\\ ~\hfill TS=\sqrt{( -4)^2 + ( 2)^2} \implies \boxed{TS=\sqrt{ 20}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE Perimeter} }{\sqrt{17}+2+3+\sqrt{20} }~~ \approx ~~ \text{\LARGE 13.6}[/tex]
Related Questions
Use the density formula (d =) to find the density of a block of metal with a mass of 21.1
kilograms and a volume of 9.37 meters³.
Round your answer to the nearest tenth of a kg/m³
Answers
Answer:
Below
Step-by-step explanation:
Density = mass
volume
Density = 21.1 kg / 9.37 m^3 = ~ 2.3 kg/m^3
A yoga instructor collected student data. He found that students who had less sleep did not tend to burn more or fewer calories during class. What can he conclude?
1)There is no correlation between amount of sleep and number of calories burned.
2)There may or may not be causation. Further studies would have to be done to determine this.
3)There is a correlation between amount of sleep and number of calories burned. There is probably also causation. This is because there is likely an increase in the number of calories burned with an increase in the amount of sleep
Answers
The correct answer is option 1) "There is no correlation between the amount of sleep and the number of calories burned."
Based on the information provided, the yoga instructor can conclude that there is no correlation between the amount of sleep and the number of calories burned during class. Therefore, the correct answer is
option 1) "There is no correlation between the amount of sleep and the number of calories burned."
Option 2) suggests that further studies would be needed to determine causation, but since there is no correlation found in this study, there is no basis for further investigation into causation.
Option 3) suggests that there is a correlation between the amount of sleep and the number of calories burned and that there is likely causation. However, this conclusion contradicts the information provided, which indicates that there is no correlation between these variables.
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3x+y=4 pls help me with this i need to get this right
Answers
Answer: y - intercept is c = 4.
Step-by-step explanation:
The line equation is 3x + y = 4.
The slope-intercept form of the line equation is y = mx + c.
Where m is the slope of line c is the y-intercept.
The equation is 3x + y = 4.
subtract 3x from each side.
y - intercept is c = 4.
The center of an ice rink is located at (0, 0) on a coordinate system measured in meters. Susan is skating along a path that can be modeled by the equation y = 6x – x2 – 5. Luke starts at (10, –21) and skates along a path that can be modeled by a quadratic function with a vertex at (8, –9). If the rink is a circle with a radius of 35 meters, which statement best interprets the solution(s) of a system of equations modeling the paths of the skaters?
The skaters’ paths intersect once, but that point is outside the rink.
The skaters’ paths intersect once, and that point is inside the rink.
The skaters’ paths intersect twice, but only one of those points is inside the rink.
The skaters’ paths intersect twice, and both points are inside the rink.
Answers
Answer:
Option C: The skaters path intersect twice, but only one of those points is inside the rink.
Step-by-step explanation:
Coordinates of center of ice rink: (0,0) Radius of ice rink circle = 35 m
We know that the equation of a circle with center coordinates (a,b) and radius of (r) is given as; (x - a)² + (y - b)² = r²
Thus, the total area on which the skaters are skating will be given by the equation;
x² + y² = 35²
Now, we are told the path along which Susan is skating is modeled by the equation: y = 6x - x² - 5
While Luke starts at (10, –21) and skates along a path that can be modeled by a quadratic function with a vertex at (8, –9)
From equation of a parabola, the path along which like is skating can be modeled by;
(x - 8)² = 4a(y + 9)
To find a, we will substitute the coordinate started at to get;
(10 - 8)² = 4a(-21 + 9)
4 = 4a × -12
Divide both sides by 4 to get;
a = -1/12
Thus;
(x - 8)² = 4(-1/12)(y + 9)
(x - 8)² = (-1/3)(y + 9)
This gives: 3(x - 8)² = -(y + 9)
I've drawn the graph on demos and attached it.
From the graph we can see that the skaters points intersect twice but one is inside the rink circle while the other is outside the rink circle. The point at which they intersect outside the rink was slightly cropped out because of size. But it is clearly seen that they are both approaching point of intersection.
Thus, correct answer is Option C.
A cylinder has a volume of 72 cubic inches. What is the volue of a cone with the same height and radius as the cylinder
Answers
A cone with the same height and radius as a cylinder has a volume of 24 cubic inches.
If a cylinder has a volume of 72 cubic inches, we can use the formula for the volume of a cylinder to find its height and radius. The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height.
So, we have:
72 = πr^2h
We can solve this equation for h:
h = 72/(πr^2)
Now, we can use the formula for the volume of a cone to find the volume of a cone with the same height and radius as the cylinder. The formula for the volume of a cone is V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.
So, we have:
V = (1/3)πr^2(72/(πr^2))
Simplifying this equation, we get:
V = 24
Therefore, the volume of a cone with the same height and radius as the cylinder is 24 cubic inches.
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Pls help
Help Algebra1
Answers
The equivalent expression is; 4a^3b(4b - 2a^2b^4 + 3a)
How do we know equivalent expressions?Two expressions are equivalent when you can manipulate one expression algebraically to transform it into the other expression. For example, you can use the distributive property, combine like terms, factor out common factors, or simplify fractions to show that two expressions are equivalent.
We have the expression;
16a^3b^2 - 8a^5b^5 + 12a^4b
4a^3b(4b - 2a^2b^4 + 3a)
It's important to note that sometimes two expressions may look different, but they can be equivalent under certain conditions or constraints.
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Help please with this maths I need to check it it’s right
Answers
Answer:
9999
Step-by-step explanation:
99x10=990
99x1=99
9999
Answer:9999
I hope it is helpful:)
Step-by-step explanation:
we can see 99 is 100-1 and 101 is 100+1
we can rewrite this as,
99*101=(100-1)(100+1)
let's use short mltiplication formula,
[tex]a^{2}-b^{2}=(a-b)(a+b)\\(100-1)(100+1)=100^{2}-1^{2}=10000-1=9999[/tex]
Which values in the data set are outliers? Show all work
72, 81, 82, 83, 83, 85, 100, 54, 75, 81,83
List the follow (and show work if needed): Q1, Median, Q3, IQR, Lower Fence, Upper Fence and outliers
Answers
Answer: The outliers are 54 and 100.
Step-by-step explanation:
And outlier is a number that doesnt belong. Learn more about outliers here https://www.itl.nist.gov/div898/handbook/prc/section1/prc16.htm#:~:text=An%20outlier%20is%20an%20observation,what%20will%20be%20considered%20abnormal.
(If you were also asking about the q1, medians, and q3 please make that a seperate question.
So this question really confuses me LOL SO PLEASE HELP LOL ;-; I WILL GIVE BRAINLIEST
Answers
The proportional equation us y = 2.5x and the constant is 2.5
6 bottles would have a volume of 15 liters.
How to solve an equation?An equation is an expression containing numbers and variables linked together by mathematical operations such as addition, subtraction, division, multiplication and exponents.
Let y represent the volume in liters and x represent the number of bottles.
A proportional relationship is in the form:
y = kx; where k is the constant of proportionality.
From the table, using the value (2, 5):
y = kx
substituting:
5 = 2k
k = 2.5
The proportional equation us y = 2.5x and the constant is 2.5
For 6 bottles:
y = 2.5(6) = 15 liters
6 bottles would have a volume of 15 liters.
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In the figure, three lines intersect at point P. If x = 65 and y = 75, what is the value of z?
Answers
The value of angle Z is 40 degrees. (Option 3). In this problem, we are given that three lines intersect at point P and we need to find the value of angle Z.
We know that angle X is 65 degrees and angle Y is 75 degrees. We also know that all six angles formed by the intersection of the three lines add up to 360 degrees.
Using these facts, we can set up an equation as
2X + 2Y + 2Z = 360.
We can simplify this equation to
X + Y + Z = 180.
We can then substitute the given values of X and Y to get
65 + 75 + Z = 180.
Simplifying this equation, we get Z = 40, which means Z is equal to 40 degrees.
Therefore, the answer is option C.
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Complete Question:
In the figure, 3 lines intersect at point P. If x = 65 and y = 75, what is the value of z?
140804020The function C (t) = StartFraction 4 t Over t squared + 2 EndFraction models the cost per student of a field trip when x students go on the trip. How is the parent function On a coordinate plane, 3 curves are shown. One curve opens up and to the right in quadrant 1 and goes through (2, 4) and (4, 1). Another curve approaches x = negative 2 in quadrant 2, changes direction at (0, 0), and then decreases in quadrant 4 and approaches y = 2. The third curve opens down and to the left in quadrant 3 and goes through (negative 4, negative 1) and (negative 2, negative 4). transformed to create the function On a coordinate plane, 2 curves are shown. One curve opens up and to the left in quadrant 2 and goes through (negative 4, 8) and (negative 6, 6). Another curve opens down and to the right and goes through (negative 1, negative 3), (0, 0), and (6, 3).?
It is vertically stretched by a factor of 200.
It is vertically stretched by a factor of 200 and shifted 10 units leftt.
It is vertically stretched by a factor of 200 and shifted 10 units up.
It is vertically stretched by a factor of 200 and shifted 10 units right.
Answers
It is vertically stretched by a factor of 200 and shifted 10 units up.
What is a function?A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.
How do you write a function?You write functions with the function name followed by the dependent variable.
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Answer:
Step-by-step explanation:
i cant see the answer
In 2009 A.D., the number of tourist who visited Nepal was 2,50,000. In 2010, was decreased by 5% and in 2011 it was increased by 40%. How many touris visited Nepal in 2011?
Answers
There were 332500 tourists who traveled to Nepal in 2011.
What is unitary method?"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."
We always count the unit or amount value first and then calculate the more or less amount value.
For this reason, this procedure is called a unified procedure.
Many set values are found by multiplying the set value by the number of sets.
A set value is obtained by dividing many set values by the number of sets.
Number of tourists in 2010 = 95% of number of tourists in 2009
= 0.95 x 250000
= 237500
Number of tourists in 2011 = 140% of number of tourists in 2010
= 1.4 x 237500
= 332500
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. The jug shown below contains some water. How many litres of water does this jug contain? 300 ml 250 ml - 200 ml -150 ml 100 ml -50 ml
Answers
Answer:
250 ml
Step-by-step explanation:
300ml + 250ml =550ml
550ml - 200ml=350ml
350ml - 150ml + 100ml=300ml
300ml - 50ml=250ml
PLEASE HELP!! ITS DUE IN 40 MINUTES!!
Measure the lengths of the following segments in BOTH centimeters and
millimeters.
Answers
The measure of the lengths of the following line segments using online ruler are given as follows:
KL = 5.11cm or = 51.1mm
FG = 8.67cm or = 86.7mm
Length is a physical quantity that refers to the measurement of the extent of an object or distance between two points. It is usually measured in units such as meters, centimeters, or feet.
A line segment is a part of a line that is bounded by two distinct endpoints. It is the shortest distance between two points on a straight line.
To convert cm to mm, we multiply by 10 because there are 10 millimeters in 1 centimeter.
Therefore, to convert 5.11 cm to mm, we can multiply 5.11 by 10:
5.11 cm * 10 = 51.1 mm
So, 5.11 cm is equal to 51.1 mm.
Also to convert 8.67 cm to mm, we can multiply 8.67 by 10:
8.67 cm * 10 = 86.7 mm
So, 8.67 cm is equal to 86.7 mm.
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Full Question:
Although part of your question is missing, you might be referring to this full question: See attached image.
I need to get this done in 5 minutes and im so confused!?
Answers
Answer: line A
Step-by-step explanation:
2x is the slope and -1 is the y-intercept
2x for the slope, also 2/1x (meaning rising up 2 places for every one place on the x axis).
Line A is the only line who has 2x for the slope.
ANSWER: LINE (A)
Answer:
Line a
Step-by-step explanation:
The equation is y= 2x - 1 so....
Slope = 2
Y-intercept = -1
Slope can be put as Rise/ Run ( up/ side)
This means the slope can be written as 2/1
Line a has a slope of 2/1 from the point -1 so the answer is line a
If there is a 5% chance that none of the items on a scratch-off lottery ticket
will be a winner, what is the probability that at least one of the scratch-off items will win?
Answers
If there is a 5% chance that none of the items on a scratch-off lottery ticket will be a winner, the probability that at least one of the scratch-off items will win is 95%.
If there is a 5% chance that none of the items on a scratch-off lottery ticket will be a winner, then the probability of winning on any one item is 1 - 0.05 = 0.95 (i.e., a 95% chance of winning on any one item).
The complement rule, which states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring, can be used to determine the likelihood that at least one of the scratch-off items will win. In this case, the event we are interested in is winning on at least one item. The complement of this event is not winning on any item.
So, the probability of winning on at least one item is:
1 - 0.05 = 0.95
Therefore, there is a 95% chance that at least one of the items on a scratch-off lottery ticket will win.
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The quadrilateral ABCD has vertices with coordinates A(1,4), B(2,3), C(0,-3) and D(-3,1). Graph ABCD and find its area.
Answers
The graph of quadrilateral ABCD is attached below and it's area is 25.5 squared units
What is the graph and area of ABCDTo graph the vertices of the quadrilateral ABCD, we need to use a graphing calculator to find the sides and then the area can be calculated as;
We can use the Shoelace Formula to find the area of the quadrilateral. The Shoelace Formula is based on the idea of using the coordinates of the vertices of the polygon to calculate its area.
The formula is:
Area = 1/2 * |(x1y2 + x2y3 + ... + xny1) - (y1x2 + y2x3 + ... + ynx1)|
where (x1,y1), (x2,y2), ..., (xn,yn) are the coordinates of the vertices of the polygon in order, either clockwise or counterclockwise.
Using this formula, we get:
Area = 1/2 * |(13 + 2(-3) + 01 + (-3)4) - (42 + 30 + (-3)(-3) + 11)|
Area = 1/2 * |(-3 - 6 - 12 - 12) - (8 + 0 + 9 + 1)|
Area = 1/2 * |-33 - 18|
Area = 1/2 * 51
Area = 25.5
Therefore, the area of quadrilateral ABCD is 25.5 square units.
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Help me ill give you brainliest and extra points Find the average rate of change of g(x)=-x²+4x+2 from x=3 to x=7
Answers
The average rate of change of g(x) from x = 3 to x = 7 is -5.
To find the average rate of change of the function g(x) = -x² + 4x + 2 over the interval [3, 7], we need to calculate the change in the function values over this interval and divide by the length of the interval.
The change in the function values between x = 3 and x = 7 is:
g(7) - g(3) = (-7² + 47 + 2) - (-3² + 43 + 2) = (-49 + 28 + 2) - (9 + 12 + 2) = -20
Therefore, the average rate of change of g(x) over the interval [3, 7] is:
average rate of change = change in function values / length of interval
= -20 / (7 - 3)
= -5
This means that on average, the function g(x) decreases by 5 units for every 1 unit increase in x over the interval [3, 7].
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To practice for a competition, Ava swam 0.69 kilometer in the pool each day for 4 weeks. How many meters did Ava swim in those 4 weeks? 1 km = 1,000 m
Answers
Answer:
14490 meters
Step-by-step explanation:
0.69 x 3weeks which is (21) days , so 0.69•21 =14.490km 14.490km=14490 meters
2. The distance by road from Newport to London is 140 miles. Tom travels by coach from Newport to London. The coach leaves Newport at 1. 30 pm (a) He assumes the coach will travel at an average speed of 50 mph Use his assumption to work out the arrival time in London.
Answers
Tom will arrive in London at 4.10 pm, after travelling 140 miles at an average speed of 50 mph.
The formula to calculate the time taken is: Time = Distance/Speed
Using Tom's assumption that the coach is travelling at an average speed of 50 mph, the time taken for the journey from Newport to London can be calculated as follows:
Time = 140 miles/50 mph = 2.8 hours
Therefore, Tom will arrive in London at 1.30 pm + 2.8 hours = 4.10 pm.
To put this in context, it means that the coach will travel at an average speed of 70 km/h, covering a distance of 224 km in 2.8 hours. This is equivalent to covering 80 km in an hour.
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Calculate 441 ÷ 3 by using long division
Answers
Answer:
the answer is 147
Step-by-step explanation:
I have attached a picture with the work. Hope this helps :)
The answer is 147 0 Remainder
EXPLANATION: MY A$* (not that hard lol)
Step 1:
Start by setting it up with the divisor 3 on the left side and the dividend 441 on the right side like this:
Step 2:
The divisor (3) goes into the first digit of the dividend (4), 1 time(s). Therefore, put 1 on top:
Step 3:
Multiply the divisor by the result in the previous step (3 x 1 = 3) and write that answer below the dividend.
Step 4:
Subtract the result in the previous step from the first digit of the dividend (4 - 3 = 1) and write the answer below.
Step 5:
Move down the 2nd digit of the dividend (4) like this:
Step 6:
The divisor (3) goes into the bottom number (14), 4 time(s). Therefore, put 4 on top:
Step 7:
Multiply the divisor by the result in the previous step (3 x 4 = 12) and write that answer at the bottom:
Step 8:
Subtract the result in the previous step from the number written above it. (14 - 12 = 2) and write the answer at the bottom.
Step 9:
Move down the last digit of the dividend (1) like this:
Step 10:
The divisor (3) goes into the bottom number (21), 7 time(s). Therefore put 7 on top:
Step 11:
Multiply the divisor by the result in the previous step (3 x 7 = 21) and write the answer at the bottom:
Step 12:
Subtract the result in the previous step from the number written above it. (21 - 21 = 0) and write the answer at the bottom.
You are done, because there are no more digits to move down from the dividend.
The answer is the top number and the remainder is the bottom number.
Therefore, the answer to 441 divided by 3 calculated using Long Division is:
147
0 Remainder
ur welcome dummyboi
events. a. A∣B b. A∣B ′ c. A∣B ' d. Are events A and B independent? a. P(A∣B)= (Round to two decimal places as needed.) b. P(A∣B ′ )= (Round to two decimal places as needed.) c. P(A ′ ∣B ′ )= (Round to two decimal places as needed.) d. Are events A and B independent? A and B are not independent. A and B are independent.
Answers
The A and B are independent then P(A∣B) = P(A).Since P(A) = 0.60 and P(A∣B) = 0.60, it can be said that A and B are not independent.
P(A∣B)= 0.60 (Round to two decimal places as needed.)b. P(A∣B ′ )= 0.45 (Round to two decimal places as needed.)c. P(A ′ ∣B ′ )= 0.20 (Round to two decimal places as needed.)d. Are events A and B independent? A and B are not independent.Explanation:A∣B means that the event A occurs when the event B occurs. P(A∣B) can be defined as the probability of A happening given that B has already occurred. By definition, A and B are independent if P(A∣B) = P(A).a. P(A∣B)= P(A∩B)/P(B)0.60 = 0.36/0.60= 3/5 b. P(A∣B ′ )= P(A∩B ′ )/P(B ′ )0.45 = 0.27/0.60= 9/20c. P(A ′ ∣B ′ )= P(A ′ ∩B ′ )/P(B ′ )0.20 = 0.12/0.60= 1/5d. If A and B are independent then P(A∣B) = P(A).Since P(A) = 0.60 and P(A∣B) = 0.60, it can be said that A and B are not independent.
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If 23 fifth grade textbooks were used for the tower and the tower was 57. 1 cm tall, how many sixth grade textbooks were used?
Answers
If 23 fifth grade textbooks were used for the tower and the tower was 57. 1 cm tall, how many sixth grade textbooks were used?
To find out how many sixth grade textbooks were used, divide 57.1 cm by the height of one sixth grade textbook. Then multiply that number by 23 to get the total number of sixth grade textbooks used.
If you want to find out how many sixth grade textbooks were used for the tower, you first have to calculate the height of one sixth grade textbook. Once you have that measurement, you can divide 57.1 cm by that height to get the number of sixth grade textbooks used in the tower. To get the total number of textbooks used, you then need to multiply the number of textbooks per tower by 23, since 23 fifth grade textbooks were used. In other words, if the height of one sixth grade textbook is h, the number of sixth grade textbooks used is (57.1 cm / h) * 23. This equation gives you the number of sixth grade textbooks used, based on the height of one sixth grade textbook and the total height of the tower.
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Mr. Tomas is making a rectangular concrete pad for shed. The area of a pad is 17. 5 square yards. The length of the pad is 5 yards. What is the width of the pad?
Answers
If the area of a pad is 17. 5 square yards, the length of the pad is 5 yards, the width of the pad is 3.5 yards.
The formula for the area of a rectangle is:
Area = length x width
We know that the area of the pad is 17.5 square yards, and the length is 5 yards. We can use this information to solve for the width.
Let's substitute the values we know into the formula:
17.5 = 5 x width
To solve for the width, we need to isolate it on one side of the equation. We can do this by dividing both sides by 5:
17.5/5 = width
Simplifying the left side gives:
3.5 = width
In conclusion, Mr. Tomas should make a rectangular concrete pad that is 5 yards long and 3.5 yards wide to have an area of 17.5 square yards.
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-10+30+58=9-54 X 50-4=
Answers
Answer:
Hi
Step-by-step explanation:
SOLUTION STEPS
−10+30+58=9−54×50−4=
Add −10 and 30 to get 20.
20+58=9−54×50−4
Add 20 and 58 to get 78.
78=9−54×50−4
Multiply 54 and 50 to get 2700.
78=9−2700−4
Subtract 2700 from 9 to get −2691.
78=−2691−4
Subtract 4 from −2691 to get −2695.
78=−2695
Compare 78 and −2695.
i need help on this question please
Answers
Vοlume οf cylinder is and when height tripled then its vοlume alsο tripled but when radius tripled its vοlume becοme which is nineth times οf οriginal vοlume.
What dο yοu mean by Vοlume?Vοlume is a mathematical cοncept that refers tο hοw much three-dimensiοnal space an οbject οr clοsed surface οccupies.
Vοlume οf cylinder = πr²h
= π × 4² × 10
= 160π m³
When the height is tripled, h becοmes 3h
So, new height = 3 × 10 = 30m
Volume of a Cylinder (when height is tripled) = π × (4)² × 30
= π × 16 × 30
= 480π m³
When height is tripled then vοlume alsο tripled.
When the radius is tripled, r becοmes 3r
So, new radius = 3 × 4 = 12m
Volume of a Cylinder (when radius is tripled)
= π × (12)² × 10
= 1440 m³
But when radius is tripled the vοlumes becοme Nine times.
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Ray only wants to cover the lateral area of his paper weight. How many square inches of paper will he need? Round your answer to the nearest square inch.
Answers
The lateral area of this paper weight is 61.42 sq inches.
What is lateral surface area?Every solid object's lateral area may be calculated using the lateral area formula. Every figure's lateral area only includes the non-base faces. Calculating the lateral surface area of various forms, such as a cuboid, cube, cylinder, cone, or sphere, is made easier with the use of lateral area formulae. The object's base and the face parallel to the base are not included in the lateral area.
The surface area of the composite figure is the addition of the area of all the shapes.
The area of triangle with height 3.5 in is:
A1 = 1/2(6.5)(3.5)
A1 = 11.375 sq. in.
There are two such triangles thus, 2A1 = 2(11.375) = 22.75.
The area of the two triangle with height 6.5 in is:
A2 = 2(1/2)(4.3)(6.5) = 27.95 sq. in.
The area of the rectangle is:
A3 = (l)(w)
A3 = (6.5)(4.2) = 27.3 sq. in.
The total lateral area is:
LA = 11.375 + 22.75 + 27.3 = 61.42 sq inches.
Hence, the lateral area of this paper weight is 61.42 sq inches.
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3.6 You have a single piece remaining, 8 points from home, and it is your roll. Your opponent will surely go out if he or she gets another turn. Show that p (your winning) <1/2 , so that a double is not called for. Then explain why this does not contradict the result stated in Exercise 3.1 - namely that the expected count on a backgammon roll is 8 6 1 , exceeding the 8 points you need to win.
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a) result does not contradict
To show that p(your winning) <1/2, we need to consider that the last piece you have on your board could land on various positions. Depending on the position, your opponent could end up winning even if you land a higher value on the dice. Therefore, the probability of your winning is less than 1/2. This shows that a double is not called for.Exercise 3.1 states that the expected count on a backgammon roll is 8 6 1, exceeding the 8 points you need to win. This is true since the expected count means the average count you are expected to land on if you roll the dice. It does not mean that every roll will result in a count higher than 8, and it does not mean that you will always win. The expected count is simply a statistical measure of the possible outcomes of rolling the dice. Therefore, this result does not contradict the fact that p(your winning) <1/2.
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In its January 25, 2012, issue, the Journal of the American Medical Association (JAMA) reported on the effects of overconsumption of low, normal, and high protein diets on weight gain, energy expenditure, and body composition. Researchers conducted a single blind, randomized controlled trial of 25 U. S. Adults. The subjects were healthy, weight-stable, male and female volunteers, aged 18 to 35 years. All subjects consumed a weight-stabilizing diet for 13 to 25 days. Afterwards, the researchers randomly assigned participants to diets containing various percentages of energy from protein: 5% (low protein), 15% (normal protein), or 25% (high protein). The subjects were not aware of the specific protein level diet to which they were assigned. On these diets the researchers overfed the participants during the last 8 weeks of their 10 to 12 week stay in the inpatient metabolic unit. The goal was to investigate the effect of overconsumption of protein on weight gain, energy expenditure, and body composition. What is the purpose of random assignment in this experiment?
a. To generalize the experiment results to a larger group
b. To avoid bias
c. To produce treatment groups with similar characteristics
d. To control for confounding variables
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Random assignment in this experiment is important to avoid bias.
By randomly assigning participants to diets with different levels of protein, the researchers are ensuring that any differences in outcomes are due to the diet, and not because of any individual characteristics of the participants. Random assignment helps to ensure that the groups being compared in the experiment are similar and that any differences seen in outcomes are due to the protein level and not other factors. Random assignment helps to eliminate any bias that could be introduced if the participants were assigned to diets based on their own characteristics. This helps to ensure that the results of the experiment are valid and accurate.
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A piece of wax has a volume of 2. 5 cm and a mass of 4. 5 g. What is the density of the wax? A. 2. 0 g/cm B. 1. 8 g/cm3 C. 11. 3 g/cm3 O D. 7. 0 g/cm
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The density of the wax is 1.8 g/ cm ³. this means that for every cubical centimeter of the wax, it has a mass of 1.8 grams.
The density of a material is defined as its mass in line with unit volume, generally expressed in grams in line with cubical centimeter( g/ cm ³). To compute the density of the presented wax, we need to divide its mass by applying its volume.
Presented that the volume of the wax is2.5 cm ³ and its mass is 4.5 g, we will compute its density as
Density = Mass/ volume = 4.5 g/2.5 cm ³ = 1.8 g/ cm ³
Thus, the density of the wax is 1.8 g/ cm ³. this means that for every cubical centimeter of the wax, it has a mass of 1.8 grams. knowing the density of a fabric can help in relating the cloth or in predicting its deportment in distinct qualifications.
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