The work done to empty the tank by pumping the water out of the top of the tank is 3.4 * 10^6 .
Given :
a tank has the shape of an inverted circular cone with height 10 m and base radius 4 m. it is filled with water to a height of 8 m. find the work done to empty the tank by pumping the water out of the top of the tank .
Formula :
[tex]W=\int_a^bpA(y)D(y)dy[/tex]
Using the base radius of 4, I found the equation of the line which was y = 5x / 2 and by solving for x gives us x = 2y / 5 .
Work = [tex]9.8*1000\int_0^{8} (\pi(\frac{2y} 5)^2)(10-y)dy[/tex]
= 3.4 * 10^6
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Two ladders are leaning against a wall at the same angle, as shown. How long is the short ladder?
Answer:
15 ft
Step-by-step explanation:
60 divide by 40 equal 1.5
1.5 x 10 = 15
18. Higher Order Thinking The student council was
preparing for the school bake sale. The members divided
each type of donated item equally on plates. Each plate
contained only one type of item, and every plate had
exactly the same number of items. There were no leftovers.
What is the greatest number of items that could have been
placed on each plate?
Bake Sale Donations
Muffins
Breadsticks
Rolls
96
48
84
3-2 Find Greatest Common Factor and Least Common M
We need 8 plates for muffins, 4 plates for breadsticks, and 7 plates for rolls, with this arrangement, all plates will have the same amount of items, 12 per plate.
What are the denominator and numerator?
A fraction's top digit is always referred to as the numerator. It displays the number of our parts. A fraction's numerator—the lowest digit—is referred to as the denominator. It displays the overall number of pieces that something can be broken down into.
we have to divide each item in a way that gives us equal groups on each plate,
we have to find a divisor for each item that gives us the same result.
Muffins.
96/2=48
96/3=32
96/4=24
96/8=12
That is, by dividing all muffins into 8 plates we would have 12 muffins per plate.
Breadsticks.
48/2=24
48/4=12
That is, by dividing all breadsticks into 4 plates we would have 12 breadsticks per plate.
Rolls.
84/2=42
84/3=28
84/4=21
84/6=16
84/7=12
By dividing all rolls in 7 plates, we would have 12 rolls per plate.
Therefore, we need 8 plates for muffins, 4 plates for breadsticks, and 7 plates for rolls, with this arrangement, all plates will have the same amount of items, 12 per plate.
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Find part b m of c and m if a. Please explain.
Answer:
Step-by-step explanation:
a) the opposite angles of a quadrilateral inscribed in a circle are supplementary
70 + angle D = 180
angle D = 180 - 70
angle D = 110 degrees
b) DAB is a semicircle, so angle A and angle C are two circumference angles whose sides passes through the extremes of the diameter.
The centre angle of a semicircle is 180 degrees and its circumference angle is half that measure, so its value is 90 degrees
A = 90 degrees
C = 90 degrees
Solve the simultaneous equation 4x+6y=21;7x-3y=3
The solution of the equations 4x + 6y = 21 and 7x - 3y = 3 will be (1.5, 2.5).
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The linear equation is given below.
4x + 6y = 21 ...1
7x - 3y = 3 ...2
From equation 2, then we have
7x - 3y = 3
3y = 7x - 3
y = (7/3)x - 1
Put in equation 1, then we have
4x + 6[(7/3)x - 1] = 21
4x + 14x - 6 = 21
18x = 27
x = 3/2
x = 1.5
Then the value of the variable 'y' is calculated as,
y = (7/3)(3/2) - 1
y = 7/2 - 1
y = 3.5 - 1
y = 2.5
The solution of the equations 4x + 6y = 21 and 7x - 3y = 3 will be (1.5, 2.5).
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John is interested in purchasing a multi-office building containing five offices. The current owner provides the following probability distribution indicating the probability that the given number of offices will be leased each year.
Number of Lease Offices 0 1 2 3 4 5
Probability 10/33 1/33 7/33 1/11 4/33 8/33
If each yearly lease is $12,000, how much could John expect to collect in yearly leases for the whole building in a given year?(in dollars)
a) E(X) = $29,130.91
b) E(X) = $29,090.91
c) E(X) = $29,170.91
d) E(X) = $29,070.91
e) E(X) = $29,100.91
AE(X) = $23,333.33 could John expect to collect in yearly leases for the whole building in a given year.
What is probability ?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
The given table is:
Number of Lease Offices : 0 1 2 3 4 5
Probability : 5/18 1/4 1/9 1/18 2/9 1/12
The expected probability is
Expected probability [tex]$=\sum_{i=0}^5 x_i p\left(x_i\right)$[/tex]
Expected probability [tex]$=0 p(0)+1 P(1)+2 P(2)+3 P(3)+4 P(4)+5 P(5)$[/tex]
Expected probability [tex]$=0 \cdot\left(\frac{5}{18}\right)+1 \cdot\left(\frac{1}{4}\right)+2 \cdot\left(\frac{1}{9}\right)+3 \cdot\left(\frac{1}{18}\right)+4 \cdot\left(\frac{2}{9}\right)+5 \cdot\left(\frac{1}{12}\right)=\frac{35}{18}$[/tex]
It is given that the yearly lease [tex]$=\$ 12,000$[/tex].
The yearly leases for the whole building in a given year is
Yearly leases [tex]$=\frac{35}{18} \times 12000=23333.3333333 \approx 23333.33$[/tex]
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Please help NOWWW!!!
Write y=2/3x+7 in standard form using integers.
A. -2x+3y=7
B. -2x+3y=21
C. 3x-2y=21
D. -2x-3y=21
1. On a journey from Dover to Sheffield, Liam drove at an average speed of 40mph
for the first three hours of his journey.
The remaining 120miles of his journey were completed at an average speed of
30mph.
According to the given statement Liam is incorrect because average speed is 34.28 miles per hour.
Why do people use average speed?The average scores of a body's speed over a duration of time is its average speed. Because a moving body's speed is not constant over time and fluctuates, the average speed formula is required.
What does "average speed" actually mean?The overall distance the thing travels in a given amount of time is its average speed. A scalar value symbolizes the average speed. It has no direction and therefore is indicated by the magnitude.
Distance covered in first three hours = 40 × 3 = 120 miles
Time taking to covered remaining 120 miles = 120/30
= 4 hours
Total time = 4 hours + 3 hours = 7 hours
Total distance = 120 miles + 120 miles
= 240 miles
Average speed = total distance / total time
Average speed = 240 miles / 7 hours = 34.28 miles per hour
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Jon Begins jogging at a steady 3 m/sec down the middle of lane one of a straight track. Laura starts even with him in the cneter of lane two but moves at 4 m.sec. At the instant they begin, Ellis is loacted 100 meters down the track in lane four, and is heading towards them in his at 6 m.sec. After how many seconds will the runners lie in a straight line?
a) Let t be the number of seconds the three have been running. Write expressions for the number of meters each has run after t seconds.
b) Consider the location of each runner as a point on a graph. What quantity might you use as the x-coordinate? What quantity might you use as the x-coordinate? What quantity might you use as the y-coordinate?
c) How can you tell if three points are on a line? Use this to solve the problem.
Answer:
The runners will be in a straight line after 1/2 seconds.
To solve this problem, we can set the y-coordinates of each runner equal to each other and solve for t. The y-coordinate represents the lane number, and if the lane numbers are equal, the runners are on a straight line.
Jon: y = 1
Laura: y = 2
Ellis: y = 4
Jon: 3t = 1
Laura: 4t = 2
Ellis: 6t = 4
Solving these equations simultaneously, we find that t = 1/2 seconds. This means that after 1/2 seconds, the runners will be in a straight line.
In need of help like rn pls nd thanks!!!!!!!!!!!!!!!
Answer: His work shows that the answer is an F. E. Which means a False Equation.
Step-by-step explanation:
This happens when an equation cannot be solved. Here is an example of a false equation answer:
Let's say that 3=6, in the equation or expression, all the letters like "x, y, z..." have been undone.
Therefore we can no longer undo, so the answer to your question is a False Equation.
A ship's destination is 30 miles north and 12 miles east. At what angle should it head to go straight to its destination?
a) 22°east of north b) 24°east of north
c) 31°east of north d) 66°east of north
The angle should it have to go straight to its destination is 66° east of north. The correct option is D.
What are trigonometric identities?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate to a triangle's side length and angle.
Given that a ship's destination is 30 miles north and 12 miles east. The angle will be calculated as,
tanθ = 30 / 12
θ = tan⁻¹ ( 30 / 12)
θ = 66°
The angle is θ = 66°
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How do I Solve this:
Answer:
x = 20
Step-by-step explanation:
x + 2x + 6x = 9x / 180
x=20
triangles = 180
angle 1 = ?
angle 2 = 160?
angle 3 = 20
evaluate 2n if n = 9
Answer:
18
Step-by-step explanation:
If n=9, then plug in 9 for n in the equation and solve. You should get 2•9, which is 18 when you simplify. Hope this helps and please mark brainliest!
Simplify 4X•1/x^-5•x^-3
The simplified form of the given expression, [tex]\frac{4x \times 1}{x^{-5} \times x^{-3} }[/tex] is equal to [tex]4x^{9}[/tex]
What are Exponents?
Powers or exponents are quantities that indicate how many times to multiply a base number by themselves.The base is the integer being raised by a power, while the exponent or power is the superscript number above it.For example, in the expression [tex]7^{5}[/tex], 7 is the base and 5 is the exponents, which implies that 7 multiplies 5 times by itself.What is the Product of Powers rule?
The Product of Powers rule is one of the seven major Laws of Exponents.According to this rule, if the bases are the same, then when multiplying two bases with different exponent value, the resulting answer is found by adding the exponents.It can be mathematically expressed using the formula, [tex]x^{m} \times x^{n} =x^{m+n}[/tex]In this question, the expression is [tex]\frac{4x \times 1}{x^{-5} \times x^{-3} }[/tex] ------(1)
Multiplying the values in the numerator, we get
[tex]\frac{4x \times 1}{x^{-5} \times x^{-3} }=\frac{4x}{x^{-5} \times x^{-3} }[/tex]
Now, the values in the denominator can be simplified using the Product of Powers rule.
The formula for the Product of Powers rule is given as, [tex]x^{m} \times x^{n} =x^{m+n}[/tex]
Simplifying the given expression using the Product of Powers rule, we get
[tex]\frac{4x \times 1}{x^{-5} \times x^{-3} }=\frac{4x}{x^{-5+(-3)} }\\\implies \frac{4x \times 1}{x^{-5} \times x^{-3} }=\frac{4x}{x^{-8} }[/tex] -----(2)
The formula for the Quotient of Powers rule is given as, [tex]\frac{x^{m} }{x^{n} } =x^{m-n}[/tex]
Simplifying the expression in (2) using the Quotient of Powers rule, we get
[tex]\frac{4x \times 1}{x^{-5} \times x^{-3} }=4x^{1-(-8)} \\\implies \frac{4x \times 1}{x^{-5} \times x^{-3} }=4x^{9}[/tex]
Therefore, the simplified form of the given expression is [tex]4x^{9}[/tex]
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What are the missing parts that correctly complete the proof? W/ picture
1. Reason: Since QA divides ∠PQR into two different parts so it is a bisector∠PQA≅∠RQA.
2. The line which divides an angle into two different angles is known as a bisector.
4. ∠QXA≅∠QYA and they are situated opposites to each other so we can say that right angles are conjugate.
5. Given, Both are situated in the same plan so QA≅QA
6.ΔQXA≅ΔQYA, by the AAS Postulate.
8. Definition of equidistant. XA=XY.
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study results indicate that the mean amount of time people live in the same house s between 5.5 and 13.5 years. what is the study's margin of error?
Answer:4.25
Step-by-step explanation: because it is daddy
Attachment 1 is answer options, attachment 2 is questions, answer all please 30 points
Any quality that pertains to a certain set is referred to in mathematics as a property. A property p that is rigorously specified for every component of a set X is typically defined as a function p: X → {true, false}.
What are the 4 properties of equality?The four properties of equality addition, subtraction, multiplication, and division can be used to solve an equation. To get the value of an equation's unknown variable, we can easily add, subtract, multiply, or divide the two sides of the equation.
The qualities of equality are those characteristics that have no effect on an equation's truth value, i.e., those characteristics that do not affect the equality of two or more values. These equality-related qualities enable us to define an equivalence relation and solve a number of algebraic equations.
9/2 x - 3 = 1/2 x + 2 Addition property of equality
9/2 x - 1/2 x - 3 = 1/2 x - 1/2 x + 2 Addition property of equality
1/4 * 4x = 1/4 * 5 Multiplication property of equality
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Hi, I need help solving quadrilateral problems.
The value of x in quadrilateral JKLM is 29
What is a quadrilateral?A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles. It is formed by joining four non-collinear points. The sum of interior angles of quadrilaterals is always equal to 360 degrees.
The sum of the interior angles in a quadrilateral is 360°
∠J + ∠K + ∠L + ∠M = 360
3X + 90 + 2X + 8 + 4X + 1 = 360
9x + 99 = 360
9x = 360 - 99
9x = 261
x = 261/9
x = 29
In conclusion 29 is the value of x in the quadrilateral.
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C-Town is advertising a Back-to-School sale on pencils. Pack A has 30 pencils and sells for $7.50, while Pack B has 12 pencils and costs $4.25. Find the unit price for each and determine which pack is the better buy.
The rate for Pack A and Pack B
The unit price for Pack A and Pack B
Which pack is the better buy? Explain your reasoning.
The best buy is pack of 30 .
What is cost and division ?
A cost function is a mathematical formula used to chart how production expenses will change at different output levels.
The general form of the cost function formula is C(x)=F+V(x) C ( x ) = F + V ( x ) , where F is the total fixed costs, V is the variable cost, x is the number of units, and C(x) is the total production cost.
Division is the opposite of multiplication.
A division is a process of splitting a specific amount into equal parts.
Pack A has 30 pencils
sells for $7.50.
pack of 30:
7.97/30 = 0.27 per pencil
Pack B has 12 pencils
costs of $4.25.
pack of 12:
4.77/12 = 0.40 per pencil
The best buy is pack of 30 because:
0.27 < 0.40
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A new club sent out 192 coupons to boost sales for next year's memberships. They provided 5 times as many to potential members than to existing members. How many coupons did they send to existing members? A. 37 B. 6 C. 32 D. 5
They send 32 coupons to existing members. Option C is correct.
What is a linear equation in two variables?
A Linear equation in two variables x and y is of the form
Ax + By = C.
Given,
They provide 5 times as many to potential members than existing members.
Let, there are y potential members and x existing members.
Therefore, x + 5y = 192
Also, x and y are whole numbers.
Hence, x=32 satisfy the equation.
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Please help, I don't really understand.
Answer:
y = [tex]\frac{2}{3}[/tex] x + [tex]\frac{26}{3}[/tex]
y = [tex]\frac{-3}{2}[/tex] x
Step-by-step explanation:
y = [tex]\frac{-3}{2}[/tex] x - 6
The slope of this line is -3/2
A perpendicular slope is the opposite reciprocal. That means you flip it upside down and take the opposite sign. Since this slope is negative, the perpendicular slope will be positive. If I turn this fraction upside down it will be 2/3, so the perpendicular slope is 2/3.
For the equation of the line we need the slope (m) and the y intercept. To find that we will use the point that goes through this line.
m = (2/3)
x = -4 from the point given (-4, 6)
y = 6 from the point given (-4,6)
y = mx + b
6 = [tex]\frac{2}{3}[/tex] [tex](\frac{-4}{1})[/tex] + b
6 = [tex]\frac{-8}{3}[/tex] + b Add [tex]\frac{8}{3}[/tex] to both sides
[tex]\frac{6}{1}[/tex] + [tex]\frac{8}{3}[/tex] = b
[tex]\frac{18}{3}[/tex] + [tex]\frac{8}{3}[/tex] = b
[tex]\frac{26}{3}[/tex]
y = [tex]\frac{2}{3}[/tex] x + [tex]\frac{26}{3}[/tex]
Parallel lines have the same slope.
m = [tex]\frac{-3}{2}[/tex]
x = -4 from the point (-4,6)
y = 6 from the point (-4,6)
y = mx + b
6 = [tex]\frac{-3}{2}[/tex][tex](\frac{-4}{1})[/tex] + b
6 = 6 + b Subtract 6 from both sides
0 = b
y = [tex]\frac{-3}{2}[/tex] x
PLEASE HELP!!!
Which choices are equivalent to the fraction below? Check all that apply.
12/32
A. 4/10
B. 3/8
C. 10/30
D. 6/16
E. 4/9
F. 2/6
PLEASE EXPLAIN HOW TO DO IT‼️‼️‼️
Answer: the answers should be B and D
Step-by-step explanation:
so basically, this is just simplifying
B is the correct answer because the numerator 12, when divided by 4 is 3, and the denominator 32, when also diving by 4, is eight. This makes the two fractions equivalent.
Same goes for D, for if you diving the numerator and denominator by 2, you get answer choice D
it’s kind of a trial and error type problem and you have to test out all possibilities
hope this helps!
Answer:
B and D
Step-by-step explanation:
12/32 (if you divide them both by three) does not equal 4/10
12/32 fully simplified is 3/8
12/32 - subtracting is not simplifying, therefore, 10/30 is not correct
12/32 - both divided by two, a common factor, is 6/16, therefore, this answer is correct
12/32 - both of them divided by three equals 4/10.7 (rounded up to the nearest tenth), therefore, 4/9 is not a correct answer
12/32 - both divided by six equals 2/5.3 (rounded down to the nearest tenth), therefore, 2/6 is not a correct answer
Ava’s pet pig is older than Izzy’s pet pig, which is 2 years old. Ava adopted her pig when it was 1 year old, and she has had it for x years.
Write a one-step inequality to represent the situation, where x is the time, in years, since Ava adopted her pet pig.
Enter the correct answers in the boxes in the form of x+p ? q, where p and q are rational numbers and ? is replaced by >, ≥, <, or ≤.
The inequality that represents this situation is, (1 + x) > 2.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, Ava’s pet pig is older than Izzy’s pet pig, which is 2 years old.
Ava adopted her pig when it was 1 year old, and she has had it for x years.
∴ The inequality that represents this situation is,
(1 + x) > 2.
x > 2 - 1.
x > 1.
Ava adopted her pig for more than one year.
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(c) The sum of the ages of two brothers is 31 years and the age of older brother is 5 years more than the younger brother. Find their present ages.
Answer:
Here is your answer,
Step-by-step explanation:
(c)
x + y = 31 ------ (i)
x - y = 5 ------ (ii)
We have subtract eqn (ii) from eqn (i). Here we get the equation as,
2y = 26
y = 13 ------(iii)
Put eqn (iii) in eqn (i), we get -
=> x + y = 31
=> x = 31 - 13
=> x = 18
Therefore, their present ages of younger brother & older brother is 13 yrs & 18 yrs respectively.
melissa's null hypothesis is that the average calories in frozen mac n cheese is 350 (that is, the population average is 350). since she only has one sample, she uses the bootstrap to estimate the average and ultimately decides to create a confidence interval. she also chooses an 8% p-value cutoff. what kind of confidence interval should she use?
For 8% p-value cutoff , Melissa should use 92% confidence interval
A confidence interval calculated for a treatment effect measure shows the range in which the true treatment effect is likely to fall.
A smaller sample size or higher variability will result in a wider confidence interval with a larger margin of error. The interval width is also influenced by the level of confidence. If you want a higher level of certainty, the interval should be wider.
The width of the confidence interval and the size of the p value are related.
The narrower the interval, the smaller the p value. The confidence interval, on the other hand, provides useful information about the likely magnitude of the effect under consideration as well as the accuracy of the estimate.
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Chase and Alonzo stand next to each other and throw baseballs in the air. The path of chases baseball is described by the equation y= -4x^2+5x+7. The path of Alonzo’s ball is shown by the graph whose baseball reaches a greater height
Quadratic equation :The maximum height reached by Alonzo's ball will be 9m.
What is a quadratic equation?
The equation whose highest degree of the variable used in the equation is 2 and has 2 roots, is called quadratic equation.
Here the quadratic equation of the path of Chase's ball is given by y = - 4x²+ 5x+ 7
To compare the height of both paths followed by the ball
we have to first calculate the height of the path of Chase's ball.
the path of Chase's ball is f(x)=-4x²+ 5x+ 7
The function will have the highest value when f'(x) will be 0.
f'(x)=-8x+5
f'(x)=0
⇒-8x+5=0
⇒-8x=-5
⇒x=5/8
at x=5/8, function value is
f(x)=-4x²+ 5x+ 7
=-4(5/8)²+ 5(5/8)+ 7
=-4(25/64)+(25/8)+7
=(-25/16)+25/8+7
=8.5625
There maximum value of f(x) is 8.5625.
The maximum height reached by Chase's ball will be 8.5625m.
From the graph of the path of Alonzo's ball, it is clear that
The maximum height reached by Alonzo's ball will be 9m.
As 8.5625m < 9m
Alonzo's baseball will reach greater height.
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Complete Question:
Chase and Alonzo stand next to each other and throw baseballs in the air. The path of Chase's ball is described by the equation y = - 4x²+ 5x+ 7. The path of Alonzo's ball is shown by the graph. In each function, x is the horizontal distance the ball travels in meters, and y represents its height. Whose baseball reaches a greater height?
A. Both baseballs reach the same height.
B. Chase's baseball
C. Alonzo's baseball
D) Non of these
Answer:
Alonzo's baseball
whompwhompwhompwhopwhompwhompwhompwhompwhompwhompwhompwhompwhompwhompwhomp
Step-by-step explanation:
What is the proportional relationship?
6
3.75
20
1/5
3
1/8
1.12
5/2
5
1/2
8
2
Answer:
I think multiples of 4
I hope this helps
Find the y-intercept of the line y=10x+ 7/13
Write your answer as an integer or as a simplified proper or improper fraction, not as an ordered pair.
Answer: 7/13 is the y intercept
a researcher studying malnutrition among children in a developing country collected weights of a random sample of children using a scale that she had set to give weights 2.5 kilograms less than the actual weight. which statement best describes this situation? measurement error has not occurred, and the researcher is not guilty of unethical statistical practice. measurement error has occurred, and the researcher is guilty of unethical statistical practice. measurement error has occurred, but the researcher is not guilty of unethical statistical practice. measurement error has not occurred, but the researcher is guilty of unethical statistical practice.
Therefore the the best statement that describes this situation is Measurement error has occurred, and the researcher is guilty of unethical statistical practice.
As per the details share in the above question are as follow,
A researcher collected weights of a random sample of children using a scale that she had set to give weights 2.5 kilograms less than the actual weight.
We have to determine the best statement that describes this situation?
It measured precisely 2.5 kg less, which is a systematic inaccuracy, thus there has been a measuring error.
The statistician was guilty because she purposefully gave them less weight in order to support her argument.
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The diameter of a circle divides the circle into two equal sectors true or false
Answer:
NO
FALSE
Step-by-step explanation:
The diameter divides the circle into two equal part called semi– circles( the image on white)
A sector is the plane figure enclosed by two radii of a circle or ellipse and the arc between them.
( the image that is dark)
i hope this helped
Answer: No, the diameter of a circle divides the circle into two equal halves called semi circle.
Step-by-step explanation:
The line that splits a circle into two identical halves is its diameter. The widest chord that divides the circle in half exactly is called the diameter. Each component is known as a semicircle.
There are 5,280 feet in a mile. There are 3 feet in a yard. How many yards are there in a mile? Please help this is due tomorrow
In mile there are 63360 inches.
The number of inches in a mile is equal to the number of inches in a foot times the number of feet in a mile
We multiply 528 by 12 and add one zero to the right of the result.
Use vertical form to perform the multiplication.
So. 12 × 5280=63360
∴ 5280/6336
= 1056
The number of inches in a mile = 12 × 5280
We multiply 528 by 12 and add one zero to the right of the result.
Use vertical form to perform the multiplication:
528 × 12 = 1056
1056 + 5280 = 6336
So, 12 × 5280 = 63360 miles
Therefore, in mile there are 63360 inches.
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