The required radius and error in radius is 13.8 cm and ± 0.12cm
Given that,
A machinist is required to manufacture a circular metal disk with an area of 600cm².
(a) What radius produces such a disk is to be determined
(b) If the machinist is allowed an error tolerance of ±5cm2 in the area of the disk, how close to the ideal radius in part is to be determined.
The area of a circle is given by the pie times square of the radius.
Area of circle = πr^2
Here,
a) The given area of disk = 600 cm²
πr² = 600
r = √600/3.14
r = 13.8 cm
b) an error tolerance of ± 5 cm² in the area of the disk,
So the percentage of error is 0.84%
Now, 0.84% of radius = 0.84 *13.8/100 = 0.12
The required error in radius will be ±0.12 cm
Similarly,
c) limx→a f(x) = L
Where a is the area of the disk and L is length, and f(x) is function of area.
Thus, the required radius and error in radius is 13.8 cm and ± 0.12cm.
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lesson 5.4
1 .Find the measurement of the angle indicated for each trapezoid.
2.Find the measure.
3.Solve for [x]. Each figure is a trapezoid.
4.Find the measurement of the angle indicated for each trapezoid.
Question 1
Opposite sides of a trapezoid are parallel. So, by the same-side interior angles theorem,
[tex]m\angle C+130^{\circ}=180^{\circ} \\ \\ m\angle C=50^{\circ}
[/tex]
Question 2
Drawing PR, we form congruent triangles PQR and PSR. Thus, using the sum of angles in a triangle,
[tex]55^{\circ}+24^{\circ}+m\angle Q=180^{\circ} \\ \\ m\angle Q=101^{\circ}[/tex]
Question 3
Opposite sides of a trapezoid are parallel. So, by the same-side interior angles theorem,
[tex]13x+6+70=180 \\ \\ 13x+76=180 \\ \\ 13x=104 \\ \\ x=8[/tex]
Question 4
Opposite sides of a trapezoid are parallel. So, by the same-side interior angles theorem,
[tex]11x+15+19x+15=180 \\ \\ 30x+30=180 \\ \\ 30x=150 \\ \\ x=5 \\ \\ m\angle B=11(5)+15=70^{\circ}[/tex]
One bar of candy A and two bars of candy B have 770 calories. Two bars of candy A and one bar of candy B contain
784 calories. Find the caloric content of each candy bar.
Candy bar A has :
Candy bar B has:
A prize is divided into the ratio 5:3 if the difference between the shares is £42 what is the total price?
Ty for helping :)
Answer:
£168
Step-by-step explanation:
Let the total prize be 8x, then the two prizes will be 5x and 3x.
Then, difference between the prizes = 2x
=> 5x - 3x = £42
=> 2x = £42
=> x = £42/2
=> x = £21
As mentioned above, the total prize is 8x.
So, total prize = 8 × x = 8 × £21 = £168
The equation that converts Celsius to Fahrenheit is C = 5/9 (F-32)
. Use it to calculate the temperature in Celsius when it is 60 degrees Fahrenheit. (Round to the nearest tenth)
Answer:
C=0
Step-by-step explanation:
C = 5/9 (60-32)
C= 5/9 (28)
C=15.55555556 (round to the nearest tenth)
C=15.6 - ANSWER
Enter the sum of the numbers as a product of their GCF and another sum
15 + 40
The sum of the numbers as a product of their GCF is ___ x (__ + ___)
Answer:
The GCF (Greatest Common Factor) is the biggest factor common to both of these numbers, so we must determine the factors for each:
15--->1,15
3,5
20--->1,20
2,10
4,5
As we can see, 1 and 5 are the common factors and 5 is the biggest (greatest). Therefore, we can "pull" out a 5 from both numbers and get a resulting equation of:
15 + 20--->5(3 + 4)
Hope this helps!
Step-by-step explanation:
help please i need it
Answer:
You need 7 strawberries to make 1 cup of smoothy
so that means 21 strawberries for 3
and 10 smoothies need 70 strawberries
Use additive inverse and their properties to find equivalent expressions 3+(-5)
The additive inverse of the given mathematical operation 3+(-5) is 2.
What is additive inverse?An additive inverse of a number is defined as the value that results in zero when added to the original number. It is the value we add to a number in order to get zero. If an is the original number, then its additive inverse is minus a, i.e., -a, such that a+(-a) = a - a = 0. 2 2 is the additive inverse of -2.So, 3+(-5):
3+(-5)-2Then, add 2 as follows:
-2 + 2 = 0Therefore, the additive inverse of the given mathematical operation is 2.
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13. Consider the two repeating decimals shown
below.
0.31313131...
0.02020202...
a. By simply looking at the decimal
representations, what is the sum of these
two rational numbers? Write as a decimal
and as a fraction.
b.
Verify your answer by finding fractions that
represent each decimal. Add the fractions.
c. Write the difference of the two numbers as a
repeating decimal.
1) The decimal 0.31313131...as a fraction is; 310/990
2) The decimal 0.02020202 as a fraction is; 200/9990
3) The difference of the two numbers as a repeating decimal is; 0.29292929
How to change decimal to fractions?We are given the decimals as;
0.31313131...
0.02020202...
1) The decimal 0.31313131... is repeating decimal.
If we write it as;
x = 0.31313131...
Multiply both sides by 10 to get;
10x = 3.131313 --- (1)
Multiply both sides of initial equation by 1000 to get;
1000x = 313.131313 ----(2)
Subtract eq 1 from eq 2 to get;
990x = 310
x = 310/990
2) The decimal 0.02020202 is a repeating decimal.
If we write it as;
x = 0.02020202...
Multiply both sides by 100 to get;
10x = 2.020202 --- (1)
Multiply both sides of initial equation by 10000 to get;
10000x = 202.0202 02 ----(2)
Subtract eq 1 from eq 2 to get;
9990x = 200
x = 200/9990
3) The difference of the two numbers as a repeating decimal is;
0.31313131 - 0.02020202 = 0.29292929
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Point G is the midpoint of segment FH. GH= 16x-19 and FG=12x+9. Find GH
The value of GH is 93.
Given,
Point G is the midpoint of segment FH.
GH= 16x-19 and FG=12x+9.
We need to find GH.
What is a midpoint?If there is a midpoint between two points the midpoint divided the line between two points into two equal lengths.
Example:
A ________B__________C
AB = BC
We have,
F_______G_______H
G is the midpoint.
GH= 16x-19
FG=12x+9.
FG = GH
16x-19 = 12x+9
16x - 12x = 9 + 19
4x = 28
x = 7
Now,
GH = 16x - 19
= 16 x 7 - 19
= 112 - 19
= 93
Thus the value of GH is 93.
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Does someone mind helping me?
Answer:
Hi there The answer should be 11.45 miles
Step-by-step explanation:
I added 3.7 + 4.5 + 3.2 = 11.45
With a calculator.
hope this helps!
LEUKEEXO Q
Which value of y makes the equation = 12 true?
After calculating equation we have come to find that the value of y is equal to 0.525 is true
What is an equation?An equation is formed by joining two expressions with the equal sign "=". The two expressions on either side of the equals sign are referred to as the "left-hand side" and "right-hand side" of the equation.
Typically, the right-hand side of an equation is assumed to be zero. This does not reduce generality because we can balance it by subtracting the expression on the right-hand side from the expressions on both sides.
We have given 12y - 1 / 2 = 8y + 8 / 5
lets solve it
⇒ 12y - 1 / 2 = 8y + 8 / 5
⇒ 12y -8y = 8 / 5 + 1 / 2
⇒ 4y = 21/10
⇒ y = 21/40
⇒ y = 0.525
Thus, the value of y is equal to 0.525 is true
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Full question
Which value of y makes this equation true?
12y - 1 / 2 = 8y + 8 / 5
Which of the following is an equivalent expression of 14x2 +18x + 5? (NEED THIS REALLY FAST)
A: 32x3 + 5
B: 14x2(18x + 5)
C: 5(14x2 + 18x)
D: 18x + 14x2 + 5
The equivalent expression of 14x2 +18x + 5 is 18x + 14x2 + 5, the correct option is D.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
We are given that;
The function 14x2 +18x + 5
Now,
18x + 14x^2 + 5
This expression is equivalent to 14x^2 + 18x + 5, because it has the same terms but in a different order. You can use the commutative property of addition to rearrange the terms in any order without changing the value of the expression. For example:
14x^2 + 18x + 5 = (14x^2 + 5) + (18x)
14x^2 + 18x + 5 = (18x) + (14x^2 + 5)
14x^2 + 18x + 5 = (18x) + (5) + (14x^2)
14x^2 + 18x + 5 = (5) + (18x) + (14x^2)
All of these expressions are equivalent to each other and to the original expression.
Therefore, the equation will be 18x + 14x^2 + 5.
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Help.........................................
Answer:
the bottom left graph is a function
Step-by-step explanation:
for questions like this pertaining a graph, you can use the vertical line test. essentially for a function, an x value cannot have multiple y values. so, the function cannot have any two or more points that lie on the same vertical line.
the top left graph is literally a vertical line, so that doesn't work
the top right is a circle. draw a vertical line and you see it always intersects two points
the bottom right graph draw a vertical line. two points again, right?
only the bottom left works with the vertical line test.
Aunt rose baked 2 1/2 dozen cookies. Her grandson, ricky ate _ of them. How many cookies did rocky eat?
The test scores for 9 students on the Unit 1 Test were 35, 25, 50, 95, 80, 60, 45, 100, and 90. What is the
value of the first quartile for this data set?
OA. 40
OB. 60
OC. 80
OD. 100
Answer:
40
Step-by-step explanation:
how many data? : 9
(9+1) x 1/4 = 2.5 (no 2.5: between 35 and 45)
(35+45)/2 = 40
the product of 2.5 and t. to a algebraic expressions
To an algebraic expression, the product of 2.5 and t is 2.5*t=2.5t.
An algebraic equation is what?In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.).
Terms comprise expressions.
As said, "The word product" refers to the result of a multiplication.
To find out which two integers are multiplied together, look for the term "AND." The result of adding 2 and 3 is 6
The two numbers being multiplied in this example are 2.5 and an unidentified number, only called t.
The formula is 2.5*t
= 2.5t.
We are at our limit at this point. Since the solution has not been provided, we are unable to write an equation.
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I will mark brainliest
Answer:
The 3rd one
Step-by-step explanation:
My mom is a teacher lol
Each folded fabric has a volume of 432 cubic inches. How many folded fabrics can fit inside a shipping box with the dimensions of 1 foot by 1 foot by 2 feet?
The folded fabrics that can fit inside a shipping box with the dimensions of 1 foot by 1 foot by 2 feet will be 18.
How to calculate the value?It should be noted that 12 inches = 1 feet
Therefore, 432 cubic inches will be converted to feet and this will be:
= 432/12
= 36
Therefore the number of folded fabric will be:
= 36 / (1 × 1 × 2)
= 36/2
= 18
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A car is driving at 45 kilometers per hour. How far, in meters, does it travel in 5 seconds?
The car travels 62.5 meters in 5 seconds
How to calculate the distance the car travelled ?
The car is driving at 45 kilometres per hour
The first step is to convert kilometres to meters
1 km= 1000 meters
= 45×1000
= 45,000
The next step is to convert hours to seconds
1 hour= 3600 seconds
= 45000/3600
= 12.5
The distance travelled in 5 seconds can be calculated as follows
= 12.5 × 5
= 62.5
Hence the distance travelled in 5 seconds is 62.5 meters
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evavluate the limit, lim x→−8 (4x − 6)
Answer: -38
Step-by-step explanation:
lim x→−8 (4x − 6)=
4(-8) − 6=
-32-6=
-(32+6)=-38
Find the measurement indicated in each parallelogram.
Answer:
EF=22
LM=19
ML=
Step-by-step explanation:
Solve the equation for v.
v over 4 minus 2 equals negative 10
v/4 - 2 = -10
v = −32
v = −48
v = 12
v = 38
Answer:
the answer is v = -32
Step-by-step explanation:
where
v/4 - 2 = -10
v/4 = -10 + 2
v/4 = -8
v = -8 × 4
v = -32
hope this helps
Answer: The answer for this question is v = -32
Step-by-step explanation: just do math.
What is the equation of a line that is perpendicular to the line x − 2y = 4? A. y = 1/2x − 4 B. y = −1/2x + 6 C. y = 2x − 3 D. y = −2x + 8
Answer:
The answer is D. y=-2x+8
Step-by-step explanation:
Hope this helps!!
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
83.5
Step-by-step explanation:
Median means middle. So in order to get that you need to write the numbers in order and then get the middle number. If the amount of numbers are even then take the 2 middle ones and add the together then divide by two.
89, 52, 78, 92, 98, 64 --> 52, 64, 78, 89, 92, 98
Since you have 2 middle numbers, you must take the middle 2 (78 and 89) and add them.
78 + 89 = 167
Now divide 167 by 2
167 / 2 = 83.5
Answer = 83.5
How do I simplify +(-11) I am just saying this to add letters
+(-11) is -11. You're "adding" -11 when in reality you're taking away 11 unless:
the equation looks like: -6+(-11)
the answer would be -17 because you're adding a negative to a negative. Taking away from a negative number is simply moving further down the negative number line, which makes the negative numbers "increase" in value
But if an equation looks like: 6+(-11)
the answer would be -5 since you are taking away 11 from a positive number.
Hope this makes sense and answers your question.
Una fotocopiadora reduce en un 30% el tamaño original de un documento. ¿Cuál es su escala de reducción?
After reduction of original size of a document by [tex]30%[/tex]%, the reduction scale is 70% of original size i.e., [tex]70:100=7:10[/tex]
As per the question statement, A photocopier reduces the original size of a document by 30%. We are supposed to find out what is the reduction scale.
Let say the document original size to be [tex]100%[/tex]% and if 30% is reduced by the photocopier, the remaining 70% will be the original size.
Hence reduction scale = [tex]70:100 = 7:10[/tex]
Therefore the reduction scale is 70% of the original size.
Reduction scale: A form can be made larger or smaller by using a scale factor. The linear scale factor of a reduction/enlargement figure can be used to compute a missing length.To know more about Reduction scale, click on the link given below:
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jijuygtfrdw34w2dddggjhtfexer34dutkeiritnty88
Answer:
The answer is 7.
-1-(-8)
Subtracting a negative number from a negative number (-) a minus sign followed by a negative sign, turns the two signs into a plus sign.
^ I forgot what I was trying to prove.
The displacement (in meters) of a particle moving in a straight line is given by s=6t^3+1t+4 where t is measured in seconds.
Find the velocity of the particle at the times given.
Velocity at time t=1, t=2, t=3, and t=a
Answer:
Velocities
t = 1 : 11 m/s
t = 2 : 27m/s
t = 3: 56.33 m/s
t = a: 6a + 1 + 4/a m/s
Step-by-step explanation:
s(t) = 6t³ + 1t + 4 where s = displacement in meters and t is time in seconds
s(t) = v(t). t where v is the velocity in m/s and t is time in seconds
So v = s/t
At time t = 1
s(1) = 6 x 1³ + 1 x 1 + 4 = 6 + 1 + 4 = 11 meters
v(1) = 11/1 = 11 m/s
At time t = 2
s(2) = 6 x 2³ + 1 x 2 + 4 = 6 x 8 + 2 + 4 = 48+ 2 + 4 = 54 m
v(2) = 54 /2 = 27m/s
At time t = 3
s(3) = 6 x 3³ + 1 x 3 + 5 = 6 x 27 + 3 + 4 = 169 m
v(3) = 169/3 = 56.33 m/s
At time t = a
s(a) = 6a³ + 1a + 4 = 6a³ + a + 4
v(a) = s(a)/a = (6a³ + a + 4)/a = 6a + 1 + 4/a m/s
(4⋅5)(x⋅y) is what property?
The given expression (4⋅5)(x⋅y) has a multiplication property.
What is the multiplication property?When we multiply both sides of an equation by the same number, the two sides remain equal, according to the multiplication property of equality. According to the Multiplication Property for Equations, an equation can be multiplied or divided by the same number on each side of the equation without changing the solution. Multiplication has the commutative property: Changing the order of the factors has no effect on the product. For instance, 4 × 3 = 3 × 4, 4 times 3 = 3 times 4 4 × 3=3 × 4 4, multiplied by 3, equals 3, multiplied by 4.Multiplication Properties
Multiplication's commutative property.Multiplication associative property.Multiplication's Distributive Property.Multiplication's Identity PropertySo, (4⋅5)(x⋅y) is a multiplication property as:
4(x-y)-5(x-y) = 5(x-y)-4(x-y)Therefore, the given expression has a multiplication property.
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if p/q=r/s then (p+q)/(r+s) is
if p/q=r/s then (p+q)/(r+s) is Ratio and proportion
(p+q)/(r+s)=q
Given,
p/q=r/s
ps=rq
p=rq/s
Putting these value of (p+q)/(r+s) is q
The ratio is used to compare two amounts of the same type. For two numbers, a and b, the ratio formula is written as a: b or a/b. The ratio and proportion concepts are based on fractions. Ratio and proportion are the fundamental building blocks for many other notions in mathematics. Ratio and proportion are useful in addressing many everyday difficulties, such as comparing heights, weights, distance, or time, or when combining ingredients in cookery, and so on.
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