The conversion of numbers are A. 58/11, B. 12 1/4, C. 61/20 and D. 6 3/100.
What are Fractions?Fractions are numbers which are of the form a/b where a and b are real numbers. This implies that a parts of a number b.
Here, a is called the numerator and b is called the denominator.
Mixed fraction consist of a whole part and a fractional part. It is of the form a b/c where a is the whole part and b/c is the fractional part.
a b/c is actually equal to a + b/c
A. 5 3/11
It is a mixed fraction. This is the result of a number divided by another number, where 5 is the quotient, 3 is the remainder and 11 is the divisor.
5 3/11 = [(5 × 11) + 3] / 11 = 58/11
Numerator is greater than denominator, so 58/11 is a fraction greater than 1.
B. 49/4
We have to convert to mixed fraction.
For that we have to divide 49 by 4 and find the quotient and remainder.
When 49 is divided by 4, 48 is a multiple of 4, where 48 = 12 × 4.
So quotient is 12 and the remainder is 49 - 48 = 1.
So 49/4 = 12 1/4
C. 3 1/20
It is a mixed fraction.
3 1/20 = [(3 × 20) + 1] / 20 = 61/20
D. 603/100
600 is a multiple of 100, where 600 = 6 × 100, so quotient = 6
Remainder = 603 - 600 = 3
603/100 = 6 3/100
Hence the numbers are converted from mixed fractions to fractions greater than 1 and vice versa.
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I need to determine whether each equation is a function or not a function and explain my reasoning and/or show my work
y⁴ = 2x² + 7 (Not a function)
y = -x + 3 (Function)
y = x² + 1 (Function)
y = 3/4 x - 5 (Function)
y² = x + 10 (Not a function)
Explanations:Note that:
An equation is a function only if there is only one value of y for a corresponding value of x
For y⁴ = 2x² + 7:\(y\text{ = }\sqrt[4]{2x^2+7}\)From the above, we can see that there will be multiple values of y for each vaue of x, therefore, y⁴ = 2x² + 7 is not a function
For y = -x + 3:This is a linear equation in which each value of x gives a distinct value of y, therefore, it is a function
For y = x² + 1:This is a quadratic equation in which there are distinct values of y for every value of x. It is a function
\(\text{For y = }\frac{3}{4}x-5\)This is also a linear equation that has distinct values of y for each value of x. It is a function
For y² = x + 10\(y\text{ = }\sqrt[]{x+10}\)This equation has two values of y for each value of x, it is not a function.
Express 31% as a fraction in its lowest form- I WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FIRST!
Answer:
31/100
Step-by-step explanation:
31% as a fraction can be represented as 0.31 as a decimal. 0.31 as a decimal can be represented as 31/100 as a fraction. Since 31 is a prime number, it cannot be simplified.
The simplest form 31% is 0.31.
What is fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
31% is number
Now, to convert the percent into fraction
=31 /100
As, 31 is prime number having no factor other than 31 and 1 .
So, 31/100= 0.31
Hence, the simplest form 31% is 0.31.
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a set of quiz scores is shown in the histogram below. the mean of the data set is 6.625 and the population standard deviation is 1.9 How many numbers in the data set are within 1 standard deviation of the mean? a)7 b)10 c)12 d)13
Given
Mean = 6.625
Standard Deviation = 1.9
Values within 1 standard deviation of mean, mean:
\(\begin{gathered} 6.625-1.9We look at the number of values at 5, 6, 7, and 8.5 = 2 people
6 = 2 people
7 = 5 people
8 = 3 people
Total = 2 + 2 + 5 + 3 = 12 people
Answer
C
NO LINKS!! URGENT HELP PLEASE!!
1. Find the area of a regular octagon. Each side is 12 m.
2. The perimeter of a regular polygon is 72 feet. An exterior angle of the polygon measures 40°. Find the length of each side.
3. If the perimeter of a regular pentagon is 50 in. Find the area. Show a drawing and work please.
Answer:
1) 695.3 m²
2) 8 ft
3) 172.0 in²
Step-by-step explanation:
Question 1To find the area of a regular polygon, we can use the following formula:
\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)
Given the polygon is an octagon, n = 8.
Given each side measures 12 m, s = 12.
Substitute the values of n and s into the formula for area and solve for A:
\(\implies A=\dfrac{(12)^2 \cdot 8}{4 \tan\left(\dfrac{180^{\circ}}{8}\right)}\)
\(\implies A=\dfrac{144 \cdot 8}{4 \tan\left(22.5^{\circ}\right)}\)
\(\implies A=\dfrac{1152}{4 \tan\left(22.5^{\circ}\right)}\)
\(\implies A=\dfrac{288}{\tan\left(22.5^{\circ}\right)}\)
\(\implies A=695.29350...\)
Therefore, the area of a regular octagon with side length 12 m is 695.3 m² rounded to the nearest tenth.
\(\hrulefill\)
Question 2The sum of an interior angle of a regular polygon and its corresponding exterior angle is always 180°.
If the exterior angle of a polygon measures 40°, then its interior angle measures 140°.
To determine the number of sides of the regular polygon given its interior angle, we can use this formula, where n is the number of sides:
\(\boxed{\textsf{Interior angle of a regular polygon} = \dfrac{180^{\circ}(n-2)}{n}}\)
Therefore:
\(\implies 140^{\circ}=\dfrac{180^{\circ}(n-2)}{n}\)
\(\implies 140^{\circ}n=180^{\circ}n - 360^{\circ}\)
\(\implies 40^{\circ}n=360^{\circ}\)
\(\implies n=\dfrac{360^{\circ}}{40^{\circ}}\)
\(\implies n=9\)
Therefore, the regular polygon has 9 sides.
To determine the length of each side, divide the given perimeter by the number of sides:
\(\implies \sf Side\;length=\dfrac{Perimeter}{\textsf{$n$}}\)
\(\implies \sf Side \;length=\dfrac{72}{9}\)
\(\implies \sf Side \;length=8\;ft\)
Therefore, the length of each side of the regular polygon is 8 ft.
\(\hrulefill\)
Question 3The area of a regular polygon can be calculated using the following formula:
\(\boxed{\begin{minipage}{5.5cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{s^2n}{4 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\end{minipage}}\)
A regular pentagon has 5 sides, so n = 5.
If its perimeter is 50 inches, then the length of one side is 10 inches, so s = 10.
Substitute the values of s and n into the formula and solve for A:
\(\implies A=\dfrac{(10)^2 \cdot 5}{4 \tan\left(\dfrac{180^{\circ}}{5}\right)}\)
\(\implies A=\dfrac{100 \cdot 5}{4 \tan\left(36^{\circ}\right)}\)
\(\implies A=\dfrac{500}{4 \tan\left(36^{\circ}\right)}\)
\(\implies A=\dfrac{125}{\tan\left(36^{\circ}\right)}\)
\(\implies A=172.047740...\)
Therefore, the area of a regular pentagon with perimeter 50 inches is 172.0 in² rounded to the nearest tenth.
Answer:
1.695.29 m^2
2.8 feet
3. 172.0477 in^2
Step-by-step explanation:
1. The area of a regular octagon can be found using the formula:
\(\boxed{\bold{Area = 2a^2(1 + \sqrt{2})}}\)
where a is the length of one side of the octagon.
In this case, a = 12 m, so the area is:
\(\bold{Area = 2(12 m)^2(1 + \sqrt{2}) = 288m^2(1 + \sqrt2)=695.29 m^2}\)
Therefore, the Area of a regular octagon is 695.29 m^2
2.
The formula for the exterior angle of a regular polygon is:
\(\boxed{\bold{Exterior \:angle = \frac{360^o}{n}}}\)
where n is the number of sides in the polygon.
In this case, the exterior angle is 40°, so we can set up the following equation:
\(\bold{40^o=\frac{ 360^0 }{n}}\)
\(n=\frac{360}{40}=9\)
Therefore, the polygon has n=9 sides.
Perimeter=72ft.
We have
\(\boxed{\bold{Perimeter = n*s}}\)
where n is the number of sides in the polygon and s is the length of one side.
Substituting Value.
72 feet = 9*s
\(\bold{s =\frac{ 72 \:feet }{ 9}}\)
s = 8 feet
Therefore, the length of each side of the polygon is 8 feet.
3.
Solution:
A regular pentagon has five sides of equal length. If the perimeter of the pentagon is 50 in, then each side has a length = \(\bold{\frac{perimeter}{n}=\frac{50}{5 }= 10 in.}\)
The area of a regular pentagon can be found using the following formula:
\(\boxed{\bold{Area = \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *s^2}}\)
where s is the length of one side of the Pentagon.
In this case, s = 10 in, so the area is:
\(\bold{Area= \frac{1}{4}\sqrt{5(5+2\sqrt{5})} *10^2=172.0477 in^2}\)
Drawing: Attachment
Which of the following is true
Answer:
The answer is answer choice E.
Step-by-step explanation:
Complementary angles add up to 90 degrees, while supplementary angles add up to 180 degrees
4j = 0.7 Solve for j
Answer:
0.175
Step-by-step explanation:
\(\frac{4j}{4} =\frac{0.7}{4}\)
j=0.175
Choose Yes or No to tell if the fraction
will make each equation true.
3
+ a
=
23
24
Choose.. v
+=
Choose.. v
13
18
Choose.. v
-=+
Choose.. v
15
Answer:
yes
yes
no
yes
Step-by-step explanation:
the following table shows the stock market performance of 40 industries from five sectors of the U.S. economy in a certain year. (Take 5 to be the set or all 40 industries represented in the table)Increased Decreased Unchanged. Totals(X) (Y). (Z)Financials (F). 3. 4. 1. 8 Manufacturing (M). 8. 3. 3. 14Information. 8. 1. 0. 9Technology (T)Health Care (M). 2. 1. 1. 4Utilities (U). 3. 1. 1. 5Totals. 24. 10. 6. 40Use symbols to describe the event that an industry increased in value but was not in the manufacturing sector.a. XⁿMb. XUMc. XⁿMd. XUMe. XⁿMHow many elements are in this event?80
A symbols to describe the event that an industry increased in value but was not in the manufacturing sector: X ∩ M'
The correct answer is an option (b)
Let us assume that event A : an industry increased in value
event B: an industry increased in the manufacturing sector
We need to describe the event that an industry increased in value but was not in the manufacturing sector.
We know that the event A but not B represents the sample values/ outcomes which are in set A but not in set B.
It is represented as A ∩ B' which is equal to A – A ∩ B.
Thus in above case the event that an industry increased in value but was not in the manufacturing sector means A ∩ B'
Here event A = X and B = M
Therefore, the symbolic form of required event = X ∩ M'
The correct answer is an option (b)
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Find the complete question below.
Determine whether the functions given are one-to-one. If not, state why.
(9,1),(-2,7),(7,4),(3,9),(2,7)}
Answer:
y
Step-by-step explanation:
1) Find the total cost (in dollars) of buying:
a) 5 toys at $300 each
b) a toys at $300 each
c) a toys at $ c each
Answer:
b
Step-by-step explanation:
because it one toy for that many dollars and i hope this will help you
Please answer this correctly
Answer:
75%
Step-by-step explanation:
There is 1 whisker and quartiles 1-3 so:
25%+25%+25%=75%
There is a bag filled with 3 blue, 4 red and 5 green marbles.
A marble is taken at random from the bag, the colour is noted and then it is not replaced.
Another marble is taken at random.
What is the probability of getting 2 different colours?
Answer:
Using the hypergeometric distribution, it is found that there is a 0.4286 = 42.86% probability of getting 2 of the same colour.
The marbles are chosen without replacement, hence the hypergeometric distribution is used to solve this question.
What is the hypergeometric distribution formula?
The parameters are:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
In this problem:
There is a total of 3 + 4 = 7 marbles, hence N = 7.
Of those, 3 are blue, hence k = 3.
2 marbles will be taken, hence n = 2.
Step-by-step explanation:
samantha mixes some amount of 25% sugar syrup with x grams of 10% sugar syrup. the result is120 grams 15% sugar syrup. how many grams of 25% sugar syrup did samantha use?
Answer:
Final mixture is 120 gm
x = 10% then (120-x) = 25%
.25(120-x) + .1 (x) = .15 (120) solve for x= 10% amount
then 25% amount = 120-x
Step-by-step explanation:
Triangle ABC with vertices at A(−4, −4), B(8, 8), C(2, 6) is dilated to create triangle A′B′C′ with vertices at A′(−2, −2), B′(4, 4), C′(1, 3). Determine the scale factor used. 2 one half 4 one fourth
Answer: It is similar to triangle ABC and has coordinates A′(8, −12), B′(4, −16), and C′(−20, 8)
Step-by-step explanation: Dilated triangles are never congruent, only similar (unless the dilation factor is exactly 1).
The coordinates of an image dilated about the origin are those of the pre-image multiplied by the dilation factor. For example,
A' = 2A
A'(8, -12) = 2×A(4, -6)
These facts are all you need to know to choose the correct answer (shown above).
Answer: 1/2
Step-by-step explanation:
I took the quiz!
what is the value of x
From the image,
2x and 48 are equal (alternate angles are equal). As such
2x = 48
Divide both sides by 2
x = 48/2
= 24
Option a
343 divided by 2,013?
Step-by-step explanation:
0.17039244908......
when 343 is divided by 2013
the answer is
5.86888....
PLS HELP!!!
simplify 3^2 x 3^4 x 3^6=
3^10
3^12
3^0
3^40
Answer:
3¹² is answer
Step-by-step explanation:
3^(2+4+6)
3^12
Answer the following questions with TRUE or FALSE. It is good practice to explain your answers. (a) The intersection of two events A and B can be larger than the union of the same two events A and B (b) The probability of a single event A must be smaller than or equal to the union of two events A and B (c) The condition probability of A given B must be smaller than the intersection of the same two events A and B
a) The statement " The intersection of two events A and B can be larger than the union of the same two events A and B" is False.
b) The statement " The probability of a single event A must be smaller than or equal to the union of two events A and B" is False.
c) The statement " The condition probability of A given B must be smaller than the intersection of the same two events A and B" is False.
(a) False. The intersection of two events A and B represents the set of outcomes that are common to both A and B, while the union of the same two events A and B represents the set of outcomes that belong to either A or B or both. Hence, it cannot be larger than the union of A and B.
(b) False. The probability of an event A must be between 0 and 1 (inclusive), while the union of two events A and B represents the set of outcomes that belong to either A or B or both. The probability of the union of A and B is the sum of the probabilities of A and B, which can be larger than the probability of A.
(c) False. The conditional probability of A given B, denoted as P(A|B), represents the probability of event A occurring given that event B has already occurred. Since the intersection of A and B must be less than or equal to 1, the conditional probability of A given B must also be less than or equal to 1.
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A side of a inner circle trapezium is a diameter of the circle. The non-parallel sides are equal to the radius of a circle. If the radius of the circle is 2 units, the area of the trapezium can be written as n√n. What is the value of n?
The value of n = 12, and the area of the trapezium can be written as 12√12.
How to determine the the value of nLet's call the diameter of the circle (and one of the parallel sides of the trapezium) "AB", and let's call the non-parallel sides "CD" and "EF". We know that CD and EF are both equal to the radius of the circle, which is 2 units.
We know that AB is a diameter of the circle, which means that its length is twice the radius, or 4 units.
We also know that CD and EF are each 2 units long.
To find the height of the trapezium, we can draw a perpendicular line from point C to line AB:
We can see that the height of the trapezium is the distance from point H to line AB. Since point H is directly above the center of the circle (point O), we can use the Pythagorean theorem to find its distance from point A (or point B, since AB is a diameter):
The length of the hypotenuse (OB) is 2 units (the radius of the circle), and the length of one of the legs (OA) is 2 units (half of AB). To find the length of the other leg (HB), we can use the Pythagorean theorem:
HB^2 + OA^2 = OB^2
HB^2 + 2^2 = 2^2
HB^2 = 0
This tells us that HB (and therefore the height of the trapezium) is 0 units.
Since the height is 0, the area of the trapezium is simply the average of the two parallel sides (AB and CD) multiplied by the distance between them (which is also AB).
Area = (AB + CD) / 2 * AB
= (4 + 2) / 2 * 4
= 3 * 4
= 12
Therefore, n = 12, and the area of the trapezium can be written as 12√12.
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please help me solve this
The area of triangle EFG is given as follows:
A = 18.63 square units.
How to obtain the area of a triangle?The area of a rectangle of base b and height h is given by half the multiplication of dimensions, according to the formula presented as follows:
A = 0.5bh
The base is given by segment EF as follows:
\(EF = \sqrt{(9 - 4)^2 + (-7 -(-9))^2}\)
EF = 5.4.
The midpoint of EF is given as follows:
M(6.5, -8).
The height is given by the segment MG as follows:
\(MG = \sqrt{(6.5 - 3)^2 + (-2 - (-8))^2}\)
MG = 6.9.
Hence the area is given as follows:
A = 0.5bh
A = 0.5 x 5.4 x 6.9
A = 18.63 square units.
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I don't think it's anything under 4in, but I'm not sure.
Answer:
5
Step-by-step explanation:
All you would have to do is read the question. Because if it is like a block than it couldn't be any closer to the bottom than five inches.
A pitcher contains 17.5 cups of iced tea. You drink 2.25 cups of the tea each morning and 1.25 cups of the tea each evening. When will you run out of iced tea?
Answer:
5 days
Step-by-step explanation:
2 (a) Simplify.
(i) a6 a2
O pop
Answer:
a4...................hope this helps
Can someone help me out math grades are bad
Answer:
First answer: 7x+19x+18+9
Second answer: 26x+27
it cost $3.50 a gallon for gas. Give an expression that represents the total cost, c, of gas given the number of gallons, g then determine the cost of 5 gallons of gas
Answer:
Step-by-step explanation:
We know that it costs 3.50 dollars for a gallon of gas, so we can write the total cost as an expression.
Expression: c= 3.50g
To find the total cost for 5 gallons, plug 5 into the variable, g.
c= 3.50g
c= 3.50(5)
c= 17.5 dollars
what number represents the same amount as 2 hundreds + 12 tens + 6 ones ?
Answer:
326
Step-by-step explanation:
The value of the given expression is 326.
Given:
The given expression 2 hundreds + 12 tens + 6 ones.
To find:
The value of the given expression.
Explanation:
The numeric form of given expression is:
2 hundreds + 12 tens + 6 ones
2 hundreds + 12 tens + 6 ones
2 hundreds + 12 tens + 6 ones
Therefore, the value of the given expression is 326.
what is the answer when you multiply 5.30 one by 5.02
Answer:
I think is there answer is 26.606
Plz help is this correct I have 10 mins left
...I think that is is...
Barbara charges $3.50, plus $2.25 for each hour she babysits. If Barbara charges $21.50, how many hours does she babysit?
Answer:
8 hours
Step-by-step explanation:
The equation is 2.25X + 3.50 = 21.50
X represents the unknown amount of hours she worked. 2.25 is the cost per hour. 3.50 is the fee she charges for every gig. That fee only happens once a gig so naturally it wasn't the number x was placed with.
2.25X + 3.50 = 21.50
2.25X + 3.50 - 3.50 = 21.50 - 3.50
2.25X = 18
2.25X = 18
2.25 2.25
X = 8
Could anyone help me on this?
Answer:
117
Step-by-step explanation:
we should subtract 63 from 180
so 180 - 63 = 117°