1. Between which two whole numbers is
√12?
Convince Me!
2. Which of the two numbers is a better
estimate for √12? Explain.
Answers
The two whole numbers between which is √12 are 3 and 4.
What is an example of a whole number?
Any positive number that does not contain a fractional or decimal component is referred to as a whole number. The numbers 0, 1, 2, 3, 4, 5, 6, and 7 are all whole numbers, for instance, as a result. -3, 2.7, or 3 12 are examples of non-whole numbers.
The closest perfect squares near 12 are 16 and 9 which are the perfect squares of 4 and 3 respectively Therefore the root of 12 lies between 3 and 4.
i.e 3 < √12 < 4
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Related Questions
The art teacher has 1 gallon of paint, which is enough for \frac{2}{3} of the class to complete a project.
How many gallons does she need for the whole class?
Answers
The teacher requires 1.5 gallons of paint for the whole class
Quantity of paint available with the teacher = 1 gallon
Fractions: In mathematics, a fraction is represented by a number that identifies a portion of a whole. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.
Portion of the class covered by 1 gallon of paint = 2/3 class
Let x represent the whole class
Formulating the equation:
The portion of the class covered out of the whole class*Total class = Paint required for the portion of the class
So, for 2/3x = 1
x = 3/2
x = 1.5 gallon
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the points (-5,r) and (2,13) lie on a with slope 3 find the missing coordinate r
Answers
Answer:
r = - 8
Step-by-step explanation:
calculate the slope m using the slope formula , then equate to 3
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 5, r ) and (x₂, y₂ ) = (2, 13 )
m = [tex]\frac{13-r}{2-(-5)}[/tex] = [tex]\frac{13-r}{2+5}[/tex] = [tex]\frac{13-r}{7}[/tex]
then equating gives
[tex]\frac{13-r}{7}[/tex] = 3 ( multiply both sides by 7 )
13 - r = 21 ( subtract 13 from both sides )
- r = 8 ( multiply both sides by - 1 )
r = - 8
Find the length of x and y
Answers
Answer:
y = 15/4 mm
x = 36/5 mm
Step-by-step explanation:
In similarity triangles, the corresponding sides are in same ratio.
[tex]\sf \dfrac{3}{y}=\dfrac{4}{5}\\\\\bf Cross \ multiply,\\\\ y*4 = 3*5\\\\ y =\dfrac{15}{4}\\\\\boxed{y = \dfrac{15}{4}}[/tex]
[tex]\sf \dfrac{x}{9}=\dfrac{4}{5}\\\\x = \dfrac{4}{5}*9\\\\x = \dfrac{36}{5}\\\\\boxed{x = \dfrac{36}{5} \ mm}[/tex]
XY is formed by X(-9,-7) and Y (-3,5 is line j is the perpendicular bisector of XY
Answers
The Equation of perpendicular bisector line l is found to be [tex]y = 2x+ 11[/tex]
Given Line XY is formed by points X(-9, -7) and Y(-3,5) therefore, it passes through these two respective points.
Let the slope of this line be n
The Slope of line passing through X and Y points is given by
n = [tex](y_{2} - y_{1} )/(x_{2} -x_{1} )[/tex]
⇒ n = {5 - (-7) }/ {(-3) - |(-9)}
⇒ n = 12/6
⇒ n = 2 (equation 1 )
Given that line l is perpendicular bisector of XY
Let the slope of l = m
We know that the product of the slopes of any two perpendicular lines is -1
Therefore, n x m = -1
⇒ m = -1 \ n
putting the value of n from the above equation 1 we get
⇒ m = - 1/2
Additionally, because l is the perpendicular bisector hence it goes through the mid point of the line XY
Mid point of two lines = [tex](x_{2} + x_{1} )/2[/tex] and [tex](y_{2} + y_{1} )/2[/tex]
Mid point of XY = [tex]\frac{-9 + (-3)}{2}[/tex] and [tex]\frac{-7 + (5)}{2}[/tex]
= (-6, -1)
The equation of perpendicular bisector l is given my the following formula:
[tex]y = nx + c[/tex]
here we have n = slope of line
we have n = 2 from equation 1
∴ y = 2x + c (equation 2)
Also equation (2) is satisfied by the point (-6,-1)
Hence we can express it as:
-1 = 2(-6) + c
⇒ c = 11
Therefore the required equation of perpendicular bisector l is
[tex]y = 2x + 11[/tex]
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Determine the sum of the integers.
a. 4 + -11=
b. 21 +-3=
C. -9 + -4 =
d. 10-15 =
e. 7 + (-7)=
f. 12+ (-19) =
g. -13+ 13 =
h.
14+ (-20) =
Answers
Answer:
a -7
b 18
c -13
d -5
e 0
f -7
g 0
h -6
Step-by-step explanation:
too lazyy
Find the area of this parallelogram. Be sure to include the correct unit in your answer.
Answers
Answer:13x9x6=702
Step-by-step explanation:
Diane wants to measure the height of a tree. She sights the top of the tree, using a mirror that is lying flat on the ground. The mirror is 35 ft from the tree, and
Diane is standing 7.9 ft from the mirror, as shown in the figure. Her eyes are 6 ft above the ground. How tall is the tree? Round your answer to the nearest foot.
Answers
The tree is approximately 27 ft tall if the answer is rounded off to the nearest foot when the similar triangle formula is applied.
What are properties of similar triangles?Two triangles can be said to be similar if their corresponding angles are seen as congruent and thereafter their corresponding sides are in proportion.
What are the 3 similar triangles?Similar Triangles Definition
Angle - Angle (AA)
Side - Angle - Side (SAS)
Side - Side - Side (SSS)Similar triangles are triangles that have the same shape, but their sizes may vary.
If Diane, mirror, and the exact bottom of the tree are placed as points on the ground all lying on one line, then the two right triangles can be stated as:
LEFT: y and 35 as the legs and unknown hypotenuse.
RIGHT: 6 and 7.9 as the legs and unknown hypotenuse.
The two angles pointed at the mirror are seen as of same measure that means that 35 and the hypotenuse of LEFT triangle makes same angle measure as the 7.9 and the hypotenuse of that of the RIGHT triangle.
Since these two are seen as similar triangles,
y/35 = 6/7.9
⇒y = 26.58
⇒ y ≈ 27 ft
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Ellie is six years older than Maisie Zoe is twice as old as Eli. The sum of their ages is 50. How old is Zoe?
Answers
Let the age of Maisie be x
From the first statement, Ellie is six years older than Maisie implying:
[tex]\text{Ellie's age = x + 6}[/tex]From the second statement, Zoe is twice as old as Eli implying:
[tex]\text{Zoe's age = 2(x+6)}[/tex]From the last statement, the sum of their ages is 50 implying:
[tex]x\text{ + x + 6 + }2(x\text{ + 6) = 50}[/tex]Solving for x:
We open the bracket and collect like terms
[tex]\begin{gathered} x+x\text{ + }6\text{ + 2x + 12 = 50} \\ x\text{ + x + 2x + 6 + 12 = 50} \\ 4x\text{ + 18 = 50} \\ 4x\text{ = 50 - 18} \\ 4x\text{ = 32 } \\ \text{Divide both sides by 4} \\ \frac{4x}{4}\text{ = }\frac{32}{4} \\ x\text{ = 8} \end{gathered}[/tex]Hence, Zoe's age is:
[tex]\begin{gathered} =2(x\text{ + 6)} \\ =\text{ 2(8+6)} \\ =\text{ 2 }\times\text{ 14} \\ =\text{ 28} \end{gathered}[/tex]Answer:
Zoe's age = 28
Expand and state your answer as a polynomial in standard form. (4x³+y³)²
Answers
Answer:
16x⁶+y⁶
Step-by-step explanation:
(4x^3+y^3) (4x^3+y^3)
= 16x^6+y^6
Write an equation that represents the line.
Use exact numbers.
Answers
The equation that represents the line is y = -2x -3 which passes through the points (0, -3) and (1, -5).
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
From the graph:
The two points are:
(0, -3) and (1, -5)
The equation of the line:
y - (-5) = [-5 - (-3)]/[1] (x - 1)
y + 5 = -2(x - 1)
y = -2x -3
Thus, the equation that represents the line is y = -2x -3 which passes through the points (0, -3) and (1, -5).
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find the 7th term 18,6,2…
Answers
If we look at the series, one third of the current term gives the numerical value of the next term.
If we need to express it algebraically, we can write the following equation.
[tex]a_{n+1}=\frac{a_{n}}{3}[/tex]Therefore, our common multiplier can be found as follows. Because this sequence is a geometric sequence.
[tex]\frac{a_{n+1}}{a_{n}} =r=\frac{1}{3}[/tex]In geometric sequences, any term can be written in terms of the first term. Below is an example.
[tex]a_{n}=a_{1}.r^{n-1}[/tex]Since we know the numerical values of the first term and the common factor of the series, we can easily find the seventh term.
[tex]a_{7}=a_{1}.r^{7-1}[/tex][tex]a_{7}=18.(\frac{1}{3} )^6[/tex][tex]a_{7}=\frac{2}{81}[/tex]A bar of steel is 300 cm long. amin cuts two 45 cm lengths off the bar. he then cuts the rest of the bar into as many 50 cm lengths as possible. work out how many 50 cm lengths of bar amin cuts.
Answers
Answer:
Here is your Answer and I'm from South Africa
Hi , good afternoon/morning/night it would be really kind if u help.
Answers
Answer:
you can ask questions for clarification
A trader is given 15% discount on goods bought from a factory. If the original price of the item bought from the factory is ¢45000000, calculate I. The discount on the item.
II. The amount the trader paid for item
Answers
If a trader is given a 15 percent discount on the factory price of certain goods, the factory price being ¢45000000, then
(I) The discount amount will be ¢6750000
(II) The final amount that the trader will have to pay to buy the goods will be ¢38250000.
As per the question statement, a trader is given 15 Percent discount on goods bought from a factory and the original price of the item bought from the factory is ¢45000000.
We are required to calculate the discount amount, and the final amount that the trader will have to pay to buy the goods.
To solve this question, we simply need to calculate 15 percent of 45000000, and then subtract the calculated discount amount from ¢45000000.
Therefore, 15 percent of ¢45000000 = ¢[(15/100) * 45000000]
= ¢(15 * 450000)
= ¢6750000
That is, on 15 percent discount on the factory price of certain goods, the factory price being ¢45000000, the discount amount is ¢6750000.
And, considering the discount of ¢6750000 on the factory price of ¢45000000, the final amount that the trader will have to pay to buy the goods = ¢(45000000 - 6750000)
= ¢38250000.
Percent: In mathematics, a percentage is a number or a ratio expressed as a fraction with 100 as the denominator, and is often denoted using the percent sign, "%".Discount: In Mathematics and basic accountancy, a Discount is an amount of rebate which is subtracted from the selling price of an item, and the customer can pay that rebated price to own the item.To learn more about percents and discounts, click on the link below.
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Please help
It’s due tonight
Answers
Answer: 21
Step-by-step explanation:
Which answer choice is not a correct method to illustratethe answer to this problem?876 ÷ 43 = ?A) 876 ÷ 43 ≈ 20 B) 876 ÷ 43 = 20 16/43C) 876 ÷ 43 = 20.16D) 876 ÷ 43 = 20r16 note: the r stands for reminder
Answers
The answer to this question represents the possible choices that we have when solving a division.
When solving this division operation, and we use technology, we get the following result:
[tex]\frac{876}{43}=20.3720930233[/tex]Then, we can conclude that:
First CaseWe can conclude that the answer to this division is, approximately, 20. This could be an answer to this operation.
Second CaseIn this case, we can see the integer part of the answer, 20, and a fraction:
[tex]20\frac{16}{43}=20+\frac{16}{43}[/tex]And we know that:
[tex]undefined[/tex]Find the measure of angles 1 and 2
Answers
Answer:
both angles 1 and 2 measure 135°
Step-by-step explanation:
angle 1 = angle 2 = 135°
Hope this helps
One triangle in the diagram below can be mapped onto the other using two reflections. Identify the
lines of reflection that would map one onto the other. Can you map one triangle onto the other using
just one basic rigid motion? If so, explain.
Answers
Two reflections can be done as a rotation with a centre where the mirrors intersect.
If the mirrors are parallel then you can use a translation (slide) instead.
if the divided is 782 and the divisor is 1523 what is the quotient
Answers
If the dividend is 782 and the divisor is 1523, then the quotient is, 0.51.
What is dividend, divisor and quotient?
The dividend in this case refers to the number that is being divided. The divisor is the integer that divides a given number. The quotient is the sum that we arrive at as a result. The residual is the number that the divisor leaves after partially dividing the original integer.
Let x be the quotient after dividing 782 by 1523.
[tex]\frac{782}{1523} = x\\0.5134 = x\\x = 0.51[/tex]
Therefore, if the dividend is 782 and the divisor is 1523, then the quotient is, 0.51.
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a sample of experienced typists revealed that their mean typing speed is 95 words per minute and the median typing speed is 77 words per minute. the standard deviation of typing speed is 16.9 words per minute. what is the pearson's coefficient of skewness?
Answers
The pearson's coefficient of skewness is found as the 1.065.
What is termed as the coefficient of skewness?The coefficient of skewness is a measurement used to evaluate the strength and direction of skewness in a sample distribution using descriptive statistics such as mean, median, or mode. The skewness coefficient is used to compare a distribution of the sample to a normal distribution.Pearson skewness:
The skewness of the a data set is calculated by subtracting the mean from the median and dividing by the standard deviation.
In this case:
The mean is 95, the median is 77, as well as the standard deviation is 16.9. So,
Pearson skewness = (95 - 77)/16.9
Pearson skewness = 1.065.
Thus, the pearson's coefficient of skewness is found as the 1.065.
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74. The product of a nonzero integer and 12 has the same value as the product of 3 and the square of the integer. What is the integer?
E. 2
F. 3
G. 4
H. 6
Answers
4*12 = 48
3*16 = 48
suppose that y is independent of explanatory variables and it takes on the values -2, -1, 0, 1, 1 with equal probability. does this violate the gauss- markov assumption
Answers
the parameters we are estimating using the OLS method must be themselves linear
What are the Gauss Markov assumptions?
Gauss Markov Assumptions
Linearity: the parameters we are estimating using the OLS method must be themselves linear. Random: our data must have been randomly sampled from the population. Non-Collinearity: the regressors being calculated aren't perfectly correlated with each other.
What are the properties of Gauss Markov Theorem?
The Gauss-Markov theorem states that if your linear regression model satisfies the first six classical assumptions, then ordinary least squares (OLS) regression produces unbiased estimates that have the smallest variance of all possible linear estimators.
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Worth 19 points, pls help
Answers
Scale factor 1/5 = 3/5
look at photo MATHHHHHHHHHHHHHHHHHHHHHHHHHHHHH
Answers
The fraction is 47/200. The decimal is 0.235.
A percentage can be written in a fraction form by putting 100 on the denominator. For example, the fraction corresponding to x % is x/100.
For converting a percentage into a decimal first it should be converted into fractions as fractions can only be converted into decimal.
For example, the decimal for the fraction 50% is 0.5, which is given by writing 50% as 50/100 = 0.5 after putting decimal on 2 places left to 50.
So here the given percentage is 23.5%.
The corresponding fraction is 23.5/100 = 235/1000 = 47/200 after eliminating the decimal on the numerator and simplifying.
Now the corresponding decimal is, 0.235. Since 1000 is in the denominator for 235/1000, we can simply find the decimal by putting decimal point on 3 places left to 235.
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A woman has a total of $15, 000 to invest. She invests part of the money in an account that pays 6% per year
and the rest in an account that pays 10% per year. If the interest earned in the first year is $1020, how much did
she invest in each account?
Answers
Answer:
$4,000 in the 10% per year account
$11,000 in the 12% per year account
Find b for the given line.
y = 3x + b; (2, 7)
Answers
The value of b for the given line is 1
What is equation of line ?The set of points that make up a line in a coordinate system are represented algebraically by a line's equation. An equation of a line is an algebraic expression that represents the many points that together make up a line in the coordinate axis as a set of variables, x, and y. We may determine whether a given point lies on a line using the equation of any line.
Given that : y = 3x + b; (2, 7)
y =3x + b
7 = 6 + b
1 = b
The value of b for the given line is 1
The line's equation is a linear equation of degree one.
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g(a)=a²+2a-63 find g(8)
Answers
Answer:
g(8)=17
Step-by-step explanation:
Given :
g(a)=a²+2a-63
Substitute a = 8 :
g(8)=8^2+2(8)-63
= 64+16-63
=17
I REALLY NEED HELP PLEASE THIS WORK IS FOR MONDAY.can y’all please help me:(
Answers
The least common multiple for 12 and 15 is 60, the least common multiple for 6 and 15 is 30, and the least common multiple for 9 and 15 is 45.
What is the least common multiple?In mathematics, the term "least common multiple" is used to refer to a multiple of two or more numbers share and that is the smallest number possible.
How to identify the least common multiple?Mulitiply the numbers given by 1, 2, 3, 4, etc. until your find the first common number.
Lets use the numbers given
12 x 1 = 12 15 x 1 = 15
12 x 2 = 24 15 x 2 = 30
12 x 3 = 36 15 x 3 = 45
12 x 4 = 48 15 x 4 = 60
12 x 5 = 60
Based on this, the least common multiple is 60
6 x 1 = 6 15 x 1 = 15
6 x 2 = 12 15 x 2 = 30
6 x 3= 18
6 x 4 =24
6 x 5 =30
Based on this, the least common multiple is 30
9 x 1 = 9 15 x 1 = 15
9 x 2 = 18 15 x 2 = 30
9 x 3= 27 15 x 3 = 45
9 x 4 =36
9 x 5 =45
Based on this, the least common multiple is 45
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y=-2
4x-3y=18
explanation needed
Answers
Answer:-2
Step-by-step explanation: Substitute the given y-value into 4x−3y=18 and solve for x
11,000 with a 5/10/25 chain discount. Calculate the net price and trade discount
Answers
After the discount the net price is $7053.75 and the trade discount is 35.875% .
The term discount designates a sum or a percentage subtracted from an item's usual selling price.
A discount is a decrease in the cost of a commodity or service. Chain discounts can also be applied using the complement approach. To calculate each discount's complement, first subtract the discount from 100%. The net-price rate can be calculated by multiplying the complements to find the percentage that you really pay. The dollar value of the discount can also be determined using the complement technique.The given marked price of the article is 11000
Price after first discount of 5% = 11000 - 5% of 11000 = 10450
Price after second discount of 10% = 10450 - 10% of 10450 = 9405
Price after third discount of 25% = 9405 - 25% of 9405 = 7053.75
Therefore the net price is 7053.75.
Therefore the trade discount is = ( 11000 - 7053.75 ) ÷ 11000 = 0.35875
Trade discount percentage = 35.875%
Hence after the discount the net price is $7053.75 and the trade discount is 35.875% .
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