The longer ladder can reach 3 8/7 feet higher than the shorter one.
The Proportionality Theory.The longer ladder can reach 4 2/7 feet higher than the shorter ladder. To calculate this, we need to subtract the shorter ladder's height (12 5/7 feet) from the taller ladder's height (16 3/7 feet).We can represent this calculation with a fraction equation, as follows:[tex]\frac{16 \frac{3}{7}}{12 \frac{5}{7}} - 12 \frac{5}{7} = \frac{4 \frac{2}{7}}{1}[/tex]To solve this equation, we first need to convert the fractions into equivalent fractions with a common denominator. In this case, the denominator is 7. This means that the first fraction becomes 16 3/7, the second fraction becomes 12 5/7, and the third fraction becomes 4 2/7.Once we have the fractions in the same denominator, we can now subtract the shorter ladder's height (12 5/7 feet) from the taller ladder's height (16 3/7 feet). This gives us a result of 4 2/7 feet. This means that the longer ladder can reach 4 2/7 feet higher than the shorter ladder.To put this into perspective, if we were to use the ladders to reach a height of 16 3/7 feet, the shorter ladder would only reach 12 5/7 feet, while the longer ladder would reach 16 3/7 feet. This means that the longer ladder can reach 4 2/7 feet higher than the shorter ladder.To learn more about The Proportionality Theory refer to:
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If a partical traveled a distance of 9.0×1012 meters at a rate of 1.8×105 meters per second. If distance = rate x time, how many seconds did it take the particle to travel the specified distance?
A particle traveled a distance of 9.0×10¹² meters in 5.0 × 10⁷ seconds.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
If a particle traveled a distance of 9.0×10¹² meters at a rate of 1.8×10⁵meters per second.
And the distance,
= rate x time.
Rearranging the formula,
Time = Distance / rate
Time = 9.0×10¹² / 1.8×10⁵
Simplifying by using division operation,
Time = (9.0/1.8) × 10¹² × 10⁻⁵
Time = 5.0 × 10⁷
Therefore, the required specified time is 5.0 × 10⁷ seconds.
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help? anyone? please
Answer:
Step-by-step explanation:
Perimeter is the addition of all the sides.
So in this question, if you add up all the sides :
14x + 8x +7x +12
Simplify by adding all terms with x :
29x + 12
(As you can not add a number constant to a variable )
Parker could pay 45% of his college tuition with his scholarship. The remaining $10,500 he paid for a with a student loan. What was the cost of Parker's tuition? Show your work.
Answer:
5,775 for the cost of parking tuition
Step-by-step explanation:
45% = 0.45
0.45(10,500)= 4,725
10,500 - 4,725 = 5,775 for the cost of parking tuition
The Top-Notch Middle School had athletes from all the grades playing on a sports team.
6th grade 7th grade 8th grade
Basketball 2 4 7
Baseball 1 6 5
Soccer 7 4 4
Football 8 15 10
The Top-Notch Middle School had athletes from all the grades playing on a sports team.
Explain what the ratio 5:73 represents.
The ratio 5:73 represents the ratio of 8th grade baseball players to total athletes.
The ratio 5:73 represents the ratio of 7th grade football players to total athletes.
The ratio 5:73 represents the ratio of total athletes to 7th grade football players.
The ratio 5:73 represents the ratio of 6th grade athletes to total athletes.
Based on the information presented, the ratio represents 8th-grade baseball players to total athletes.
What is a ratio?A ratio is a mathematical expression that shows the proportion or the number of a specific element in a category compared to the number of another element in the same category. For example, if you count the animals on a farm the ratio of cows to chickens can be 5:7, which means that for every 5 cows there are 7 chickens.
What does the ratio 5:73 mean?5 : This is the number of baseball players who are in 8th-grade
73: This is the total of players. You get this number if you add all the numbers given.
Based on this, this ratio is comparing the number of baseball players and total players, which means the meaning of this ratio is " the ratio of 8th grade baseball players to total athletes".
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If you have 20 balls (10 black, 10 white) and two urns, how could you place the balls into the urns so as to maximize your chance of drawing a black ball
To fill one urn with one white ball and the second urn with the remaining nine white and ten black balls.
Explain about the probability?Probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
By dividing the number of preferable possibilities by the total number of potential outcomes, probability, which measures the likelihood that an event will occur, is obtained. A coin flip is the most basic illustration. There are only two outcomes that can occur when you flip a coin: either heads or tails.
The basic probability formula is: Probability = Number of Favorable Outcomes / Total Number of Outcomes. or P(A) = f/N
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please help: If ray AD bisects ∠BAC, find each measure:
∠DAC=
∠BAC=
PL=
BD=
∠DAC = 28°
∠BAC = 56°
PL = 20
BD = 31
What is Bisection?Bisection is the division of something into two equal or congruent parts, usually by a line, which is then called a bisector.
An angle bisector divides an angle into equal angles. If the angle is p°, the two angles made will be (p/2)°. This angle bisector passes through the vertex of an angle.
Example: Consider an Angle ∠ABC = 90°. An angle bisector will cut it into two equal angles of 45° each.
Given, AD bisects ∠BAC
MP = 20
DC = 31
∠BAD = 28°
AD bisects ∠BAC
⇒ ∠BAD = ∠DAC
⇒ ∠DAC = 28°
∠BAC = ∠BAD + ∠DAC
∠BAC = 28° + 28°
∠BAC = 56°
Since, In a figure, sides opposite to the equal angles are also equal
∠BAD = ∠DAC
⇒ BD = DC
⇒ BD = 31
⇒ BD = 31
By the figure,
∠MAP = ∠BAD and ∠PAL = ∠DAC
⇒ ∠MAP = ∠PAL
⇒ MP = PL
⇒ PL = 20
Hence, by the above calculation the measure of ∠DAC = 28°,
∠BAC = 56°, PL = 20, BD = 31.
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Is 2 a zero of the polynomial x³ 4x² 3x?
2 is not a polynomial root of [tex]x^{3} + 4x^{2} + 3x[/tex] . A polynomial is an equation that employs addition, subtraction .
what is polynomial ?A polynomial is a mathematical statement made up of variables (also known as indeterminates) and coefficients that uses solely the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. A polynomial is an equation that employs addition, subtraction, multiplication, and division of numbers to combine variables, constants, and exponents (No division operation by a variable).
given
[tex]x^{3} + 4x^{2} + 3x[/tex]
= [tex]2^{3} + 2^{2} + 3(2) = 0\\8 + 4 + 6 = 0 \\18= 0[/tex]
Consequently, 2 is not a polynomial root of [tex]x^{3} + 4x^{2} + 3x[/tex] .
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11. Which of the following is a solution to the
inequality c + 4 <-7?
(1) -15
(2) -10
(3) -5
(4) O 0
(5) 10
Answer:
-15
Step-by-step explanation:
That's the answer because
-15+4=-11
-15+4=-11-11<-7
A card is drawn from a standard deck of 52 cards. What is the theoretical probability, as a decimal, of drawing a number 8? Round the decimal to the nearest hundredth.
The probability of picking a card at random from a standard deck of 52 cards is 0.019 or 0.02(approx)
What is probability?Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening being equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.
Given here: A card is drawn from a standard deck of 52 cards. Let the probability be P then P= 1/52
=0.02
Hence, The probability of picking a card at random from a standard deck of 52 cards is 0.019 or 0.02(approx)
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A certain paint is to be mixed with 3 parts yellow to 2 parts blue. What is the ratio of yellow paint to the total amount of mixed paint
The ratio of yellow paint to mixed paint is 3/5.
What are ratio and proportion?A ratio is a comparison or relationship between two amounts of the same quantity to determine how much larger one number is than the other. Where b is not equal to zero, it is written as a/b or a: b. An equality of two ratios is a proportion. In order to write equivalent ratios, proportions are used, which aids in resolving the unknown quantities. As an illustration, a proportion is written as a: b = c: d.
Solution:-
Given,
Amount of yellow paint=3
Amount of blue paint=2
Ratio=yellow paint/total mixed paint
Ratio=3/(3+2)
Ratio=3/5
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PLEASE HELP ME ASAP!!!!!!!!!
In a school, 10% of students have 7 ball pens, 30% of students have 3 ball pens, 40% of students have 2 ball pens and 20% of students have 1 ball pens. What is the expected number of ball pens of a student?
The expected number of ball pens of a student is 2.4.
What is the expected number?
In statistics and probability analysis, the expected value is calculated by multiplying each of the possible outcomes by the likelihood that each outcome will occur and then summing all of those values.
The expected number of ball pens of a student can be calculated by taking a weighted average of the number of ball pens that each group of students has.
The weight for each group is the percentage of students that are in that group.
So, we can calculate the expected number of ball pens of a student by:
(10% * 7) + (30% * 3) + (40% * 2) + (20% * 1)
0.7 + 0.9 + 0.8 + 0.2
The expected value is also known as the population means and it can be calculated by summing the product of each outcome’s probability and its corresponding value.
Here, the outcome is the number of ball pens.
Hence, the expected number of ball pens of a student is 2.4.
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What is a algebraic expression for 1,10,19
The algebraic expression for the given sequence 1, 10, 19 as required to be determined is; a (n) = 1 + ( n - 1 ) 9.
What is the algebraic expression for the given sequence?As evident in the task content; it follows that the common difference of the given sequence is constant since; 19 - 10 = 10 - 1 = 9.
On this note, since the nth term of arithmetic sequences take the form;
a (n) = a (1) + ( n - 1 )d
Since the first term is; 1 and the common difference is; 9; the resulting algebraic expression is;
a (n) = 1 + (n - 1)9.
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Each grid square is 1 square unit. Find the area, in square units, of the shape without counting every square. Be prepared to explain your reasoning.
The total area of the two rectangles is given by the equation A = 33 units²
What is the Area of a Rectangle?The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle
Area of Rectangle = Length x Width
Given data ,
Let the total area of the 2 rectangles be A
Now , each grid square represents = 1 square unit
Now , let the first rectangle be represented as P
The length of P = 4 grid squares
The width of P = 3 grid squares
Let the second rectangle be represented as Q
The length of Q = 7 grid squares
The width of Q = 3 grid squares
So , Area of Rectangle = Length x Width
The area of rectangle P = 4 x 3
The area of rectangle P = 12 units²
The area of rectangle Q = 7 x 3
The area of rectangle Q = 21 units²
So , the total area of figure A = area of P + area of Q
On simplifying the equation , we get
Total area of figure A = 12 units² + 21 units²
Total area of figure A = 33 units²
Therefore , the value of A is 33 units²
Hence , the area is 33 units²
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HELPPPPPPP MEEEEE
If a trapezoid has an area of 135cm^2 and it’s height is 10cm and one base is 12 cm, find the other base length.
thxxx <333
The length of other base is 15 cm.
The area of a trapezoid can be found by using the formula:
Area = (b1+b2) * h / 2 where b1 and b2 are the lengths of the bases, and h is the height.
Given that the area of the trapezoid is 135 cm^2, the height is 10 cm, and one base is 12 cm, we can substitute these values into the formula to find the length of the other base.
Area = (b1+b2) * h / 2 = 135cm^2
We can solve for the other base length by isolating b1
b1 = 2*Area/h - b2
b1 = 2*135/10 - 12 = 27 - 12 = 15
So, the other base length is 15 cm.
Therefore, The length of other base is 15 cm.
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five plus two times a number n is less than or equal to eleven. select all of the representation's that are solutions.
1) n less than or equal to 3
2) 3 less than or equal to n
3) n less than or equal to 8
4) 3 greater than or equal to n
Answer:
The worded problem translates to n ≤ 3
The options that are solutions to the problem are 1 and 4:
1) n less than or equal to 3, and
4) 3 greater than or equal to n (since 3 ≥ n)
Step-by-step explanation:
Let's translate the e=words into expressions:
"five plus two times a number n" becomes 5 + 2n
"is less than or equal to eleven" becomes ≤ 11
Put the two expressions together, with the word "is" and the "=" sign:
5 + 2n ≤ 11
Solving:
2n ≤ 11 - 5
2n ≤ 6
n ≤ 3
The options are:
1) n less than or equal to 3 Correct
2) 3 less than or equal to n Incorrect. 3 is greater than or equal to n
3) n less than or equal to 8 Incorrect. n is less than or equal to 3
4) 3 greater than or equal to n Correct 3 ≥ n
Jay and kevin are shoveling the snow off a driveway. working together, they can clear the driveway of snow in 14 minutes. working alone, it would take kevin 21 minutes longer to clear the driveway of snow than it would take jay working alone. when j is the number of minutes it would take jay to clear the driveway of snow when working alone, the situation is modeled by this rational equation: how long would it take jay to clear the driveway of snow working alone?
a. 7 minutes
b. 21 minutes
c. 35 minutes
d. 42 minutes
Therefore, As a result, the answer to the given equation problem is Jay would need to work alone for 21 minutes to remove the snow from the driveway.
Define equation .
A number, a variable, or a mix of both plus certain operation symbols make up an expression. An equal sign separates two expressions that make up an equation. Word illustration The product of 8 and 3 is 11.
Here,
The formula is: 1/j +1/j+ 21 = 11/ 4.
LCM = j+21+j / j(j+21)=1/14
Thus, 2j+21 / j(j+21) = 1/14 is obtained.
14(2j+21) times itself yields j(j+21).
28j+294 expanded to j²+21j
Gather comparable terms
j²+21j-28j-294=0
j²- 7j-294=0
With the use of a graphing calculator, we have:
j = 21 or j= -14
Due to the context,
j's value cannot be negative.
As a result, the answer to the given equation's problem is Jay would need to work alone for 21 minutes to remove the snow from the driveway.
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I need help with six and seven
Answer: Perimeters Are Shown Below
Step-by-step explanation:
6. 2 Hexagons; 1+1+1+1+1+1+1+1+1+1 OR 1 x 10
6. 3 Hexagons; 1+1+1+1+1+1+1+1+1+1+1+1+1+1 OR 1 x 14
7. 2 Pentagons; 1+1+1+1+1+1+1+1 OR 1 x 8
7. 3 Pentagons; 1+1+1+1+1+1+1+1+1+1+1 OR 1 x 11
What is the Contrapositive of P → Q?
"If p then q" is a conditional statement, and its contrapositive is If ~q then ~p.
Knowing about the inverse statement makes it simple to comprehend how to build a contrapositive statement. Take the negation of the hypothesis and the conclusion to produce the conditional statement's opposite.
Create the inverted statement first, then swap the hypothesis and conclusion to create the contrapositive of the conditional statement. Adding "not" to both component statements and switching the order of the provided conditional statements will result in contrapositive assertions, in other words.
If a number n is even, then n2 is even, and vice versa, is the contrapositive statement to "If a number n is even, then n2 is even."
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F= 5 9 (K−273)+32space, F, equals, start fraction, 9, divided by, 5, end fraction, left parenthesis, K, minus, 273, right parenthesis, plus, 32 In order to convert a temperature in Kelvin, KKK, into a temperature in degrees Fahrenheit, FFF, the equation above can be used. Which of the following equations correctly expresses the temperature in Kelvin in terms of the temperature in degrees Fahrenheit?
The formula for K in terms of F is [tex]K = \frac{5}{9} (F-32) + 273[/tex]
The given expression:
[tex]F = \frac{9}{5} (K-273) + 32[/tex]
Conversion from Kelvin (K) to degrees Fahrenheit (F)To find the formula for K
The formula for K is obtained by making K the subject of the formula as shown below:
[tex]F = \frac{9}{5} (K-273) + 32[/tex]
subtract 32 from LHS.
[tex]F-32 = \frac{9}{5} (K-273)[/tex]
multiply 5 with LHS
[tex]5(F-32) = 9(K-273)[/tex]
Take numerator 9 to LHS
[tex]\frac{5}{9}(F-32) = K-273[/tex]
take -273 from RHS to LHS
[tex]\frac{5}{9}(F-32) + 273 = K[/tex]
Thus the formula for K in terms of F is [tex]K = \frac{5}{9} (F-32) + 273[/tex]
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Question 2 of 15
Select the table that represents a linear function (Graph them if necessary)
OA
0123
1437
8 x 0
-
012
#2
203
23
24816
2
m
19
1125
(a+b+c)(a-b+c)=a2+b2+c2 prove
Answer:
There might be an error in the question, the result below should be the correct answer. It is not possible for a^2+b^2+c^2 to be the answer.
(a+b+c)(a-b+c) = a^2 +2ac - b^2 + c^2
Step-by-step explanation:
(a+b+c)(a-b+c) = a^2 - ab +ac + ba - b^2 +bc + ca - cb + c^2 (expanding the two terms in brackets first)
Since ab = ba, ac = ca and bc = cb,
-ab and ba can be cancelled out
bc and -cb can be cancelled out
Hence, (a+b+c)(a-b+c) = a^2 +2ac - b^2 + c^2
This is what I have obtained through expansion, then simplification by cancelling out the common terms.
Could you help check the question again?
35. Solve the following, giving your answer as a fraction in its lowest terms 5 3/4 ÷ 1 1/2
The fraction after solving and simplifying the mixed fraction 5 3/4 ÷ 1 1/2 is 23 / 6.
What is the mixed fraction?A mixed fraction is a fraction that is created by fusing a fraction with a whole number. For instance, 8 1 / 2 is a mixed fraction if 8 is a whole number and 1/2 is a fraction.
Given:
5 3/4 ÷ 1 1/2
Solve the mixed fraction into improper fractions as shown below,
5 × 4 + 3 / 4 ÷ 1 × 2 + 1 / 2
20 + 3 / 4 ÷ 2 + 1 / 2
23 / 4 ÷ 3 / 2
23 / 4 × 2 / 3
23 × 2 / 4 × 3
On simplifying,
23 × 1 / 2 × 3
23 / 6
Thus, the value is 23 / 6.
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Given ƒ(x) = − x² – 14, find ƒ (6)
Answer:
f(6) = - 50
Step-by-step explanation:
substitute x = 6 into f(x) , that is
f(6) = - 6² - 14 = - 36 - 14 = - 50
Answer:
-50
Step-by-step explanation:
f ( x ) = - x² - 14
Accordingly, to find the value of f ( 6 ) you have to replace x with ( 6 ).
f ( 6 ) = - (6)² - 14
f ( 6 ) = - 36 - 14
f ( 6 ) = -50
If triangle NPZ ~ triangle HBZ find the measure of angle B.
Please show the steps
The measure of angle B is 107°.
What do similar triangles mean?
If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable. Similar figures are described as items with the same shape but varying sizes, such as two or more figures.
Given a triangle, NPZ is similar to triangle HBZ.
Which can also be written as ΔNPZ ≈ ΔHBZ
So, by equating the corresponding angles that are angle P = angle B:
8x-37°=180-(2x-5+42)°
10x=180
x=18°
So, H=36-5=31°
Since the sum of all angles in a triangle is 180°, angle B can be calculated as
B= 180°-(42+31)°
B=107°
Therefore the measure of angle B is 107 degrees
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The volume of a cylinder is 60 cubic centimeters. What is the number of cubic centimeters in the volume of the sphere it circumscribes
Call the radius of the cylinder and sphere, r And the height of the cylinder = 2r
How to Calculate Volume in Cubic Centimeters?Calculating volume is just another way of saying that you're measuring the amount of space inside a three-dimensional object. You can use standardized formulas for calculating the volume of shapes like cubes, cylinders and spheres, as long as you know their basic measurements.So60 = pi * r^2 * 2r30 = pi * r^330/pi = r^3[30/pi]^1/3 = rSo...the volume of the sphere is(4/3)pi [ (30/pi)^1/3 ]^3 =(4/3) pi * 30/pi =40 cm^3A cubic centimetre (or cubic centimeter in US English) (SI unit symbol: cm3; non-SI abbreviations: cc and ccm) is a commonly used unit of volume that corresponds to the volume of a cube that measures 1 cm × 1 cm × 1 cm. One cubic centimetre corresponds to a volume of one millilitre.How to Work out Volume with Cubic Centimetres. If a container was filled with water and it had a length of 20 cm, a height of 5 cm and a depth of 4 cm to work out the volume of water you would need to multiply all 3 numbers together. 20 cm x 5 cm x 4 cm = 400 cm³To learn more about Volume in Cubic Centimeters refers to:
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I need help.
professional?
- needed
The equation of the linear function after a translation down 9 units is given as follows:
f(x) = x - 11.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change of the output variable relative to the input variable.b is the y-intercept, representing the value of y at which the graph cross the y-axis.The graph of the function crosses the y-axis at y = -2, hence the intercept b is given as follows:
b = -2.
When x increases by 2 units, from x = 0 to x = 2, y increases by 2 units, from y = -2 to y = 0, hence the slope is calculated as follows:
m = 2/2.
Then the function is of:
y = x - 2.
After the translation down 9 units, 9 is subtracted from the function, hence:
f(x) = x - 2 - 9
f(x) = x - 11.
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How do you find the x-intercept and vertex of a quadratic function?
We can find the x-intercept by writing the equation in intercept form which is also known as factored form, y= (x-p) (x-q) where p, q are the x-intercepts.
To find the vertex of the quadratic function we can write the function in standard form , the vertex is located at the point where y=f (x).
A function which has a degree of two is known as a quadratic function.
Example, 3x² + 2 , here the maximum degree is 2 , hence the given function is quadratic. The general form of a quadratic equation is given as ,
f(x) = ax2 + bx + c .
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Please Answer This For Me<33
Answer:
a) 4.2 - 2.8 = 1.4
b) 72.1 - 45.6 = 26.5
c) 82.2 - 41.3 - 29.2 = 11.7
d) 17.1 - 11.7 - 0.8 = 4.6
e) 29.2 - 12.5 - 0.9 = 15.8
f) 21 - 14 = 7
g) 71 - 37 - 18 = 16
h) 50 - 19 - 8 = 23
i) 92 - 57 - 16 = 19
j) 44 - 18 - 9 = 17
Jump to level 1
Housing prices in a small town are normally distributed with a mean of
$142,000 and a standard deviation of $7. 0. Use the empirical rule to
complete the following statement.
Approximately 95% of housing prices are between a low price of
$ Ex: 5000 and a high price of $
Modul Three Assignment Gui.
4. 2. Normal distribution - Goog.
By standard deviation, 68% housing price are between a low price of $135000 and a high price of $149000.
What is standard deviation in math?
The variability in your dataset is measured by its standard deviation. It reveals the average deviation between each result and the mean.
A low standard deviation denotes that values are grouped close to the mean, whereas a large standard deviation shows that values are often far from the mean.
Given,
mean (μ) = 142000
standard deviation (σ ) = 7000
By using empirial rule,
P( μ - σ ≤ X ≤ μ + σ ) ≈ 68%
Then,
P(142000 - 7000 ≤ x ≤ 142000 + 7000 ) ≅ 68%
P( 135000 ≤ x ≤ 149000 ) ≅ 68%
68% housing price are between a low price of $135000 and a high price of $149000.
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In tenpin bowling, the height of each bowling pin must be 15 inches with an absolute deviation of 0.03125 inches find the minimum and maximum possible heights of the bowling pin.
The minimum and maximum possible heights of the bowling pin are 14.96875 inches and 15.03125 inches
How to find the minimum and maximum possible heights of the bowling pin.From the question, we have the following parameters that can be used in our computation:
Absolute deviation = 0.03125 inches
Height = 15 inches
The minimum is calculated as
Minimum = Height - Absolute deviation
Substitute the known values in the above equation, so, we have the following representation
Minimum = 15 - 0.03125 inches
Minimum = 14.96875 inches
The maximum is calculated as
Maximum = Height + Absolute deviation
Substitute the known values in the above equation, so, we have the following representation
Maximum = 15 + 0.03125 inches
Minimum = 15.03125 inches
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