The experimental probability of landing on a number greater than 4 is 0.25 or 25%.
To find this probability, we need to determine the number of successful outcomes (landing on a number greater than 4) and divide that by the total number of trials (60).
The successful outcomes are 5 and 6, with a frequency of 10 and 8 respectively. To add these two frequencies together, we can use 10 + 8 = 18.
So, the experimental probability is 18/60 = 0.3 or 25%.
It's important to note that experimental probability is based on the outcomes of an experiment or a sample and it may not be the same as a theoretical probability which is based on the ratio of favorable outcomes to the total number of outcomes in a theoretical model.
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the answer in fraction form is 18/60
if thats what you are looking for.
2. Use function notation to represent each statement.
a. Six hours after it started raining, the amount of rain was 37 millimeters.
b. The amount of rain 90 minutes after it started raining was the same as the amount 120 minutes after it started raining
a. Let t represent the time in hours when it started raining. We can use function notation to represent the amount of rain r at any time t with r(t) = 37 millimeters. This is because after 6 hours, the amount of rain was 37 millimeters. Therefore, we can use the equation r(t) = 37 millimeters to represent this statement.
b. We can use function notation to represent the amount of rain at any time t with r(t) = r(t-1.5). This is because the amount of rain 90 minutes after it started raining was the same as the amount 120 minutes after it started raining. Therefore, we can use the equation r(t) = r(t-1.5) to represent this statement.
This type of function notation is useful for representing relationships between different values related to the same property or phenomenon. It allows us to quickly and easily analyse and compare data, as well as make predictions about future values. It is also useful for describing how certain parameters are changing over time.
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Workout the maximum number of hiker who could have walked between 6 mile and 17 mile
The minimum number of hikers who could have walked between 6 miles and 17 miles is 9 and the maximum number of hikers who could have walked between 6 miles and 17 miles is 19.
The minimum number refers to the smallest value that is possible, allowed, or required based on the given interval. The maximum number refers to the largest value that is possible, allowed, or required based on given interval. The provided table provides intervals for the number of miles x the number of hikers can walk and the corresponding number of hikers.
In order to determine the minimum and maximum number of hikers that could walk between 6 miles and 17 miles, we look at the intervals which include the range between 6 miles and 17 miles.
a) The minimum value is determined by considering the common interval 10 ≤ x < 15 (5 ≤ x < 10 and 15 ≤ x < 20 are not considered as it includes values outside the range). Hence the corresponding number of hikers is 9.
b) The maximum value is determined by considering all the intervals which include the range between 6 miles and 17 miles, i.e. 5 ≤ x < 10, 10 ≤ x < 15, 15 ≤ x < 20. Hence, the maximum number of hikers is 2 + 9 + 8 = 19.
Note: The question is incomplete. The complete question probably is: The table below shows information about the distance walked by some hikers. a) Work out the minimum number of hikers who could have walked between 6 miles and 17 miles. b) Work out the maximum number of hikers who could have walked between 6 miles and 17 miles.
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Doug etimate that hi occer team will win 7 game thi year. The team actually win 10 game. What i the percent error of Doug' etimate? Round the anwer to the nearet tenth percent if neceary
Doug's estimate was incorrect by 30% because probability his team won 10 games instead of the 7 he predicted.
Doug estimated 7 wins
Actual number of wins was 10
Error = (Actual - Estimate) / Estimate x 100
Error = (10 - 7) / 7 x 100
Error = 3 / 7 x 100
Error = 30%
Doug estimated that his soccer team would win 7 games this year. However, the team ended up winning 10 games in total. This means that Doug's estimate was incorrect by 30%. To calculate this percent error, we used the following formula: Error = (Actual - Estimate) / Estimate x 100. In this case, the actual number of wins was 10 and the estimate was 7. Plugging these numbers into the formula, we got that the error was 3/7 x 100, which is equal to 30%. This means that Doug's estimate was off by 30%. This is a significant overestimate since the team ended up winning 3 more games than what Doug had predicted.
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How many three digit numbers are divisible by 7?.
There are 128 three digit numbers divisible by 7
We know that the divisibility rule of 7 is:
If the difference between twice the unit digit of the given number and the remaining part of the given number is multiple of 7 or the difference is 0, then the number is divisible by 7.
the range of three digit numbers is 100 to 999
The first three-digit number divisible by 7 is 105 and the last three-digit number divisible by 7 is 994.
The numbers divisible by 7 must be: 105, 112, . . ., 994
We can observe that the above series represents the arithmetic progression with common difference d = 7, the first term a = 105 and the last term a_n = 994
We know that the formula for the n-th term of AP is:
a_n = a1 + (n - 1)d
994 = 105 + (n - 1)7
7n - 7 = 889
7n = 889 + 7
7n = 896
n = 128
Thus, there are 128 three digit numbers.
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(Theoretical Probability LC)
When rolling a fair, eight-sided number cube, determine P(number greater than 6).
A: 0.25
B: 0.50
C: 0.66
D: 0.75
Answer:0.25
Step-by-step explanation:
i passed the test
A giant balloon i dropped from a plane landing on tahir and zach at point w(42,-15) and ending two friend flying off an equal ditance in oppoite direction. Of tahir end up at coordinate t(-18,36) where would we expect to find zack
Zack is expected to be at (-12,-10.5) by finding the midpoint of line segment WT and reflecting T over it.
What is coordinate ?
A coordinate is a set of numerical values that are used to identify the position of a point in a specific space, such as a two-dimensional plane or a three-dimensional space. In two-dimensional space, coordinates are commonly represented by an ordered pair (x, y) or (x, y, z) in three-dimensional space.
The problem states that the balloon lands at point W(42,-15) and Tahir ends up at point T(-18,36). We know that Tahir and Zack are flying off in opposite directions from point W at equal distances. To find the point where Zack is expected to land, we can use the midpoint formula which states that the midpoint of a line segment is the average of the x-coordinates and the average of the y-coordinates.
We can find the midpoint of line segment WT by taking the average of the x-coordinates and y-coordinates:
x_midpoint = (x1 + x2) / 2 = (42 + -18) / 2 = 12
y_midpoint = (y1 + y2) / 2 = (-15 + 36) / 2 = 10.5
So the midpoint of line segment WT is (12,10.5). Since Zack is flying off in the opposite direction from Tahir at the same distance, we can expect Zack to end up at the point which is the reflection of point T over the midpoint of line segment WT.
This point would be (-12,-10.5)
Therefore , Zack is expected to be at (-12,-10.5) by finding the midpoint of line segment WT and reflecting T over it.
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What is the difference between a frequency histogram and a relative frequency histogram?
The vertical axis of a relative frequency histogram employs relative or proportional frequency rather than plain frequency, which is the only difference between it and a frequency histogram.
Explain the difference between frequency and relative frequency?Frequency can be expressed most simply in absolute terms. The number of times a specific value for a variable (data item) has been seen to occur in relation to the overall number of values for that variable is referred to as the relative frequency.Histogram is a term from the quality glossary. The frequency distribution of a collection of data reveals how frequently each unique value appears. The most typical graph for displaying frequency distributions is a histogram. Although it closely resembles a bar chart, there are significant variances.Relative frequencies, on the other hand, do not employ raw counts. Instead, they use percentages, proportions, or fractions to compare the count for one type of event to the entire number of events. The word "relative" refers to a specific tally in relation to the overall number, which is where it is used.Learn more about frequency histogram refer to :
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What is the value sin 45?.
The Sin 45 value is 1/√2.For the purpose of determining the Sin 45 value, let's use the ABC right angle triangle.
The ratio of a triangle's opposing side's length to its hypotenuse is known as the Sin of an angle.
Sin ϴ = Opposite side or perpendicular / Hypotenuse
Sin ϴ = AC/AB
Sin ϴ = B/C
Calculation of the Value of Sin 45 Degree in Fraction
Sin 45 = √2/
= 1 / √2
Consider a right triangle with angle X= 45°,then it is obvious that third will also be 45°.hence the side length of triangle are L, L, √2L .then apply
sin 45°= L/√2L
Sin 45°= 1/√2
Sin 45°=0.7071
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How do you find the height of a 45 45 90 triangle?.
The height of a right triangle can be calculated, given the length of the base, and the height of a right triangle formula can be calculated using the Pythagoras theorem as, (Hypotenuse)² = (Height)² + (Base)².
A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.
In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.
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What is meant by a substitution reaction give an example with equation of the substitution reaction of an alkene?.
A substitution reaction is one in which one (or more) hydrogen atoms from a hydrocarbon are swapped out for another atom (like chlorine).
Example: Substitution reaction of methane with chlorine:
Methane reacts with chlorine in the presence of sunlight to form chloromethane and hydrogen chloride.
[tex]CH_{4} + Cl_{2}[/tex] ---------> [tex]CH_{3} Cl + HCl[/tex]
When one functional group in a chemical molecule is replaced by another functional group, the chemical reaction is known as a substitution reaction. In organic chemistry, substitution reactions are of utmost significance.
An alkene is a hydrocarbon with a carbon-carbon double bond in organic chemistry. Alkene, which refers to any hydrocarbon with one or more double bonds, is frequently used as a synonym for olefin.
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(−9,7)left parenthesis, minus, 9, comma, 7, right parenthesis and
(
−
6
,
−
3
)
(−6,−3)left parenthesis, minus, 6, comma, minus, 3, right parenthesis.
The equation of the line through (-9,7) and (-6,-3) is y = (10/3)x + (61/3).
What is equation?An equation is a mathematical statement that expresses the equality of two expressions. It typically consists of two expressions on either side of an equals sign, and it indicates that the expressions have the same value.
The equation of the line through (-9,7)(−9,7)left parenthesis, minus, 9, comma, 7, right parenthesis and (-6,-3)(−6,−3)left parenthesis, minus, 6, comma, minus, 3, right parenthesis can be expressed in slope-intercept form as y = mx + b, where m is the slope and b is the y-intercept.
To calculate the slope, we can use the formula m = (y2 - y1)/(x2 - x1). Plugging in the coordinates, we get m = (7 - (-3))/(-9 - (-6)) = 10/3.
To calculate the y-intercept, we can use the formula b = y - mx. Plugging in the coordinates and the slope we just calculated, we get b = 7 - (10/3)(-9) = 61/3.
Therefore, the equation of the line through (-9,7) and (-6,-3) is y = (10/3)x + (61/3).
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Complete Question:
Complete the equation of the line through (-9,7)(−9,7)left parenthesis, minus, 9, comma, 7, right parenthesis and (-6,-3)(−6,−3)left parenthesis, minus, 6, comma, minus, 3, right parenthesis.
The equation of the line through (-9,7) and (-6,-3) is y = (10/3)x + (61/3).
What is the equation?A mathematical statement that expresses the equivalence of two expressions is known as an equation. It typically consists of two expressions on either side of an equal sign, and it indicates that the expressions have the same value.
The equation of the line through (-9,7)(−9,7), and (-6,-3)(−6,−3) can be expressed in slope-intercept form as y = mx + b, where m is the slope and b is the y-intercept.
To calculate the slope, we can use the formula m = (y₂ - y₁)/(x₂ - x₁). Plugging in the coordinates, we get
m = (7 - (-3))/(-9 - (-6))
= 10/3.
To calculate the y-intercept, we can use the formula b = y - mx. Plugging in the coordinates and the slope we just calculated, we get b = 7 - (10/3)(-9) = 61/3.
Therefore, the equation of the line through (-9,7) and (-6,-3) is y = (10/3)x + (61/3).
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The complete question:
Complete the equation of the line through (-9,7)(−9,7)left parenthesis, minus, 9, comma, 7, right parenthesis and (-6,-3)(−6,−3)left parenthesis, minus, 6, comma, minus, 3, right parenthesis.
Write the ratio 1.8 : 4.2 inches Simplest for
The most simplified form of the given ratio 1.8: 4.2, which is a ratio of lengths in inches is 3/7.
What is meant by ratios?
In mathematics, a ratio shows how frequently one number appears in another. When expressed as a:b, a fraction has the form of a ratio. A ratio is a comparison or compressed version of two identical values. Like fractions, ratios can be entirely simplified. Divide all of the numbers in a ratio by the same number to make it simpler. Divide each integer in a ratio by their largest common factor to fully simplify the ratio. The ratio's numbers must always be whole numbers.
Given the ratio, 1.8: 4.2
The ratio can be simplified by dividing both the terms in the ratio by the highest common factor.
The highest common factor of 1.8 and 4.2 is 0.6.
So we divide both terms by 0.6.
1.8: 4.2 = 1.8/0.6 : 4.2/0.6 = 3:7
Therefore the simplified form of the given ratio, 1.8: 4.2 is 3:7.
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Nate has $50 to go spend at the grocery store. He feels shopping cart with items total and $46. I’ll check out he will have to pay 6% sales tax on all items in the cart. Does he have enough money to buy everything in his cart?
Nate have enough money to buy everything in his cart because his total expenses is lees than 50 dollars.
How to check if his money is enough to buy the grocery using the sales tax?Nate has $50 to go spend at the grocery store. He fills his shopping cart with items total and $46. He will have to pay a sales tax of 6% on al items on the cart.
Therefore, let's check if Nate have enough money to buy the groceries.
Hence,
sales tax amount = 6% of 46
sales tax amount = 6 / 100 × 46
sales tax amount = 276 / 100
sales tax amount = 2.76 dollars
Therefore,
the amount in total of the grocery = 46 + 2.76 = 48.76 dollars
Therefore, he has enough money to pay for his groceries.
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What is the range of f/x )= Logbx?.
The range of the function f(x) = logbx is {y | y > 0}.
The range of the function f(x) = logbx is the set of all possible output values (or "y-values") that the function can produce. In this case, the function is a logarithm in base b, where b is a positive real number, and x is the argument of the logarithm, also a positive real number.
For a logarithm function, the range is all real numbers y such that y > 0, because the logarithm of a positive number is always positive. The domain of the function is all positive real numbers x because the logarithm of a positive number is always defined.
So, the range of the function f(x) = logbx is {y | y > 0}.
It's worth noting that the logarithm function is defined only for positive real numbers x, hence the domain of this function is x > 0 and the range is y > 0.
Also, the base of the logarithm b is a positive real number, different than 1, this ensures that the logarithm function is defined for all x > 0, for b = 1 it would not be defined for x = 1.
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Select the number below that is irrational.
O 5462.263
O √19
O 13/24
O 3.33333
The number that is irrational is √19.
An irrational number is a number that cannot be expressed as a ratio of two integers (a fraction) and it cannot be represented as a repeating or terminating decimal. The square root of 19 is an irrational number because it cannot be expressed as a ratio of two integers. It is non-repeating, non-terminating decimal that goes on forever, so it cannot be represented as a decimal.
NEED HELP ASAP!!
Which ratio is equal to the ratios plotted on the graph?
A- 4/2
B- 2/3
C- 1/2
D- 10/14
Answer:
Hi i found the answer 3/2 could you please check your options?
if you apply the slope formula here,
12-6/8-4 gives you the value 6/4 which is 3/2
good luck!
Which equation goes through the point (-6,2) and is perpendicular to y=3x-8
A. Y - 2 = 1/3 (x+6)
B. Y = 3x - 5
C. Y - 2 = -1/3 (x + 6)
D. Y = -3x + 6
Correct option is C, the correct equation is Y - 2 = -1/3 (x + 6).
Y=mx+b, where m is the slope and b is the y-intercept, is the slope intercept form. The graph of the linear equation can be drawn on the x-y coordinate plane using this form of the equation. Y = m x + b y=mx+b y=mx+by, equals, m, x, plus, b, where m is the slope and b is the y-intercept, is the slope intercept form.
Given points are (-6,2)
The required line should be perpendicular to y=3x-8.
When two lines are perpendicular,
their slopes are such that,
m1 = - 1/m2 [1]
⇒ slope of line 2 =
⇒ -1/3 [using (1) relationship ]
Now substituting the points are slope in the equation of line -
y - y₀ = m (x - x₀)
⇒ y - 2 = -1/3 (x + 6)
⇒ 3y - 6 = -x - 6
⇒ 3y + x = 0
⇒ x = -3y
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To make 4 cups of rice, Iain needs 5 cups of water. To make 16 cups of rice, he needs 20 cups of water. Write this as a proportion. 4/?=?/?
Answer: Don't use this if you are taking a test, please!
Step-by-step explanation:
Hello! This is actually easier than you think! All you have to do is make what is already written as a proportion. You don't have to solve anything! You are already given one number which represents the first thing you were told, 4 cups of rice. For 4 cups of rice, 5 cups of water are needed. As a proportion, you would write 4/5. For the second proportion you would write the 16 cups of rice per 20 cups of water as 16/20. The answer is 4/5 = 16/20. Hope this helps with your homework!
What is the solution to the system of linear equations y =- 5x 3?.
The Solution to the system of linear equations given as "y = -5x+3" and "y= 1" is that x = 2/5 and y = 1 .
Linear equations are the equations that are made up of Variables and Constants which are joined by mathematical operators .
The system of linear equations is given to us is: "y = -5x+3" and "y= 1"
Substituting the values of y=1 in y = -5x+3 ,
we get ;
⇒ 1 = -5x + 3 ;
⇒ -5x = 1 - 3 ;
⇒ -5x = -2 ;
⇒ x = (-2)/(-5) ⇒ x = 2/5 .
Therefore , solution can be written as : x = 2/5 and y = 1 .
The given question is incomplete , the complete question is
What is the solution to the system of linear equations y = -5x+3 and y = 1 ?
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I need help on this asap!
Receives some cash from his mother for his journey. He has already put aside a total of $\$ 220$ for the trip. There is a 55-gallon gas purchase cap .
What is the greatest number of gallons ?[tex]$$\begin{aligned}& 3.25 \mathrm{~g}+40 \leq 220 \\& -403.25 \mathrm{~g} \\& \frac{3.25}{3.25} \leq \frac{180}{3.25} g \leq 55.38 \approx 55\end{aligned}$$[/tex]
Chang-to has a gas purchase limit of 55 gallons.
[tex]$$\begin{aligned}& 3.25 g+40 > 92 \\& \frac{-40}{\frac{3.25 g}{3.25} > \frac{-40}{32}} \\& \mathrm{~g} > 16\end{aligned}$$[/tex]
More than 16 gallons of gas could have been purchased by him .
[tex]$$\begin{aligned}& 3.259+40 \leq 170 \\& \frac{3.2 / 59}{3.2^{\prime} 5} \leq \frac{130}{3.25} \\& g \leqslant 40\end{aligned}$$[/tex]
He only allowed to purchase 40 gallons of gas during the journey.
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Solve x2 + 2 = 6 by graphing the related function.
A) 2
B) there are two solutions +v8
C) no real number solutions
D) +2
The solutions of the given equation are 2 or -2
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given is an equation, x²+2 = 6
x²+2 = 6
Solving we get,
x²+2 = 6
x² = 6-2
x² = 4
x = ±2
Hence, there are two solutions of the equation 2 or -2
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Find the missing length.
ADEF~AVUT
D
140
37
50
U
E
60
168
T
F
DELL
Jona i given a tet quetion aking him to how that the um of two odd integer i alway an even integer. Which choice i the bet proof of hi conjecture?
B. Let (2a + 1) and (2b + 1) are different odd numbers. sum of these odd number is 2(a+ b +1) is a multiple of 2.
Whole numbers in mathematics can be divided into even and odd numbers. There isn't a single number that can be both even and odd, making odd and even numbers distinct sets of numbers. A number can be even or odd. Odd numbers are ones that are not entirely divisible by two, whereas even numbers are entirely divisible by two.
Let (2a + 1) and (2b + 1) are different odd numbers. the sum of these odd numbers is 2(a+b+1) is a multiple of 2. furthermore, let 2a and 2b be two even numbers so the sum of those two will also be an even number. Therefore the summation of two odd numbers is always even.
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The complete question is:
Jona is given a test question asking him how that the um of two odd integers is always an even integer. Which choice is the best proof of his conjecture?
A) Every time you add two odd numbers, the sum is an even number.
B) Let a and b both represent odd numbers and a+b be an even number. Therefore, a+b=b+a which shows that the sum of two odd numbers is even.
C) Look at these different examples: 5+3=8, 15+7=22, 21+13=34. So the sum of two odd numbers must be even.
D) Let (2a+1) be one odd number and let (2b+1) be the other odd number. (2a+1)+ (2b+1) = 2a+2b+2 = 2(a+b+1). Because 2(a+b+1) is a multiple of 2,it is an even number.
what’s a geometry concept you’ve learned or found really helpful
Hey there!
There are various concepts that are used in the world of Geometry, however there are some simple concepts that may be easier to work with.
Simple Concepts in GeometryPoints - In geometry, a point is a location represented often by a dot on a x-y graph. The point does not have any length, width, shape or size, it only has a position.Lines - In geometry, a line is a straight one-dimensional figure having no thickness and extending infinitely in both directions.Segments - In geometry, a line segment is a piece or part of a line having two endpoints. The length of a line segment can be measured either in metric units such as millimeters, centimeters, or customary units such as feet or inches.Rays - In geometry, a ray is usually taken as a half-infinite line (also referred to as a 'half line') with one or the two points and taken to be at infinity._____________________________________________________
So, in summary to all of this, it really depends on what concepts in geometry you are currently learning and which concept(s) you personally find the most useful and helpful.
NEED HELP ASAP! CMON
Answer:
A: x < 3
Step-by-step explanation:
Answer: x < 3
Step-by-step explanation:
We start by subtracting 6 from both sides -
x + 6 - 6 < 9 - 6
Then, we get this -
x < 3
Which is the answer
Taylor and Raimi each earn an hourly wage. Taylor earn $308 for working 14 hour. Raimi earn $288 for working 12 hour. Which tatement i true?
The statement that is true is that Taylor earned more than Raimi for the hours worked.
Taylor earned $308 for working 14 hours, which is equivalent to $22 per hour. Raimi earned $288 for working 12 hours, which is equivalent to $24 per hour. Therefore, Taylor earned a higher hourly wage than Raimi.
This statement can be further verified by computing the total wages earned by both Taylor and Raimi for the same amount of hours: if both Taylor and Raimi worked 14 hours, Taylor would have earned more than Raimi by $20. To demonstrate, Taylor would have earned $308 for 14 hours and Raimi would have earned $336 for 14 hours.
Therefore, Taylor would have earned the higher wage.
In conclusion, Taylor earned more than Raimi for the hours worked, verifying the statement that Taylor earned more than Raimi.
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If a rectangle' perimeter i 999 ft, give at leat one poible meaurement of it length and width
The possible measurement of Length and Width will be 249.75 feet each.
What is Rectangle?
The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.
The whole distance that a rectangle's boundaries, or its sides, the cover is known as its perimeter. Given that a rectangle has four sides, the perimeter of the rectangle will be equal to the sum of its four sides. Since a rectangle's perimeter is a linear measurement, the unit will be in meters, centimeters, inches, feet, etc.
Perimeter of a rectangle = 2(Length + Width) square units
Area of a rectangle = Length × Width = a × b
In our question, it is given that the Perimeter is 999 ft.
Putting this in our Perimeter formula.
2(Length + width) = 999
Length + width = 499.5
Therefore our possible measurement of Length and Width will be 249.75 feet each.
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The lengths of salamanders have a normal distribution with mean 15cm, and standard deviation 2cm.
In a collection of 200 salamanders, about how many have length greater than 16.5cm?
Answer:
2cm
Step-by-step explanation:
103. 68 in. 2
2cmo salamanders
Adam is traveling from NY to Washington, a distance of 450 miles. If his car averages 15 miles per gallon, what is the cost of his trip from NY to Washington and back if gasoline costs 50 cents per
gallon?
Step-by-step explanation:
15 miles consume 1 gallon
450 miles consume 450÷15 = 30 gallon per a way
For round trip, it will consume 30*2=60 galloon
1 gallon costs 50 cents
30 galloon costs 30*50=1500 cents per a way
For round trip, 1500*2=3000 cents
Given a polynomial and one of its factors, find the remaining factors of the polynomial.
x^3-9x^2+27x-27; x-3
Answer:
(x-3)^3
Step-by-step explanation:
[tex]= x^3-9x^2+27x-27 \\ =(x − 3) (x² + 3x + 9) − 9x (x - 3) \\ =(x − 3) · (x² + 3x + 9 − 9x) \\ =(x-3)·(x²-6x+9) \\ =(x − 3) · (x − 3)^2 \\ = {(x - 3)}^{3} [/tex]
Or Apply cube of difference rule
[tex]{x}^{3} - 3 {x}^{2} y + 3x {y}^{2} - {y}^{3} [/tex]
Answer:
[tex](x-3)^3[/tex]
Step-by-step explanation:
Given polynomial:
[tex]x^3-9x^2+27x-27[/tex]
Given (x - 3) is a factor of the polynomial, divide the polynomial by the factor using long division to find the other factor:
[tex]\large \begin{array}{r}x^2-6x+9\phantom{)}\\x-3{\overline{\smash{\big)}\,x^3-9x^2+27x-27\phantom{)}}}\\{-~\phantom{(}\underline{(x^3-3x^2)\phantom{-b0000000)}}\\-6x^2+27x-27\phantom{)}\\-~\phantom{()}\underline{(-6x^2+18x)\phantom{0000.}}\\9x-27\phantom{)}\\-~\phantom{()}\underline{(9x-27)\phantom{}}\\0\phantom{)}\end{array}[/tex]
Therefore:
[tex]x^3-9x^2+27x-27=(x-3)(x^2-6x+9)[/tex]
Factor (x² - 6x + 9):
[tex]\implies x^2-6x+9[/tex]
[tex]\implies x^2-3x-3x+9[/tex]
[tex]\implies x(x-3)-3(x-3)[/tex]
[tex]\implies (x-3)(x-3)[/tex]
Therefore, the fully factored polynomial is:
[tex]\implies x^3-9x^2+27x-27=(x-3)(x-3)(x-3)[/tex]
[tex]\implies x^3-9x^2+27x-27=(x-3)^3[/tex]
