The percentage reduction is 40% if the original number was 5 and the new quantity is 3.
What is the percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics.
If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.
The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.
A percentage is a value expressed as a decimal. Divide the percentage value by 100 to convert percentages to decimals and fractions.
The Latin word per centum, which means "hundred" or "by the hundred," is where the word "percent" originates.
The Italian word per cento, which means "for a hundred," gradually shrank to become the symbol for "percent."
Per was frequently shortened to "p" and eventually vanished entirely. The contemporary "%" symbol was created by condensing the "cento" to two circles divided by a horizontal line.
According to our question-
5 were originally ordered, however only 3 were added, resulting in a net drop of 1.
(5 - 3) = 2.
Now, we'll divide net change by the initial amount and multiply it by 100% to get the percentage change, which is,
(2/5)×100%.
= 40%,
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in how many ways can 66 people be seated in a row if 1) there are no restrictions on the seating arrangement?
240 people can seat in a row without restriction in an arrangement.
A permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or process of changing the linear order of an ordered set.
Permutations differ from combinations, which are selections of some members of a set regardless of order. For example, written as tuples, there are six permutations of the set {1, 2, 3}, namely (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1). These are all the possible orderings of this three-element set. Anagrams of words whose letters are different are also permutations: the letters are already ordered in the original word, and the anagram is a reordering of the letters. The study of permutations of finite sets is an important topic in the fields of combinatorics and group theory.
According to the question:
Consider A and B being the people sitting next to each other, as one entity AB or BA.
There are now 5 entities (one of two persons A and B and five of one single person) that have to be placed in a row.
With AB, there are thus 5! possibilities. With BA, there are also 6! possibilities.
Considering both, there are thus 2× 5! = 240 ways to seat 6 people in a row of six seats if two people insist on sitting next to each other.
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A fence is to enclose a field and divide it into 3 equal areas. If there is 1600m of fencing available. Find the dimensions of the field that will allow for the maximum area. HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
The dimensions of the field that will allow for the maximum area are 200 meters by 400/3 meters
How to determine the dimensions of the field that will allow for the maximum area.From the question, we have
Fencing available, Perimeter = 1600 meters
Number of sections, n = 3
Represent the dimensions with x and y
So, we have:
Area = Number of sections* x * y = 3xy
Perimeter = (Number of sections * 2x + 2(Number of sections) * y) = 6x + 4y
Recall that
Perimeter = 1600 meters
So, we have
6x + 4y = 1600
A = 3xy
Divide 6x + 4y = 1600 by 2
3x + 2y = 800
Make y the subject
y = (800 - 3x)/2
Substitute y = (800 - 3x)/2 in A = 3xy
A = 3x(800 - 3x)/2
So, we have
A = 1200x - 4.5x²
Differentiate and set to 0
1200 - 9x = 0
So, we have
9x = 1200
Divide by 9
x = 400/3
Recall that y = (800 - 3x)/2
So, we have
y = (800 - 3 x 400/3)/2
Evaluate
y = 200
Hence, the dimensions are 200 by 400/3
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the telephone lines serving an airline reservation office are all busy about 60% of the time. a if you are calling this office, what is the probability that you will complete your call on the first try? the second try? the third try? b if you and a friend must both complete calls to this office, what is the probability that a total of four tries will be necessary for both of you to get through?
The probability that a total of four tries will be necessary for both of you to get through is 0.1728.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty. A probability is a numerical representation of the possibility or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
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a ladder reaches a maximum length of about 23 m. for any ladder to be safe, the angle it makes with the ground should be between 65° and 70°. one storey of a building is about 4 m. a fire breaks out on the fifth storey of a building. will the extension ladder reach the fifth storey safely?
Answer:
Given,
Let's assume the maximum safe height of wall = h
angle formed between ladder and ground = 70°
length of ladder = 16 ft
From the given data, it can be seen that ladder will form a right angle triangle structure with the wall
So,from the concept of trigonometry,
Sin70^o\ =\ \dfrac{\textrm{maximum safe height of wall}}{\textrm{length of ladder}}Sin70
o
=
length of ladder
maximum safe height of wall
= > Sin70^o\ =\ \dfrac{h}{16\ ft}=>Sin70
o
=
16 ft
h
= > \ h\ =\ 16\times Sin70^o=> h = 16×Sin70
o
=> h = 16 x 0.9396
=> h = 15.03 ft
So, the maximum safe height that can be reached by the ladder will be 15.03 ft.
Here is the Correct asnwer.
given a circle that is divided into n identical sectors, and we have k different colors to paint it. how many ways can we paint it under the condition that no adjacent pieces have the same color?
The number of ways we can paint is g(nk)=1/n ∑d | n ϕ(d) ((k−1)^n/d +(−1)^n/d (k−1))
Given,
Whether your circle has named sectors (i.e., is fixed) or lacks labels will determine this (i.e. is free).
In the first scenario, inclusion-exclusion can be used to create sets Ai,j of colorings with adjacent sectors I and j having the same color. Next, generally
|Ai1,j1∩⋯∩Air,jr|={(k^n − r r<n) ( k r=n)
And inclusion-exclusion yields f(n, k), the number of sectors that are colored with k colors that are not related to any of Ai, j (i.e., do not have similar adjacent colors):
f(n, k) = ∑r = 0 n−1 (−1)^r (n, r) k^n - r + (−1)^n (n, n)k
And the result of adding and subtracting (1) is:
⟹f(n, k) = ∑r = 0 n−1 (−1)^r (n, r) k^n−r + (−1)^n (n, n)k = (k−1)^n + (−1)^n (k−1)
That is your response to the fixed circle.
Burnside's Lemma, which generates the cycle index of a combinatorial necklace, must be applied if you want the solution for a free circle (assuming the symmetries involved are merely rotations):
Z(Cn) = 1n∑d∣nϕ(d)an/dd
Then, n/d cycles with dN sectors in each cycle, an/dd permutations representing rotations of sectors, and (d) is the Euler Totient Function[4] are used.
Since each cycle must contain a single color from the n available options, we must swap out an/dd with f(n/d, k), resulting in a total of g(n, k) free colorings for n>1*:
g(n, k)=1/n ∑d∣n ϕ(d) ((k−1)^n/d +(−1)^n/d (k−1))
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A perfect square has length n if its last n digits (in base 10) are the same and non-zero. What is the longest possible length? What is the smallest square achieving this length?
The longest possible length is 3 uints and the smallest square achieving this length is [tex]38^2[/tex] = 1444.
All squares end in the digit 0, 1, 4, 5, 6, or 9. A square ending in 11, 66, 55, 99 would be congruent to 3, 3, 2, 3 mod 4, but squares are congruent to 1 mod 4 or 0. So for a length > 1, the square should end in 4. For example, [tex]12^2[/tex] = 144.
A square ending in 4444 would be congruent to 12 mod 16, but squares are congruent to 0, 1 mod 16, 4 mod 16, or 9 mod 16. So, the maximum length should be 2 or 3.
If [tex]n^2[/tex] ends in 4, then n should end in 2 or 8. [tex](100a + 10b + 2) ^2[/tex]= 10000[tex]a^2[/tex] + 1000 (2ab) + 100 (4a + [tex]b^2[/tex]) + 10 (4b) + 4. So, if this ends in 44, then b = 6 or 1.
If b = 1, then 4a + [tex]b^2[/tex] is odd, so the square will not end in 444. If b = 6, then the square would be 1000k + (4a + 38) 100 + 44. This would end in 444 if we take, a= 9 or 4.
Thus the smallest numbers that end in 2 and whose square ends in 444 are 462 (square 213444) and 962 (square 925444).
[tex](100a + 10b + 8)^2[/tex] = 1000k + 100 ([tex]16a^2 + b^2[/tex]) + 10 (16b + 6) + 4.
Now, if this ends in 44, then b = 3 or 8.
let us take b=3, then [tex](100a + 38)^2[/tex] = 1000k + 100 (76a) + 1444, so this ends in 444 if a = 0. Hence, this should be the smallest solution.
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Write in lope intercept form an equation of the line that pae through the given point. (5,4) & (10,8)
The equation of the line in slope intercept form is y = 4/5 x.
Define the term slope intercept form?A line's equation of the sort y = mx + b can be given in slope intercept form. The m stands for the line's slope, and the b for the y-intercept. If you need to find a point on a line or compute for y given x, you utilize the slope intercept form.For the stated question-
The given points are-
(x1, y1) = (5,4)
(x2, y2) = (10,8)
Slope m = (y2 -y1)/ (x2 - x1)
m = (8 - 4)/(10 - 5)
m = 4/5
Equation of the line;
y - y1 = m(x - x1)
y - 4 = 4/5 (x - 5)
y = 4/5 x - 4 + 4
y = 4/5 x
Thus, the equation of the line in slope intercept form is y = 4/5 x.
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problem 1. (12 points) light bulbs of a certain type are advertised as having an average lifetime of 800 hours. the price of these bulbs is very favorable, so a potential customer has decided to go ahead with a purchase arrangement unless it can be conclusively demonstrated that the true average lifetime is smaller than what is advertised. a random sample of 50 bulbs was selected, the lifetime of each bulb determined, and the appropriate hypotheses were tested, resulting in the accompanying output: variable n mean st. dev se of mean z p-value lifetime 50 738.44 38.20 5.40 -2.14 0.016 a) what conclusion would be appropriate for a significance level of .05? b) what about at a significance level of .01? c) which significance level would you recommend? why?
the test's finding at the 5% level of significance is that the true average longevity is not less than claimed.
The following is a definition of the test's hypothesis:
H0: The actual average lifetime, which is > 750 hours, is not less than what is stated
Ha! The actual average lifespan, at 750 hours, is less than what is advertised.
The examination is left-tailed.
Making a decision:
The null hypothesis is rejected if the test's p-value is less than the significance level (), and vice versa.
The test's p-value is calculated as,
0.016 as the p-value
(a)
The level of significance is 0.05.
The p-value is equal to 0.016/0.05.
The null hypothesis was rejected since the test's p-value was lower than the threshold for significance.
Consequently, the test's finding at the 5% level of significance is that the genuine average lifetime is shorter than
(b)
The level of significance is = 0.01.
The p-value is equal to 0.016 > = 0.01.
The null hypothesis could not be rejected since the p-value of the test was greater than the level of significance.
Therefore, the test's finding at the 5% level of significance is that the true average longevity is not less than claimed.
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3 2/3 divided by 2/5
Answer:
9 1/6
Step-by-step explanation:
3 2/3 divided by 2/3
First convert 3 2/3 into a whole number
3 2/3 = 11/3
11/3 x 2/3 = 55/3
55/3 into a mixed number is 9 1/6
If the first equation is multiplied by 3 and then the equations are added, the result is _____. 3x + y = 3 x - 3y = -2 10 x = 7 10 x = 11 8 x = 7.
Answer:
if the first equation 3x - 3y = -2 is multiplication by 3
therefore, 3x - 3y = -2
multiplied by 3
:9x - 9y = -6
then the equations are added,
9x - 9y = -2 + 10x + 710x + 118x + 7
9x + 10x + 710x + 118x + 9y + 7
947x + 9y = 7
If Josh can run 1.5 miles in 12minutes, how long will it take him to run 4 miles?
Answer:
if he can run 1.5 miles in 12 min he can run 4 miles in 0.5
Maura runs 6 miles in 75 minutes. Ava runs 5 miles in 45 minutes.
Who runs faster?
Answer:
Ava is running faster than Maura.
Step-by-step explanation:
We are finding the speed in miles/minute.
6/75=0.08miles/minute
5/45=0.(1)miles/minute
0.(1)is greater than 0/08
Ava is running faster than Maura.
need help on 3 and 4 please!!
Answer:
Step-by-step explanation:
Which inequality is a true statement?
Select each correct answer.
−3<−1
−3≤−1
−3>−1
−3≥−1
−3=−1
(please answer correctly)
Answer:
−3 < −1
−3 ≤ −1
Step-by-step explanation:
Symbol explanation
< means "less than".> means "more than".≤ means "less than or equal to".≥ means "more than or equal to".= means "equal to".A negative number is any number that is less than zero.
On the number line the negative numbers are to the left of the zero.
-3 is less than -1 because -3 lies to the left of -1 on the number line.
Therefore, the only given inequalities that are true statements are:
-3 < -1 as -3 is less than -1.-3 ≤ −1 as -3 is less than or equal to -1.How is a thermometer related to rectangular coordinate system
The thermometer relates with the rectangular coordinate system in the sense that both have
the y-coordinate is similar to the vertical tube of a thermometerthe x coordinate is similar to the substance or object being measuredgraduated scale for measurementWhat governs a thermometer's operation?The idea behind how a thermometer works is that solids and liquids tend to expand as a function of temperature.
Mercury starts to rise when a thermometer lamp is submerged in a particular solution or material. On a temperature scale, this increase in mercury is investigated.
The mercury in the tube is similar to the y coordinate which gives the output while the object being measured is similar to the x coordinate which is the input
The graduation in thermometers into units that rises and falls is a similar feature in the rectangular coordinate system
The functions from thermometer can be plotted on a graph in a rectangular coordinate system
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Samuel has been planting young trees in her garden. The maple tree that is 125 centimeters tall is growing 3 centimeters per month, whereas the oak tree that is 83 centimeters tall is growing 10 centimeters per month. In a few months, the two trees will be the same height. What will that height be? How long will that take?
It will take 6 month to reach the same height for both maple tree and oak tree.
Explain the term rate of growth?the country, region, or geographic area's yearly average rate of change in population size over a certain time period.
The given data is -
Present height of maple tree = 125 cmRate of growth = 3 centimeters per month.Present height of oak tree = 83 cmRate of growth of oak tree = 10 centimeters per month.Let the number of months when both will have the same height be 'x'.
Thus,
For maple tree,the final height be-
125 + 3x
For oak tree,the final height be-
83 + 10x
Equating both
125 + 3x = 83 + 10x
7x = 125 - 83
7x = 42
x = 6 months
Thus, it will take 6 month to reach the same height for both maple tree and oak tree.
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Which of the following examples represents a proportional relationship?
The example that represents a proportional relationship is A. y = -x
What is a proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other.
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form of y = kx.
In the proportional relationship, the constant of proportionality k is equal to the slope m and the line passes through the origin
It should be noted that y = -x is a linear equation that passes through the origin.
In conclusion, the correct option is A.
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if a tree is 10 inches tall after 1 year and grows 40 inches every 5 years how tall would it be in 19 years
Answer:
The total length of the tree in the total of 19 years (including the first year) would be 210 inches.
Answer: 210in
Step-by-step explanation:
an iphone 13 is on sale for $519.35. it is on sale for 35 off the regular price. what is the original price of the phone?
Answer:
Step-by-step explanation:
$519.35 + $35
The original price of the iPhone 13 is $554.35
What is the 62 th term of the sequence 11, 14, 17, 20...?
14.95x4.1
can someone explain how to like do it like how u get the answer
The stem-and-leaf display represents scores achieved on a 100-point biology exam by the
34 members of the class. Identify the mean, median and mode for the data represented.
The measures of central tendency from the given stem-and-leaf plot are given as follows:
Mean: 74.62Median: 74.5.Mode: 73.What is shown by the stem-and-leaf plot?The stem-and-leaf plot shows the measures of the data-set, in which:
The left digit is the first digit.The right digit is the second digit.For example:
4|7 = 47.
Hence all the measures of the data-set are given as follows:
47, 51, 56, 57, 62, 63, 63, 66, 66, 68, 68, 70, 71, 73, 73, 73, 73, 76, 76, 77, 77, 79, 80, 81, 82, 83, 86, 88, 88, 90, 91, 93, 93, 97.
The mean is given by the sum of all scores divided by the number of scores, hence it is given as follows:
Mean = 74.62.
The median is the middle value of the data-set. The data-set has 34 elements, which is an even cardinality, hence the median is given by the mean of the 17th and of the 18th element, as follows:
Median = (73 + 76)/2 = 74.5.
The mode is the value that appears the most times in the data-set, which is of 73, as it is the only score to appear four times in the data-set.
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1 1/6 + 1/6 what it the answer to the problem i showed
Answer:
1 1/3 or 4/3
Step-by-step explanation:
1/6 + 1/6 = 2/6
simplified, it would be 1/3 then you add the one, and you get 1 1/3 or (written as a mixed number,) 4/3
Answer:
2
Step-by-step explanation:
Since the denominator is the same, we can add the numerators.
11/6 + 1/6 = 12/6
We can simplify this to 2.
So, the answer is 2.
after constructing a confidence interval estimate for a population mean, you believe that the interval is useless because it is too wide. in order to correct this problem, you need to:
By using the concept of confidence interval, it can be concluded that-
To reduce confidence interval, it is needed to increase sample size.
Option c is correct
What is confidence interval?
Suppose there is an unknown parameter whose range of estimate is required. Confidence interval gives the range of estimate of this unknown parameter.
Formula for percentage confidence interval
[tex]\bar{x} \pm z_\frac{\alpha}{2} \times \frac{\sigma}{\sqrt{n}}[/tex]
We have to reduce the size of the confidence interval
Confidence interval has no effect on mean, directly proportional to standard deviation and inversely proportional to sample size
So to reduce confidence interval, it is needed to increase sample size.
Option c is correct
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Complete Question
After constructing a confidence interval estimate for a population mean, you believe that the interval is useless because it is too wide. in order to correct this problem, you need to:
Select one:
a. increase the population standard deviation
b. increase the level of confidence
c. increase the sample size
d. increase the sample mean
e. none of these would help
what is the answer for shrinking 6x-2(x-3)
Answer:
4x +6
Step-by-step explanation:
You want the simplified form of 6x -2(x -3).
SimplifyGenerally, the first step in simplifying an expression is elimination of parentheses. This is done using the distributive property.
6x -2(x -3) = 6x -2x -2(-3) = 6x -2x +6
Then, like terms can be combined:
6x -2x +6 = (6 -2)x +6 = 4x +6
The simplified expression is 4x +6.
__
Additional comment
We notice the terms have a common factor of 2, so we can use the distributive property to factor that out:
= 2(2x +3)
This form may be useful in some circumstances, but is generally not considered to be the simplified form.
<95141404393>
3x+4/2=9.5 what is x
Answer:
x = 2.5
Step-by-step explanation:
Answer:
[tex]\boxed{\boxed{\tt x=5}}[/tex]
Step-by-step explanation:
[tex]\tt \cfrac{3x+4}{2}=9.5[/tex]
Multiply both sides by 2:-
[tex]\tt \cfrac{2\left(3x+4\right)}{2}=9.5\times\:2[/tex]
[tex]\tt 3x+4=19[/tex]
Subtract 4 from both sides:-
[tex]\tt 3x=15[/tex]
Divide both sides by 3:-
[tex]\tt \cfrac{3x}{3}=\cfrac{15}{3}[/tex]
[tex]\tt x=5[/tex]
__
Hope this helps you!
Have a nice day!
The mean number of years Americans work before retiring is 34. Which of the following will be a Type I error? (A) We conclude that the mean is 34 years when it really is not 34 years. (B) We conclude that the mean is 34 years when it really is 34 years. (C) We conclude that the mean is not 34 years when it really is 34 years. (D) We conclude that the mean is not 34 years when it really is not 34 years.
Type I error is We conclude that the mean is not 34 years when it really is 34 years. The correct option to this question is C.
Rejecting the null hypothesis when it is in fact true is a Type I mistake. It entails drawing conclusions about outcomes that are statistically significant when, in fact, they were just the consequence of chance or unrelated causes.
The significance level you select (alpha or ) determines the likelihood that you will make this mistake. You determined that figure at the start of your research to determine the statistical likelihood of getting your results (p-value).
The typical significance level is 0.05 or 5%. If the null hypothesis is accurate, your results only have a 5% chance or less of occurring.
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Suppose our student center published data that the average starting salary for college graduates is 59k. You randomly sampled 49 college graduates and calculated the sample average salary is 44k. What test can you use to check whether the true average is 59k?.
One sample mean t test is used to to check whether the true average is 59k.
Average:
In statistics, average means a mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.
Given,
Here we need to find in what test can you use to check whether the true average is 59k.
While we looking into the given question we have identified the following details,
Number of students = 49
True average = 59k
Sample average = 44k
In this given situation, the perfectly suitable test is one sample t test,
Why we used this because of a statistical hypothesis test used to determine whether an unknown population mean is different from a specific value.
Suppose our student center published data that the average starting salary for college graduates is 59k. You randomly sampled 49 college graduates and calculated the sample average salary is 44k.
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consider the following page reference string: 7, 2, 3, 1, 2, 5, 3, 4, 6, 7, 7, 1, 0, 5, 4, 6, 2, 3, 0 , 1. assuming demand paging with four frames, how many page faults would occur for the following replacement algorithms?
Answer:
Step-by-step explanation:
(2r+4) = (r+4) solve for r
Answer:
r = 0
Step-by-step explanation:
the first thing you can do to solve this equation is to remove the parenthesis
2r + 4 = r + 4
now subtract 4 from both sides
2r = r
subtract 4 from both sides
r = 0
that is your answer