We calculated the required interval is 13.341 and 11.46 to estimate true average.
What is confidence level?
It is a statistical term that express that the value of a specific parameter located within a boundary.
What is confidence interval?
A statistical expression that has upper and lower limit. This value gives assurances to the average or mean value to be within the limit.
Given, number of samples, n =25
sample standard deviation, σ = 2.4%
average tip = sample mean, X = 12.4%
confidence level =95%
We need to construct an interval to estimate the true average tip with 95% confidence level.
We know that confidence level value Zc for 95% = 1.96
Now, confidence interval CI = X±Zc (σ/√n)
by putting the given value, CI= 12.4±1.96(2.4/√25)
the interval is 13.341 and 11.46
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Can someone explain how to do this? Normally i’d know how to do it but I’m clueless. HELP!!!
The length of unknown side of the triangle will be 18 inch.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The two triangles are shown in figure.
Now,
Since, Both the triangle are similar.
Hence, There corresponding sides of the triangle are similar.
So, We get by definition of proportion visit:
⇒ 4 / 12 = 6 / x
⇒ 1/3 = 6/x
⇒ x = 6 × 3
⇒ x = 18 in
Thus, The length of unknown side of the triangle = 18 inch.
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A group of people was selected randomly and asked how many hours per day each person spends on gaming The results of the survey are displayed in the following histogram.What percentage of the people surveyed spend 3 hours or less per day gaming 1O 5O 32.5 O 52.5 O 67,54
The percentage of the people surveyed that spend 3 hours or less per day would be = 52.5%. That is option C.
What is a histogram?A histogram is defined as the graphical representation of the result of a data set with the use of bars that varies in length but of the same width.
From the given diagram, the total number of persons that participated in the games = 4+9+8+6+4+2+2+2+1+1+1= 40.
The number of people that spent 3 hours or less per day gaming = 4+9+8 = 21
Therefore the percentage of people that spent 3 hours or less per day gaming;
= 21/40 × 100/1
= 2100/40
= 52.5%
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Si on a une perfusion d'héparine 20 000 unités dans 500 ml de dextrose 5 % à 1 000 ml/heure, à combien d'unités/heure l'héparine est-elle perfusée?
Answer:
28.
Step-by-step explanation:
Si on a une perfusion d'héparine 20 000 unités dans 500 ml de dextrose 5 % à un débit de 1 000 ml/heure, le débit en unités/heure d'héparine est calculé en divisant le nombre d'unités d'héparine (20 000) par le volume de la solution de dextrose (500 ml) pour obtenir la concentration en unités/ml d'héparine dans la solution (40 unités/ml). Ensuite, on multiplie la concentration par le débit de la solution (1 000 ml/heure) pour obtenir le nombre d'unités/heure d'héparine qui sont perfusées. 40 unités/ml x 1 000 ml/heure = 40 000 unités/heure, et puisque 1 heure = 60 minutes, le débit en unités/minute est de 40 000 unités/heure / 60 minutes/heure = 666,67 unités/minute. Enfin, on divise le débit en unités/minute par la concentration en unités/ml pour obtenir le débit en ml/minute, soit 666,67 unités/minute / 40 unités/ml = 16,67 ml/minute. Comme 1 litre = 1 000 ml, le débit en litres/heure est de 16,67 ml/minute x 60 minutes/heure = 1 000 ml/heure, et puisque la concentration d'héparine dans la solution est de 20 000 unités/500 ml = 40 unités/ml, le débit en unités/heure est de 1 000 ml/heure x 40 unités/ml = 40 000 unités/heure. Par conséquent, la réponse finale est de 40 000 unités/heure / 60 minutes/heure = 666,67 unités/minute / 40 unités/ml = 16,67 ml/minute x 60 minutes/heure = 1 000 ml/heure x 40 unités/ml = 40 000 unités/heure = 28 unités/heure.
the table compares the average daily temperature and ice cream sales each day using technology, determine the line of fit, where x represents the average daily temperatures and y represents the total icecream sales. round values to the nearest tenth
Answer:
representa 48
Step-by-step explanation:
Complete the square to solve the equation below.
Check all that apply.
will mark brainliest
x2 + 8x- 5 = 15
A. x=3
B. x=-2
C. x= -10
D. x= 2
Answer:
+2 or –10
Step-by-step explanation:
x² + 8x –5 = 15
x² + 8x = 15 + 5
x² + 8x = 20
using completing the square method
(½(8))² to be applied in both sides
x² + 8x + 16 = 20 + 16
factorise the LHS
(x+4)² = 36
x + 4 = √36
x + 4 = ±6
x = –4±6
x = –4 + 6 or –4–6
x = +2 or –10
pls mark as brainliest
A researcher is interested in finding a 98% confidence interval for the mean number of times per day that college students text. The study included 119 students who averaged 34.2 texts per day. The standard deviation was 12.7 texts. Round answers to 3 decimal places where possible.
a. To compute the confidence interval use a ? t z distribution.
b. With 98% confidence the population mean number of texts per day is between and texts.
c. If many groups of 119 randomly selected members are studied, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population number of texts per day and about percent will not contain the true population mean number of texts per day.
a. t distribution
b. 98% confidence the population mean number of texts per day is between and texts is 31. 455 and 36.945
c. Two percent will not contain the true population mean number of texts per day.
Confidence interval
A confidence interval, in statistics, refers to the probability that a population parameter will fall between a set of values for a certain proportion of times. Analysts often use confidence intervals than contain either 95% or 99% of expected observations.Given that,
xbar = 34.2
s = 12.7
n = 119
degrees of freedom, df = n - 1 = 118
a. t distribution
b. CI level is 98%, hence α = 1 - 0.98 = 0.02
α/2 = 0.02/2
= 0.01,
tc = t (α/2, df) = 2.358
CI = [tex](34.2 - 2.358 * \frac{12.7}{\sqrt{119} } , 34.2 + 2.358 *\frac{12.7}{\sqrt{119} } )[/tex]
CI = (31.455 , 36.945)
With 98% confidence the population mean number of texts per day is between 31.455 and 36.945 texts.
(c) Approximately 98 percent of these confidence intervals will contain the true population mean number of texts per day, while approximately 2 percent will not.
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the questions in this activity refer back to prelab 0, which would be a good place to look if you need any help. in test a, suppose you make 100 experimental measurements of some quantity and then calculate mean, standard deviation, and standard error of the numbers you obtain. in test b, suppose you make 400 experimental measurements of the same quantity and you again calculate mean, standard deviation, and standard error. 1)which of the following statements is the most likely description of the comparison of the standard deviations found in test a and test b ?
For measurements of the same quantity, there won't be a significant difference in the standard deviation.
The standard deviation for Tests A and B is almost the same.
Total quantity in test a = n1 = 100
Total quantity in test b = n2=400
We know that the standard error is defined as: [tex]S E=\frac{\sigma}{\sqrt{n}}[/tex]
where we have, for test A [tex]$$S E_A=\frac{\sigma}{\sqrt{100}}$$[/tex]
and for Test B [tex]$$S E_B=\frac{\sigma}{\sqrt{400}}=\frac{1}{2} * \frac{\sigma}{\sqrt{100}}$$[/tex]
So, from here, we can conclude that,
The standard error in Test A is twice as big as in Test B.
The complete question will be:
Which of the following statements is the most likely description of the comparison of the standard errors found in Test A and Test B?
The standard errors found in Test A and Test B will be about the same.
The standard error found in Test A will about be twice as big as the standard error found in Test B.
The standard error found in Test A will about be four times as big as the standard error found in Test B.
The standard error found in Test B will about be twice as big as the standard error found in Test A.
The standard error found in Test B will about be four times as big as the standard error found in Test A.
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you are playing blackjack in a casino. the casino is using a single, 52 card deck. shuffling the deck takes time. so rather than shuffling the deck after each hand, the casino deals three hands before shuffling. the used cards are put to the side and not used again until the deck is reshuffled. after two hands, you observe that the following cards have been removed from the deck.
2,2,4,5,6,8,8,10,J,J (ten cards total)
What is the probability that you will be dealt a blackjack on the next hand?
The probability of being dealt a blackjack on the next hand is 4.8%. This is because there are only 4 cards that could make up a blackjack (an Ace and a 10-valued card), and there are only 82 cards left in the deck after two hands. Therefore, the probability of being dealt a blackjack is 4/82, or 4.8%.
The probability of being dealt a blackjack on the next hand is 4.8%. This is because a blackjack is made up of an Ace and a 10-valued card, so the probability of being dealt one is 4/82, or 4.8%. This is because after two hands, there are only 82 cards left in the deck. Of those 82 cards, there are only 4 that can make up a blackjack. Therefore, the probability of being dealt a blackjack is 4/82, or 4.8%. The fact that the deck is not being shuffled after each hand does not affect the probability, as the used cards are being put to the side and not used again until the deck is reshuffled.
Probability of blackjack = (number of cards that can make a blackjack / total number of cards remaining in the deck)
Probability of blackjack
= (4 / 82)
Probability of blackjack
= 4.8%
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question 2 determine whether the events a and b are independent. a card is selected at random from a standard deck of 52 cards. it is then replaced and a second card is selected at random. event a: a club is selected on the first draw event b: an ace is selected on the second draw
No
Yes
The answer is yes, events A and B are independent to each other when A random card is chosen from a 52-card standard deck.
Given that,
We have to identify the independence of the events a and b. A random card is chosen from a 52-card standard deck. Then it is changed, and a second card is chosen at random. event a: The initial draw selects a club event b: The second draw yields an ace.
We know that,
Here a card is selected randomly from the deck of 52 cards. Then this card is replaced, that means the deck has again 52 cards. Now, Second card is then selected randomly from the deck.
Here as we are replacing the first drawn card that means probability of drawing first card doesn't affect the probability of drawing second card. So here the given events A and B are independent.
P(A and B) = P(A) P(B)
Therefore, The answer is yes, events A and B are independent to each other when A random card is chosen from a 52-card standard deck.
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Help pls I cant solve this problem
Answer:
12 x 9 x 15 is 1620. then start multiplication on the subject
Assume that the probability that there is a significant accident in a nuclear power plant during one year’s time is .001. If a country has 100 nuclear plants, estimate the probability that there is at least one such accident during a given year.
please help with explantion
The estimate probability that there is at least one such accident during a given year, P(X≥1) is equals to the 0.0952..
We have, the probability that there is a significant accident in a nuclear power plant during one year, p = 0.01
Total nuclear plants in country , n = 100
we have to calculate probability that there is at least one such accident during a given year.
Using Binomial Probability distribution,
X ~ Bin( 100, 0.01)
P(X= x ) = ⁿCₓ(p)ˣ (1-p)⁽ⁿ⁻ˣ⁾
Thus, the probability that there is at least one such accident during a given year, P(X≥1)
= 1 - P(there is no such event, P(X= 0)
= 1 - P(X= r ) = 1 - ⁿCᵣpʳ(1-p )⁽ⁿ⁻ʳ⁾
where p is probability of success
r = 0 , n = 100, p = 0.001
plugging all known values in above formula,
P(X≥ 1) = 1 - ¹⁰⁰C₀ (0.001)⁰(1- 0.001)⁽¹⁰⁰⁻⁰⁾
= 1 - ¹⁰⁰C₀ (0.001)⁰(0.999)¹⁰⁰
= 1 - 1 ×1 ×0.904792
=1 - 0.904792
=0.0952
Hence, required probability is 0.0952.
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Which of the following are true? 1. If velocity is constant and positive, then distance traveled during a time interval is the velocity multiplied by the length of the interval. 2. If velocity is positive but decreasing, using the velocity at the beginning of each subinterval in a rectangle sum gives an overestimate of the distance traveled. Select one:a. Both 1 and 2 b. Just 1 c. Neither 1 or 2 d. Just 2
According to the statement given, Distance = Velocity X time = V1 X (t2 - t1), but this is the overestimate value
What is velocity?Velocity is the rate at which a moving object's location changes as observed from a specific frame of reference and measured at a specific time standard.
1. Distance = velocity X time
= V X (t2 - t2)
2. According to the statement given,
Distance = Velocity X time
= V1 X (t2 - t1)
but this is the overestimate value, because
Distance = Area under velocity - time curve
therefore, statement 2 is correct
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The mean of a sample is a) Always equal to the mean of the population b) Always smaller than the mean of the population c) Computed by summing the data values and dividing the sum by (n -1) d) Computed by summing all the data values and dividing the sum by the number of items e) None of the above answers is correct. #11 Since the mode is the most frequently occurring data value, it a) Can never be larger than the mean b) Is always larger than the median c) Is always larger than the mearn d) Must have a value of at least two e) None of the above answers is correct. #12. The difference between the largest and the smallest data values is the a) Variance b) Interquartile range c) Range d) Coefficient of variation e) None of the above answers is correct. #18 Let X and Y be independent random variables with Calculate E (X+1) (Y-1) 1 a) 1 b) 9/2 c) 16 d) 17 e) 27 f) None of these
The expected value of X + 1 (Y - 1) can be calculated using the formula E(X + 1)(Y - 1) = E(X)E(Y) + E(X) - E(Y) + 1. Thus, the expected value of X + 1 (Y - 1) = 9/2 * 9/2 + 9/2 - 9/2 + 1 = 17. Therefore, the correct answer is d) 17.
The expected value of X + 1 (Y - 1) is a measure of the average value of the product of two independent random variables, X and Y. To calculate this expected value, we can use the formula E(X + 1)(Y - 1) = E(X)E(Y) + E(X) - E(Y) + 1. Since X and Y are independent random variables, we know that E(X) = E(Y) = 9/2. Plugging this value into the formula, we get E(X + 1)(Y - 1) = 9/2 * 9/2 + 9/2 - 9/2 + 1 = 17. This is the expected value of X + 1 (Y - 1). Therefore, the correct answer is d) 17.
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PLEASE HELP WILL MARK BRAINLIEST
Answer: [tex]\cos P=r/q[/tex]
Step-by-step explanation:
Cosine is defined as adjacent/hypotenuse.
In relation to [tex]\angle P[/tex], the adjacent side is [tex]r[/tex] and the hypotenuse is [tex]q[/tex].
So, [tex]\cos P=r/q[/tex].
rearrange the formula to make x the subject 4(x-3)/a=y
Answer:
x=3+ay/4a
Step-by-step explanation:
4(x-3)/a=y
a*4(x-3)/a=a*y
4a(x-3)=ay
4a(x-3)/4a=ay/4a
x-3=ay/4a
x-3+3=3+ay/4a
x=3+ay/4a
What is this question's answer?
The surface area of the figure given which is a rectangular prism is 1362cm²
Surface Area of Rectangular PrismThe total region or area covered by all the faces of a rectangular prism is defined as the surface area of a rectangular prism. A rectangular prism is a three-dimensional shape. It has six faces, and all the faces are rectangular-shaped. Therefore, both the bases of a rectangular prism must also be rectangles.
The surface area of the prism is calculated by the formula
A = 2[(lw) + (lh) + (wh)]
A = Surface areal = length of the prismh = height of prismw = width of prismTo solve this problem, we have to divide the prism into two different parts and solve for the area.
For the first rectangular prism;
h = 14cmw = 14cml = 8cmA = 2[(lw) + (lh) + (wh)]
A = 2[(8 * 14) + (8 * 14) + (14 * 14)]
A = 840cm²
The area of the second figure will be;
l = 8cmh = 17cmw = 5cmA = 2[(8 * 17) + (17 * 5) + (8 * 5)]
A = 552cm²
The total surface area of the figure is 840cm² + 552cm² = 1362cm²
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Write an equation in standard form of the line that contains the point (-2,3) and is parallel to (has the same slope as) the line
y = 4x-1.
Answer:
y=4x+11
Step-by-step explanation:
How long does it take to for a ball to travel 27 m at a rate of 18m/s?
It will take a ball 1.8 seconds to travel 27 m at a rate of 18m/s
How to find the time it will take a ball to travelThe time it will take a ball to travel is solved from the formula of speed given as
speed = distance covered / time taken
from the problem
distance covered = 27 m
time taken = ?
speed = 15 m/s
substituting into the formula
15 = 27 / time
time = 27 / 15
time = 1.8 seconds
the time is 1.8 s
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we are interested in generating functions for the number of different ways to compose a bag of n donuts subject to various restrictions. for each of the restrictions in parts (a)-(e) below, find a closed form for the corresponding generating function
A closed form for the corresponding generating function is all the donuts are chocolate and there are at least 3, therefore, x³/1 − x.
In math the word function refers the a set X to a set Y in mathematics assigns each element of X exactly one element of Y.
Here the domain and codomain of the function are denoted by the sets X and Y, respectively.
Here we have to find a closed form for the corresponding generating function.
While we looking into the given question, we have identified the the concept of function was first discussed by two Persian mathematicians named Al-Bruni and Sharaf al-Din al-Tutsi.
And the functions were originally used to represent the idealized relationship between varying quantities and other variables.
As for example, time has an impact on a planet's position.
Here the the number of different ways to compose a bag of n donuts subject to various restrictions. As per these condition, we now that the option (a) is correct.
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Kelly has the following income and expenses:
$200 per month paychecks
$50 cell phone
$40 gasoline
$40 Miscellaneous expenses
How much money does Kelly have remaining after paying her monthly expenses?
9. Patty's Pies produces pies. The company has a fixed cost of $20,000. Each pie sells for $8.75 with a variable cost of $4.00 per pie. Find the breakeven
point for Patty's Pies. (Round your answer to the nearest whole pie.)
A. 2,411 pies
B. 4,000 pies
C. 4,211 pies
D. 5,000 pies
The break-even point for Patty's Pies is C. 4,211 pies.
What is the break-even point?The break-even point is the sales units that equate the sales revenue with the total costs (fixed and variable).
At the break-even point, there is no profit, there is no loss. Above this point, profits are generated. Below it, losses are recorded.
Fixed cost = $20,000
Selling price per pie = $8.75
Variable cost per pie = $4.00
Contribution margin per pie = $4.75 ($8.75 - $4.00)
Contribution margin ratio = 54.29% ($4.75/$8.75 x 100)
Break-even point in sales units = Fixed costs ÷ Contribution margin per unit
= $20,000 ÷ $4.75
= 4,211 units
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Solve for z in the system of equations.
x + y - z = -5
2x - y + z = 8
x - 4y + 3z = 5
Answer:
z = 20
Step-by-step explanation:
Elimination Method:We can use the elimination method in a systems of 3 equations, just as we did when we were solving systems of 2 equations. While the method we apply it is the same, we have to apply it multiple times as elimination gets rid of one variable (usually) and since we're dealing with 3 variables, that still leaves us with 2 variables and we need to cancel once more.
Applying Elimination Method:
We want to develop two linear equations, by applying elimination twice to each equation at least once, and then from there we can apply elimination once more.
Since we're solving for "z", we don't want to immediately cancel it out. So let's use the following two equations:
[tex]x+y-z=-5\\\\x-4y+3z[/tex]
Let's cancel out the "x", by manipulating one equation to be -x. We can do this by multiplying one equation by -1, but remember we have to apply this to both sides of the equation. Let's do it to the top one (you could also do it to the bottom one)
[tex]-1(x+y-z)=-(-5)\implies -x-y+z=5[/tex]
So now let's add the two equations:
[tex]\ \ \ (-x-\ y+\ z)=5\\+(\ \ x-4y + 3z) = 5\\ ------------\\ -5y+4z=10[/tex]
Now let's apply the same thing, but to the middle and bottom equation. Since they don't have the same absolute value coefficients (ignoring the sign) we need to multiple one by a value other than just negative one. So let's multiply the bottom equation by -2 so that the bottom will have a -2x which will cancel when adding it to 2x
[tex]-2(x - 4y + 3z) = -2(5)\\-2x + 8y - 6z = -10[/tex]
Now let's add the equations:
[tex]\ \ \ (\ \ 2x-y+z)=8\\+(-2x + 8y - 6z)=-10\\\\-----------\\7y - 5z = -2[/tex]
So now we have the two equations:
[tex]7y-5z=-2\\-5y+4z=10[/tex]
From here we can apply any method we want, from here I'll use substitution. Since we want to get rid of the "y", let's solve for "y" in terms of z, so once we substitute we have no "y" terms left.
[tex]7y-5z=-2\\7y=5z-2\\y=\frac{5z-2}{7}[/tex]
Now let's plug this into the second two-variable equation we made.
[tex]-5(\frac{5x-2}{7})+4z=10\\\\\frac{-25x+10}{7}+4z=10\\\\\frac{-25}{7}z+\frac{10}{7} + \frac{28}{7}z = \frac{70}{7}\\\\\frac{-25+28}{7}z = \frac{70-10}{7}\\\\\frac{3}{7}z = \frac{60}{7}\\\\z = \frac{60}{7} * \frac{7}{3}\\\\z = 20[/tex]
Write the equation of a line passing through (-6,8) and is perpendicular to the line y=x+9 in point slope form and slope intercept form.
The equation of the line in point slope form and slope intercept form are y - 8 = -(x + 6) and y = -x + 2. respectively.
How to represent equation in slope intercept form and point slope form?The equation of a line in slope intercept form is as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, equation of a line passing through (-6,8) and is perpendicular to the line y = x + 9.
Perpendicular lines have slopes that are the opposite of the reciprocal of each other.
Therefore, the slope is - 1.
Hence,
y = -x + b
Using (-6, 8)
8 = -(-6) + b
b = 8 - 6
b = 2
Therefore, the slope intercept form is y = -x + 2.
The equation of the line in point slope form is represented as follows:
y - y₁ = m(x - x₁)
where
m = slope
Using (-6, 8)
Therefore, the equation in point slope form is y - 8 = -(x + 6)
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State Farm Insurance studies show that in Colorado, 55% of the auto insurance claims submitted for property damage were submitted by males under 25 years of age. Suppose 8 property
damage claims involving automobiles are selected at random.
(a) Letr be the number of claims made by males under age 25. Make a histogram for the r-distribution probabilities.
Answer:
I don't know the answer so how will I tell you
there are 279 students going on a field trip to an art museum. they are going on buses that hold 24 students each.
How many buses are needed? How many students will ride on the bus that isn't full? Show your work.
The number of buses needed is calculated to be 12 and the number of students that will ride on the bus that isn't full is calculated to be 10.
The number of buses needed if each bus held 24 students can be calculated as follows;
Number of buses = number of students / number of students in each bus = 279 / 24 = 11.625 = 12
Therefore 12 buses were needed if each bus can hold a maximum of 24 buses. Now we first determine the number of students in 11 buses that were full by multiplication as follows;
number of students in 11 buses = 11 × 24 = 264 students
Now we can calculate the number of students on the bus that isn't full by subtraction as follows;
Students = total students - students in 11 buses that are full
Students = 274 - 264 = 10 students
Therefore 10 students will ride on the bus that isn't full.
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i need help with this problem
Malik has 28 red marbles and he has 35 blue marbles. Malik wants to divide the marbles into groups so each group has the same contents. How many groups can Malik make, so there would be the same contents (red and blue marbles) in each group? There should be no marbles left over.
The number of groups will be 7. And each group contains 4 red and 5 blue marbles.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Malik has 28 red marbles and he has 35 blue marbles. Malik needs to partition the marbles into bunches so each gathering has similar items.
The factor of the number 28 is given as,
28 = 2 x 2 x 7
The factor of the number 35 is given as,
35 = 5 x 7
The common factor of the numbers 28 and 35 is 7. Then the number of groups will be 7. And each group contains 4 red and 5 blue marbles.
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One sweater + 3 shirts =$37
3 sweaters + 2 shirts =$55. Find the price of one sweater and the price of one shirt
Answer: One sweater: $13 and One shirt: $8
Step-by-step explanation: You have to use elimination. The first formula would be 1x + 3y = 37 and the other is 3x + 2y = 55. Once you use elimination, you just solve a one step equation. When you get x = 13, you plug the 13 into one of the formulas to get 8.
Use your function in part (b) to determine how many times you must fold a piece of paper to make the folded paper have a thickness that is the same as the distance from the earth to the moon_ (Assume the distance from the earth to the moon is 384,472,300,000 mm) folds Preview
The paper must be folded 43 times to get the thickness same as the distance from the earth to the moon.
Note that the function g is defined as [tex]g(n)=0.052^n.[/tex]
Let g(n) be the thickness that is g(n)=t.
Thus,
[tex]t & =0.05\left(2^n\right) \\\frac{t}{0.05} & =2^n \\\frac{100 t}{5} & =2^n \\20 t & =2^n\end{aligned}[/tex]
Take logarithms on both sides, thus
[tex]$$\begin{aligned}\log (20 t) & =\log \left(2^n\right) \\\log (20 t) & =n \log (2) \\n & =\frac{\log (20 t)}{\log (2)} \\n & =\log _2 20 t\end{aligned}$$[/tex]
Thus, [tex]g^{-1}=\log _2 20t[/tex] is the required inverse function.
c) Given that the thickness of the paper is same as the distance from the earth to the moon that is t=384,472,300,000 mm.
To determine the corresponding value of n.
Note that the inverse function is defined as [tex]g^{-1}(t)=\log _2 20t[/tex]...
Substitute 384,472,300,000 in equation (1), thus
[tex]$$\begin{aligned}& g^{-1}(384,472,300,000)=\log _2(20 \times 384,472,300,000) \\& g^{-1}(384,472,300,000)=\log _2(20 \times 384,472,300,000) \\& g^{-1}(384,472,300,000)=42.806\end{aligned}$$[/tex]
Since, [tex]g^{-1}[/tex] determines the number of folds of the paper, the value must be the whole number.
Thus, [tex]g^{-1}(384,472,300,000)[/tex] is approximately equal to 43 .
Thus, the paper must be folded 43 times to get the thickness same as the distance from the earth to the moon.
The complete questions should be:
b. The function g has an inverse. The function g^{-1} determines the number of folds needed to give the folded paper a thickness of t mm. Write a function formula for g^{-1}.
c. Use your function in part (b) to determine how many times you must fold a piece of paper to make the folded paper have a thickness that is the same as the distance from the earth to the moon. (Assume the distance from the earth to the moon is 384,472,300,000 mm. folds
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Why is -x < 3 equivalent to x>-3? Explain.
The two expressions are equivalent because they both represent the same concept: a number that is less than 3 but negative. In the first expression, -x, the negative sign in front of the x indicates that the value of the expression is the opposite of x. So if x is a positive number, then -x will be a negative number, and vice versa. In the second expression, x > -3, the greater than sign indicates that the value of x is greater than -3. Since we know that x is negative, this means that x is less than -3.
Therefore, both expressions represent the same thing: a number that is less than 3 but negative. This is why they are equivalent.