The Central Limit Theorem is a valuable tool to make inferences about the population mean, provided that you have a large enough sample size.
If you are not reasonably sure that the variable under consideration is normally distributed but are reasonably sure that it has a symmetric distribution, use the median as a measure of central tendency instead of the mean.
The median is the middle value of a dataset when it is arranged in order, and it is not affected by extreme values or outliers in the way that the mean is.
In addition, use non-parametric statistical tests instead of parametric tests. Non-parametric tests do not assume any particular distribution for the data, so they can be used when the data are not normally distributed.
Examples of non-parametric tests include the Wilcoxon rank-sum test and the Kruskal-Wallis test for comparing two or more groups, respectively.
It is important to note, however, that using the median and non-parametric tests may result in a loss of statistical power compared to using the mean and parametric tests when the data are normally distributed.
Therefore,
It is important to consider the nature of the data and the research question when deciding on the appropriate statistical analysis.
Overall, if you are not reasonably sure that the variable under consideration is normally distributed but are reasonably sure that it has a symmetric distribution.
Using the median as a measure of central tendency and non-parametric tests can provide a robust approach to statistical analysis.
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The standard normal probability distribution:a. is a special case of the normal probability distribution.b. has a mean equal to 0 and a standard deviation equal to 1.c. measures the distance from the mean in units of the standard deviation.d. all of the above.
The correct answer is (d) all of the above.
Is the standard normal distribution a special case of the normal distribution with a mean of 0 and a standard deviation of 1, measuring distance from the mean in units of standard deviation?The standard normal distribution is a special case of the normal distribution, where the mean is equal to 0 and the standard deviation is equal to 1. It is also sometimes called the "z-distribution" or "z-score distribution," because it is often used to calculate z-scores, which measure the distance between an observation and the mean in units of the standard deviation. Therefore, all of the statements (a), (b), and (c) are true.
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In the Founder's Day Parade in Happy, USA, many organizations participate by building floats. The Float Committee has issued a decree that each float can only have 367,200 flowers on it this year. The Happy Campers have already attached 19,125 flowers to their float. If the flowers come in containers which hold 153 flowers, which equation represents how many more containers they can use on their float?
A. 153x + 19,125 = 367,200
B. 28x + 153 = 367,200
C. 28x = 367,200 + 153
D. 153x = 367,200 + 19,125
The equation represents how many more containers they can use on their float will be 153x + 19,125 = 367,200. Then the correct option is A.
Already, 19,125 flowers have been fastened to the Happy Campers' float. Say they utilize additional x pots with 153 blooms each. In that case, there would be the following number of flowers on their float:
19,125 + (x × 153)
The calculation that illustrates how many more containers they may utilize since they are only allowed to put 367,200 flowers on their float is:
19,125 + (x × 153) ≤ 367,200
153x + 19,125 ≤ 367,200
Thus, the correct option is A.
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A scale drawing of a billboard uses the scale 4 cm :11 ft. The
length of the billboard in the drawing is 15 cm. How long is the
actual billboard?
1.81.8 ft
2.41.25 ft
3.2.93 ft
4.165 ft
Each year Upchester United plays against Upchester City in a local derby match. The number of goals scored in a match by United is denoted by u and the number of goals scored in a match by City is denoted by c. The number of goals scored in the past 15 matches are summarised by u ( 1 ) 2 2 5 Σ − = , u ( 1 ) 9 Σ − = , c 39 2 Σ = and c 19 Σ = . a How many goals have been scored altogether in these 15 matches? b Show that u 58 2 Σ = . c Find, correct to 3 decimal places, the variance of the number of goals scored by the two teams together in these 15 matches.
1. The total number of goals for the 15 matches is 43.
2. To show that Σ u² = 58, we use Σ(u - 1)² = 25
Σ(u - 1)² = 25 ⇒ Σ(u² - 2u + 1) = 25
Σu² - 2Σu + Σ = 25 ⇒ Σu² - 2(24) + 15 = 25
Σu² = 25 + 48 - 15 → Σu² = 58
3. The variance of the teams together is 39.311
How did we calculate the total number of goal and variance?1. To find the total number of goals, we must establish that Σ(u + x) is the total number of goals.
TNG = Σu + Σx
Given that Σ(u - 1) = 9, it becomes
Σu - 15 = 9 ⇒ Σu = 9 + 15
Σu = 24
Given that Σu = 24 and Σx = 19
TNG = 24 + 19 = 43
we say
43 ÷ 15 = 2.866
We already know that Σx² = 39, Σu² = 58.
Σ(u - 1)Σx = 9 × 19 = 171
Σux - Σx = 171
Σux - 19 = 171
Σux = 190
Σt² = 58 + 2(190) + 39
= 58 + 380 + 39
= 477
Variance = 477
15 - 2.866
Variance = 477/12.134
Variance = 39.311
The answer provided is based on the full question below;
Each year Upchester United plays against Upchester City in a local derby match. The number of goals scored in a match by United is denoted by u and the number of goals scored in a match by City is denoted by c.
The number of goals scored in the past 15 matches are summarized by
Σ(u - 1)² = 25, Σ(u - 1) = 9 Σx² = 39 and Σx = 19
a How many goals have been scored altogether in these 15 matches?
b Show that Σu² = 58.
c. Find, correct to 3 decimal places, the variance of the number of goals scored by the two teams together in these 15 matches.
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Jules is working on a title for his most recent work. he wants to call it "x meters under the sea" where x is rounded to the nearest whole number. to determine x he needs to find the number of meters in 20,000 leagues. he knows that there are 1609.3 meters in 1 mile. he also knows that there are 3.452 miles in 1 league. what is the correct value for x?
Answer: To find the number of meters in 20,000 leagues, we first need to convert the number of leagues to miles:
20,000 leagues * 3.452 miles/league = 69,040 miles
Next, we can convert the miles to meters:
69,040 miles * 1609.3 meters/mile = 111,030,472 meters
So the number of meters in 20,000 leagues is approximately 111,030,472 meters. To round this to the nearest whole number and use it as the value of x in the title, we can round it to:
x = 111,030,472 rounded to the nearest whole number = 111,030,000 meters
Therefore, Jules can call his most recent work "111,030,000 meters under the sea".
How many qt are in 28 cups
Answer: There are 7 quarts for 28 cups.
Step-by-step explanation:
1 quart equals 4 cups.
28/4=7
Answer: 7
Step-by-step explanation:
A bank offers a CD that pays a simple interest rate of 7%. How much must you put in this CD now in order to have $10,920 to replace all the windows in your house in 8 years?
You would need to put approximately $19,500 into the CD now in order to have $10,920 in 8 years.
To determine how much you must put into the CD now, we can use the formula for simple interest:
I = P * r * t
Where:
I is the interest earned
P is the principal amount (initial investment)
r is the interest rate
t is the time in years
In this case, we know the interest rate is 7% (or 0.07) and the time is 8 years. We want to find the principal amount (P) that will result in $10,920 in 8 years. So we rearrange the formula to solve for P:
P = I / (r * t)
Substituting the given values:
P = 10,920 / (0.07 * 8)
P = 10,920 / 0.56
P ≈ $19,500
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The base of a 25-foot ladder is positioned 10 feet from the bottom of the building it leans against.
How high can the ladder reach?
The ladder can reach the wall up to 22.9 ft height.
Given that, the base of a 25-foot ladder is positioned 10 feet from the bottom of the building it leans against.
We need to find the height that can the ladder reach,
Here the ladder and wall together making a right triangle,
Let the required height be h,
So, we will use the Pythagorean theorem,
25² = 10² + h²
h² = 25² - 10²
h = √625-100
h ≈ 22.9
Hence, the ladder can reach the wall up to 22.9 ft height.
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Each bag of Candy can fill 85 square centimeters. How many bags of candy will Jada need to purchase to fill the pinata?
Assume that a hat contains four​ bills: a
​$5 bill, a $10 ​bill, a ​$20
​bill, and a $100
bill. Each bill is equally likely to be selected. Two bills are to be selected at random with replacement. Construct a sample space and determine the probability that both bills are $100
bills.
The probability that both bills are $100 bills when selecting two bills at random with replacement from the hat is 1/16.
To find the probability that both bills are $100 bills when selecting two bills at random with replacement from a hat containing a $5, $10, $20, and $100 bill, we'll first construct a sample space and then calculate the probability.
Step 1: Construct the sample space.
Since there are four bills and we're selecting two with replacement, there are a total of 4 x 4 = 16 possible outcomes. The sample space is as follows:
{$5, $5}, {$5, $10}, {$5, $20}, {$5, $100},
{$10, $5}, {$10, $10}, {$10, $20}, {$10, $100},
{$20, $5}, {$20, $10}, {$20, $20}, {$20, $100},
{$100, $5}, {$100, $10}, {$100, $20}, {$100, $100}.
Step 2: Determine the probability that both bills are $100 bills.
In the sample space, there's only 1 outcome where both bills are $100 bills: {$100, $100}. Since there are 16 possible outcomes in total, the probability of both bills being $100 bills is:
1 (desired outcome) / 16 (total outcomes) = 1/16
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May Someone Help Me?
if you are given a right triangle whose legs are labeled with the letters m,n,and p. write the Pythagorean Theorem for this triangle. What would be the measure fro side m?
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Let's assume that side m and side n are the two legs of the right triangle, and side p is the hypotenuse. According to the Pythagorean Theorem, the relationship between these sides can be written as:
m^2 + n^2 = p^2
To find the measure of side m, we would need more information about the lengths of sides n and p. However, this equation shows the relationship between the three sides of the triangle and can be used to determine the length of side m when given the lengths of sides n and p.
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Consider one side ab of a square abcd on the line y=2x-17 and the other two vertices c,d on the parabola y=x^2
The minimum intercept of line CD on the y-axis is 1.
Since AB is on the line y=2x-17, we can write the equation of the line as y=2x-17. We know that AB is a side of a square, so its length is equal to the distance between A and B. Therefore, we need to find the coordinates of A and B. Since the square is symmetric with respect to the line y=2x-17, the x-coordinate of the midpoint of AB is (17/2). Therefore, the x-coordinates of A and B are (17/2)-s and (17/2)+s, where s is half the length of AB.
Now, we need to find the value of s. Since AB is a side of a square, it is equal in length to the distance between C and D. We can find the equation of the line CD by using the coordinates of C and D, which are (x, x²) and (y, y²), respectively. Substituting these coordinates into the equation of the line, we get:
x² = 2x - 17 (equation 1)y² = 2y - 17 (equation 2)Solving for x and y in equations 1 and 2, we get:
x = 1 ± √18y = 1 ± √18Since AB is a side of a square, its length is equal to the distance between C and D, which is:
√[(y^2-x²)²+(y-x)²]
= √[(2√18)²+2²]
= 2√82
Therefore, s = √82.
Finally, we can find the y-intercept of CD by plugging in x=0 into the equation of the line CD, which is:
y = x + (y-x)/2y = (x+y)/2Substituting the values of x and y, we get:
y = (1 + √18)/2Therefore, the minimum intercept of line CD on the y-axis is 1.
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The complete question is:
Consider one sides AB of a square ABCD in order on line y=2x−17, and other two vertices C, D on y=x². The minimum intercept of line CD on the y-axis is
Which test should he use to analyze the data?
a. single sample t-test
b. independent t- test
c. paired t-test
d. One way ANOVA
To provide an accurate answer, I would need more context about the data and the research question being asked. However, I can provide a brief explanation of each test option:
a. Single sample t-test: Used when comparing a sample mean to a known population mean.
b. Independent t-test: Used when comparing the means of two independent groups.
c. Paired t-test: Used when comparing the means of two related groups or repeated measures.
d. One-way ANOVA: Used when comparing the means of three or more independent groups.
Please provide more information about the data and research question so I can recommend the appropriate test to analyze the data.
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Find the length of the missing measurement
[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a=2\\ h=1.6\\ A=2.2 \end{cases}\implies 2.2=\cfrac{1.6(2+b)}{2} \\\\\\ 4.4=1.6(2+b)\implies \cfrac{4.4}{1.6}=2+b\implies 2.75=2+b\implies \boxed{0.75=b}[/tex]
When Craig started contributing to superannuation, he paid $500 into the fund at the beginning of each financial year. His fund pays 8.7% p.a annually compounding.
Craig decided to increase his yearly investment to $900 because inflation was increasing the cost of living. He made 4 investments of $500, all the following investments were $900 pa.
Using the formula for sum of a geometric progression to calculate how much Craig's superannuation will be worth at the end of 15 years.
The correct answer is $9732.09, with each amount at the end the two periods of different contribution being $6194.64, and $16,905.13, but please show working out and all steps to produce final answer.
[tex]\Large \textsf{Sum of a geometric progression: $\rm S_n = \frac{a(1-r^n)}{1-r}$ ,}\\\normalsize \textsf{where a = first term, r = common ratio, S$_{\sf n}$ = sum of $n$ terms}[/tex]
Thanks!
Craig's superannuation will be worth of $22,099.77 at the end of 15 years.
Given that Craig made 4 investments of $500 in four years. To find out the superannuation we have to find the remaining 11 investments he made in the remaining 11 years from a total of 15 years.
For the first four investments,
a = $500
r = 1.087 [ given interest rate is 8.7% per annum ]
n = 4
By, substituting all these values in the given equation,
S1 = [tex]\frac{500(1-1.087^{4}) }{1-1.087}[/tex] = $6194.64
Similarly for the remaining 11 years,
a = $900
r = 1.087
n = 11
S2 = [tex]\frac{500(1-1.087^{11}) }{1-1.087}[/tex] = $16,905.13
Total superannuation = S1 + S2 = $6194.64 + $16,905.13 = $22,099.77.
From the above explanation, we can conclude that Craig's total superannuation will be worth $22,099.77
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Geometry Pleeeease help !!!!Find the values of x and y. Write your answer in simplest form.
The value of x is 1.5 and value of y is 1.8 from the given triangle.
In the right triangle let us find the hypotenuse
9²+6²=x²
81+36=x²
117=x²
Take square root on both sides
√117=x
x=10.8=11
11/y=6
value y=11/6=1.8
9/x=6
x=9/6
=1.5
Hence, the value of x is 1.5 and value of y is 1.8 from the given triangle.
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Find the volume of a sphere with a surface
area of 16 square feet. Round your answer
to the nearest hundredth.
The volume is about
cubic feet.
The approximate volume of the sphere is 6.01 ft³.
What is the volume of the sphere?A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.
The volume of a sphere is expressed as:
Volume = (4/3)πr³
Where r is the radius of the sphere and π is the mathematical constant pi (approximately equal to 3.14).
Given that the surface area of the sphere is 16 square feet.
First, we determine the radius r:
Surface area = 4πr²
Hence
16 = 4πr²
Dividing both sides by 4π, we get:
r² = 16/4πr
r = √( 16/4πr )
r = 1.128 ft
Plugging in the value of r that we just found, we get:
Volume = (4/3)πr³
Volume = (4/3) × 3.14 × (1.128 ft)³
Volume = 6.01 ft³
Therefore, teh volume is 6.01 ft³.
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Antonio is working with a new geometric series generated by the equation A(n)=20(1. 1)n-1. His sister challenged him to find the sum of the first 22 terms
The sum of the first 22 terms of the series is approximately 970.876.
The series generated by the equation [tex]A(n) = 20(1.1)^(n-1)[/tex] is a geometric series because it has a common ratio of 1.1. To find the sum of the first 22 terms, we can use the formula for the sum of a geometric series:
Sn = [tex]a(1 - r^n) / (1 - r)[/tex]
where Sn is the sum of the first n terms, a is the first term, r is the common ratio.
In this case, a = 20, r = 1.1, and n = 22. So we can plug these values into the formula:
[tex]S22 = 20(1 - 1.1^22) / (1 - 1.1)[/tex]
Simplifying this expression, we get:
[tex]S22 = 20(1 - 1.1^22) / (-0.1)[/tex]
[tex]S22 = -200(1 - 1.1^22)[/tex]
[tex]S22 = -200(1 - 5.85438)[/tex]
[tex]S22 = -200(-4.85438)[/tex]
[tex]S22 = 970.876[/tex]
Therefore, the sum of the first 22 terms of the series is approximately 970.876.
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You are asked to solve for y in the equation –3 = 5y – 2x, given that x = –4. What is the first step you would take? A. Substitute –4 for x in the equation. B. Add 3 to both sides of the equation. C. Divide both sides of the equation by 3. D. Add 2x to both sides of the equation. Please select the best answer from the choices provided A B C D
Answer:
to get y easily you have to substitute for x in the first equation. the answer is A
Step-by-step explanation:
proving it:
-3=5y-2(-4)
-3=5y+8
then you can collect the like terms to get the final answer.
Show that the numbers are all rational by writing each number as a ratio of integers.
0.3737373737...
0.3737373737... is a rational number and can be written as the ratio of two integers 37 and 99.
Let x = 0.3737373737...
Multiplying both sides of the equation by 100, we get:
100x = 37.37373737...
Subtracting x from 100x, we get:
99x = 37
Hence, x = 37/99, which is a rational number.
Therefore, we have shown that 0.3737373737... is a rational number and can be written as the ratio of two integers 37 and 99.
To check our answer, we can simplify 37/99 by dividing both the numerator and denominator by their greatest common factor, which is 1. This gives us the same expression, 37/99, confirming that it is indeed a rational number.
In general, any decimal that has a repeating pattern can be written as a ratio of two integers and is therefore a rational number. This is because the repeating pattern can be expressed as a finite sequence of digits that can be represented as a fraction with a power of 10 in the denominator, which can be simplified to a ratio of two integers.
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Find the height and slant height of the cone.
Round your answers to the nearest whole
number.
Surface area = 75.4 cm²
22
h≈
l
3 cm
cm
cm
The Height ≈ 4 cm and the Slant height ≈ 5 cm.
To solve for the height and slant height of the cone, we first use the formula for the surface area of a cone:
Surface Area = πrℓ + πr²,where r is the radius of the base, ℓ is the slant height, and π is approximately 3.14.
Since we are given the surface area (75.4 cm²) and the radius (3 cm), we can substitute these values into the formula and solve for ℓ:
75.4 = 3.14(3)(ℓ) + 3.14(3)²75.4 = 9.42ℓ + 28.2646.14 = 9.42ℓℓ ≈ 4.89Now that we have the slant height, we can use the Pythagorean theorem to find the height, h:
h² + 3² = 4.89²h² + 9 = 23.92h² ≈ 14.92h ≈ 3.86Rounding to the nearest whole number, we get the height ≈ 4 cm and the slant height ≈ 5 cm.
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21. In a right triangle b = 14, c = 20, find a. Round to the nearest tenth.
Answer:
a = 14.3
Step-by-step explanation:
Since you have a right triangle you can use the Pythagorean Theorem.
a^2 + b^2 = c^2
we know b and c, so fill them in.
b = 14, c = 20 (this was given in the question)
a^2 + 14^2 = 20^2
simplify the squares.
a^2 + 196 = 400
subtract 196
a^2 = 204
square root both sides.
a = sqrt204
(use a calculator for this part)
a = 14.2828568571
round to the nearest tenth (one decimal place)
a = 14.3
. use a model to predict the car's value after 5 years, rounded to the nearest dollar.
The predicted value of the car after 5 years is $6,000 (rounded to the nearest dollar).
To predict the car's value after 5 years, we can use a linear regression model. We will use the data points given in the problem statement to find the equation of a straight line that fits the trend in the data. Once we have this equation, we can plug in the value of 5 for x to predict the corresponding value of y, which represents the car's value after 5 years.
Using the data points (1, 18000) and (3, 12000), we can find the slope of the line:
slope = (y2 - y1) / (x2 - x1) = (12000 - 18000) / (3 - 1) = -3000
Next, we can use the slope-intercept form of a line to find the equation of the line:
y = mx + b, where m is the slope and b is the y-intercept
Using the point (1, 18000) and the slope we just found, we can solve for b:
18000 = -3000(1) + b
b = 21000
So, the equation of the line is:
y = -3000x + 21000
To predict the car's value after 5 years, we can plug in x = 5 and solve for y:
y = -3000(5) + 21000 = 6000
Therefore, the predicted value of the car after 5 years is $6,000 (rounded to the nearest dollar).
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A beekeeper observes the growth of a bee population in a beehive. The beekeeper finds that the initial population of 125 bees doubles each week.
Which equation can be used to find the number of weeks, w, it takes for the number of bees in the beehive to reach 2,500?
A. 2,500 = 2+125w
B. 2,500 = 2(125)^w
C. 2,500 = 125+2w
D. 2,500 = 125(2)^w
The correct equation can be given by; 2,500 = 125(2)^w. Option D
How do you form equation from sentence?If we have a sentence that we want to convert to equation;
Determine the mathematical relationships or procedures that are being described by carefully reading the statement.Any unknown quantities in the phrase should be given variables.To represent the processes or relationships, use conventional mathematical symbols.Create a clear and succinct written version of the equation.We can see that the beekeeper finds that the initial population of 125 bees doubles each week thus the correct equation is; 2,500 = 125(2)^w.
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The correct equation can be given by; 2,500 = 125(2)^w. Option D
How do you form equation from sentence?
If we have a sentence that we want to convert to equation;
Determine the mathematical relationships or procedures that are being described by carefully reading the statement.
Any unknown quantities in the phrase should be given variables.
To represent the processes or relationships, use conventional mathematical symbols.
Create a clear and succinct written version of the equation.
We can see that the beekeeper finds that the initial population of 125 bees doubles each week thus the correct equation is; 2,500 = 125(2)^w.
An unbiased coin is tossed 15 times. In how many ways can the coin land tails either exactly 7 times or exactly 2 times
Answer:
6688877887
Step-by-step explanation:
B. Write an expression for 3 added to X:
Write an expression for 2 subtracted from x:
The algebraic expression for 3 added to X as required in the task content is; x + 3.
The algebraic expression for 2 subtracted from x as required in the task content is; x - 2.
Which algebraic expressions represent the given word phrase?It follows from the task content that the algebraic expression which represents the given word phrases are to be determined.
There, for the word phrase 3 added to x; we have; x + 3.
On the other hand, for the word phrase; 2 subtracted from x; we have; x - 2.
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Hannah brought $40. 50 to the state fair. She bought a burger, a souvenir, and a pass. The burger was 1/4 as much as the souvenir, and the souvenir cost 2/3 the cost of the pass. Hannah had $2. 00 left over after buying these items
The cost of the souvenir is approximately $15.92.
Let's assume the cost of the souvenir is S.
According to the given information, the cost of the burger is 1/4 of the cost of the souvenir, which means the cost of the burger is (1/4)S.
The cost of the pass is 2/3 of the cost of the souvenir, which means the cost of the pass is (2/3)S.
Hannah had $2.00 left over after buying these items, so we can write the equation:
$40.50 - (1/4)S - S - (2/3)S = $2.00
To solve for S, we'll combine like terms:
$40.50 - (9/12)S - (12/12)S - (8/12)S = $2.00
$40.50 - (29/12)S = $2.00
Next, we'll isolate the variable by subtracting $40.50 from both sides:
-(29/12)S = $2.00 - $40.50
-(29/12)S = -$38.50
To solve for S, we'll divide both sides by -(29/12):
S = (-$38.50) / -(29/12)
S ≈ $15.92
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Show that the numbers are all rational by writing each number as a ratio of integers.
-29/5
-29/5 is rational and can be expressed as a ratio of two integers (-29 and 5).
To show that -29/5 is rational, we need to express it as a ratio of two integers.
We know that -29 is an integer and 5 is also an integer. Therefore, we can write:
-29/5 = (-29) / 5
Since both -29 and 5 are integers, their ratio is a rational number. Therefore, -29/5 is also a rational number.
Another way to see this is to note that any fraction a/b can be written in lowest terms as:
a/b = p/q
where p and q are integers with no common factors (other than 1). To find p and q, we can simplify the fraction by dividing both the numerator and denominator by their greatest common factor (GCF). In this case, the GCF of -29 and 5 is 1, so -29/5 is already in its simplest form.
Therefore, -29/5 is rational and can be expressed as a ratio of two integers (-29 and 5).
To know more about rational number refer to-
https://brainly.com/question/24540810
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Difference between REF and RREF
Answer: if a column contains a leading 1 then the rest of the entries in that column are zeroes
Step-by-step explanation:
