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Simplify quantity 4 x squared plus 12 x minus 16 all over quantity 2x plus 10 over quantity 6 x plus 24 over quantity x squared plus 9x plus 20 . (2 points)

The length of the third side of ALMN is 20 units.

If AGHI and ALMN are similar, then their corresponding sides are proportional.

Let's call the length of the third side of ALMN "x". We can set up the proportion using the two sides of AGHI and ALMN that we know:

10/8 = 15/12 = x/16

To find x, we can cross-multiply and simplify:

15 × 16 = 12x

240 = 12x

x = 240/12

x = 20

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If the circumference of a circular field is 308 m, then it's Area is (b) 7546 m²  .

The formula for the Circumference of circle is = 2πr  ; Where r is = radius ;

The circumference is 308m, so we substitute in the required value and solve for r  ;

⇒ 308 = 2πr

⇒ r = 308/(2π)

⇒ r = 49  ;

Now that we have the radius, Next , we use the formula for the area of a circle to find the area  ;

The area of circle is ⇒ Area = πr² ;

Substituting in the value of radius(r) , we get ;

⇒ Area = π(49)²  ;

⇒ Area = 7546 m²   ;

Therefore , area of the circular field is 7546 square meters.

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The given question is incomplete , the complete question is

The circumference of a circular field is 308m, Find its Area .

(a) 7050 m²

(b) 7546 m²

(c) 7946 m²

(d) 8129 m²

The value of the angle 'x' in the right-angle triangle will be 42.99°.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

The value of the variable 'x' is given by the sine of the angle 'x'. Then we have

sin x = 15 / 22

sin x = 0.6818

sin x = sin 42.99°

x = 42.99°

The value of the angle 'x' in the right-angle triangle will be 42.99°.

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Answer:

Step-by-step explanation:

$3120 and $3888

width of the road=2m

outer Rectangle, I = 40m, b = 16m

Inner Rectangle, I = 36m, b = 12m

Area of Outer rectangle = 40x16= 640m2

Area of inner Rectangle = 36x12= 432m2

Area of the road=640-432 =208m2

cost of paving bricks  $15

=208x15 = $3120. Ans

Area of inner Rectangle 432m2

cost of covering with grass  $9

= 432x9= $3888.

Answer: brick cost= 3120 grass cost =3888

Step-by-step explanation:

Calculate area of the road by subtracting the area of the inner plot (36x12) from the area of the whole plot (40x16). Multiply the individual costs by the area of their respective places.

(40x16) - (36x12) = 208

208x16 = 3120

36x12 = 432

432x9 = 3888

Answer:

If A=30 and B= 70 the first unknown angle Y would be 100. When using the E.A.T  (exterior angle theorem) you add the 2 remote interior angles to get the exterior angle. (Y)

Unknown angle 2 is a interior angle, so we know all 3 of the interior angles must equal 180.

30+70=100

180-100=80

C=80

Step-by-step explanation:

Answer:

(- 12x ^ 2 + 8x + 27y)/(3x * y ^ 2)

Step-by-step explanation:

Answer:because

Step-by-step explanation:a

Answer: 0.56

Step-by-step explanation:

The probability that when a theft occurs, at least one of the 5 systems will detect it is approximately 0.9997.

How likely something is to occur is known as its probability. We can discuss the probabilities of different outcomes, or how likely they are, whenever we are unsure of how an event will turn out.

We can solve this problem using the complement rule. The probability that none of the 5 systems detect the theft is given by:

(1 - 0.82)^5 = 0.00033124

So the probability that at least one system detects the theft is:

1 - 0.00033124 = 0.99966876

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The test static is 1.60 and the p-value is 0.1096, null hypothesis is not rejected and the population mean is not significantly  different from $1000.

Assuming normal distribution

N( μ₀ , σ )

In this case N ( 1000, 200)

From a random sample of 64 accounts we get:

n  = 64

x = sample mean      x = 1040

σ = standard deviation of the population     σ = 200

a) Test Hypothesis

Null Hypothesis               H₀          x =  μ₀ = 1000

Alternative Hypothesis    Hₐ          x ≠ μ₀    

The alternative hypothesis implies a two tail-test. Given that  n > 30 and σ is known we will use z-table

b) z(s) = ( x  - μ₀ ) / σ/√n

z(s) = ( 1040 - 1000 ) / 200/ √64

z(s) = 40*8/200

z(s) = 1.60

c) P-value for  z (score 1.6)     p-value = 0.1096

d) If significance level is 0.05  then  α = 0.05  and   α/2 = 0.025

p-value >  α/2        

Then  the z(s) < z(c)      1.6 < 1.96            where  z(c) is z score for α/2

Hence, null hypothesis is not rejected

e) We can claim that at 95 % (of Confidence Interval) the population mean is not significantly  different from $1000.

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Question is not complete. The complete question is :

A sample of 64 account balances from a credit company showed an average daily balance of $1,040. The standard deviation of the population is known to be $200. We are interested in determining if the mean of all account balances (i.e., population mean) is significantly different from $1,000. 1. State the null and alternative hypothesis. 2. Compute the test statistic. 3. Compute the p-value. 4. Based on the p-value and the significance level of 0.05% make a decision regarding the hypotheses. 5. Interpret your results in the context of the problem.

Answer:

162

Step-by-step explanation:

Whether the zero is in the ones position or the tens position, there are only 9 possibilities for each of the other two digits and they can occur (with possible repetition) in either order. That’s 81 for each zero position for a total of 162.

There are 171 three-digit numbers that have exactly one zero. The zero can be in either the tens or units places, yielding 90 and 81 possibilities respectively.

To determine how many 3-digit numbers have exactly one zero, we need to consider the possible placements of the zero. A 3-digit number has three positions: the hundreds place, tens place, and units place. The zero cannot be in the hundreds place, as that would make it a 2-digit number. So, the zero can only have two possible positions: the tens or units place.

For each case:

So, in total, we have 90 + 81 = 171 3-digit numbers with exactly one zero.

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Answer:

-1/6

Step-by-step explanation:

To solve the inequality 4x-(6x+1)≤ 8x + 2(x-3), we can simplify both sides of the inequality and isolate x on one side:

4x - (6x + 1) ≤ 8x + 2(x-3)

4x - 6x - 1 ≤ 8x + 2x - 6

-2x - 1 ≤ 10x - 6

Subtract 10x from both sides:

-12x - 1 ≤ -6

Add 12x to both sides:

-1 ≤ 6x

Divide both sides by 6:

-1/6 ≤ x

The solution to the inequality is x ≥ -1/6. This means that x is greater than or equal to -1/6, so any value of x that is greater than or equal to -1/6 will satisfy the inequality.

The equation of line r is x = -3/2y + 5/2.

A line's equation is typically expressed in the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. A line's equation expresses the y coordinate of any point on the line in terms of its x coordinate. In other terms, a line equation is a formula that can be used to compute the y coordinate of any point on a line given its x coordinate.

In the given question,

The equation of line r is y = -1/3x + 7.

Line r is perpendicular to line q, so the slopes of the two lines must be opposite reciprocals of one another. The slope of line q is 3, so the slope of line r must be -1/3.

To find the equation of line r, we can use the point-slope formula. The point-slope formula is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.

In line r, (x1, y1) is (1, 3). The slope, m, is -1/3.

Substituting values into the point-slope formula, we have y - 3 = -1/3(x - 1).

Solving for y, we have y = -1/3x + 7.

This equation is written in slope-intercept form, which is the form y = mx + b, where m is the slope and b is the y-intercept.

In line r, the slope is -1/3 and the y-intercept is 7.

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The measure <h = 45 degree, <g= 135 degree, <h = 55 degree and

<k = 125 degree.

When two lines converge, vertical angles are created. Because the angles are opposite one another, vertical angles are also known as vertically opposite angles. They are constantly on par.

Given:

As, from the Figure

<h + 135 = 180 (Linear Pair)

<h = 180 - 135

<h = 45

and, <g = 135 (Vertical Opposite Angle)

Now, <m + 125 = 180 (Linear Pair)

<m = 180 - 125

<h = 55

and, <k = 125 (Vertical Opposite Angle)

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The proof that AE = EF is done from the congruency theorem of triangles and the Pythagorean identity.

In order to prove that AE = EF, note that angle CEF is a right angle since EF is perpendicular to the diameter CD and intersects it at E.

Since AE = EB, triangles AEB and CED are congruent (SAS theorem)

Therefore, angle EAF is congruent to angle ECF.

Also, angle EAF is a right angle, since it is inscribed in a semicircle with a diameter CD.

Therefore, triangles EAF and ECF are similar by the Angle-Angle (AA) theorem.

Since they are similar, the ratio of corresponding side lengths is the same.

Since AE = EB, we have that:

AE / EF = EC / CF

But we also know that EC = ED + DC = ED + 2EF, since CD is the diameter of the semicircle and EF meets it at E perpendicularly.

Similarly, we have CF = CD + DF

CF = 2EF + DF, where DF is the other leg of the right triangle CDF.

Substituting these expressions for EC and CF in the above equation, we get:

AE / EF = (ED + 2EF) / (2EF + DF)

Simplifying this equation, we get:

AE / EF = (ED/EF) + 2 / (2 + DF/EF)

But ED/EF = sin(DEF) and DF/EF = sin(EFD) by the definition of sine in right triangle DEF. Since the angles DEF and EFD add up to 90 degrees, their sines are complementary.

Therefore, we have that:

ED/EF = cos(EFD) and DF/EF = sin(DEF)

Substituting these expressions in the above equation, we get:

AE / EF = cos(EFD) + 2 / (2 + sin(DEF))

But cos(EFD) + 2 = sin(DEF) (Pythagorean identity).

Therefore, we have:

AE / EF = sin(DEF) / (2 + sin(DEF))

Multiplying both sides by (2 + sin(DEF)), we get:

AE = EF

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Answer: 258 envelopes

Step-by-step explanation:

Answer:

resistant

because the median is not affected by the size of an outlier and does not change even if a particular outlier is replaced by an even more extreme value, we say the median is resistant to outliers.

The largest possible side length of the tiles that can be used is `12` inches as it can cover the entire bathroom without any gaps or cutting of tiles.

The largest tile that can be used is a square tile. To calculate the side length of the largest possible tile, divide the length and width of the bathroom by 4.

`48/4 = 12`

`60/4 = 15`

The largest possible side length of the tiles that can be used is `12` inches. Jayla's parents are replacing their bathroom floor with square tiles. The floor is a rectangle that is `48` inches by `60` inches. To cover the entire bathroom with no gaps, and without having to cut any of the tiles, they need to use a tile that is the same size as the largest possible tile that can cover the entire floor without any gaps.

To calculate the side length of the largest possible tile, divide the length and width of the bathroom by 4. This is because a tile needs to cover 4 sides of the floor without any gaps, so the side length of the tile needs to be equal to the length divided by 4, or the width divided by 4.

In this case, the side length of the largest possible tile is `12` inches. This is because `48/4 = 12`, and `60/4 = 15`. As `15` is larger than `12`, the side length of the largest possible tile is `12` inches. This means that the tiles need to be `12` inches by `12` inches in size to cover the entire bathroom without any gaps.

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The estimated quantity of dye left in a healthy pancreas 30 minutes after the injection, rounded to the closest hundredth of a grams, is 0.07 grams.

As per the question given,  

After the dye is injected, a healthy pancreas will secrete 4% of the remaining amount of dye each minute. Let's use exponential decay to model the amount of dye remaining in the pancreas over time.

The amount of dye remaining after t minutes can be expressed as:

R(t) = 0.3 * (1 - 0.04)^t

We want to find the amount of dye remaining after 30 minutes, so we can substitute t=30 into the equation and calculate:

R(30) = 0.3 * (1 - 0.04)^30

R(30) = 0.3 * (0.96)^30

R(30) = 0.3 * 0.2312

R(30) = 0.0694

Rounding to the nearest hundredth of a gram, the predicted amount of dye remaining in a healthy pancreas 30 minutes after the injection is 0.07 grams.

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Answer:

  0.09 g

Step-by-step explanation:

You want to know the amount remaining of 0.3 g of dye after 30 minutes if the amount decreases by 4% per minute.

The amount can be modeled by the exponential function ...

  q = a·b^t

where q is the quantity remaining, 'a' is the initial quantity, b is the growth factor per minute, and t is the number of minutes.

The growth factor is related to the growth rate by ...

  b = 1 + growth rate

Here, the growth rate is -4% per minute, so the growth factor is ...

  b = 1 +(-0.04) = 0.96

The initial quantity is 0.3 grams, so the remaining quantity after 30 minutes is ...

  q = 0.30·0.96^30 ≈ 0.08816 ≈ 0.09 . . . . grams

The amount of dye remaining after 30 minutes is predicted to be 0.09 g.

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The probability of randomly drawing a candy that is not brown, replacing it, and then drawing a white candy is 0.08, or 8%.

There are 70 sweets in the jar, 14 of which are brown, hence the likelihood of getting a candy that is not brown on the first draw is:

(70 - 14) / 70 = 56 / 70 = 0.8 P(not brown)

The jar still has 70 candies after replacing the candy, and there are now 7 white candies. As a result, the likelihood of drawing a white candy on the second draw is:

P(white) = 0.1 / 70

Because the two drawings are independent (the first candy is replaced before the second), we can multiply the odds to get the likelihood of both events occurring:

P(not brown and white) = P(white) * P(not brown) = 0.8 * 0.1 = 0.08

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The estimated percentage of states with an average per capita income greater than 32.5 k  is:we need to use the ogive (cumulative frequency curve) to determine the percentage of states with an average per capita income greater than 32.5k.

Assuming that the ogive is a continuous curve, we can estimate the percentage by finding the value on the horizontal axis corresponding to the 50% mark on the vertical axis, and then subtracting it from 100%. From the graph, we can see that the 50% mark corresponds to a value of around 30 k, which is between the values for Oklahoma and Pennsylvania. To get a more accurate estimate, we can use linear interpolation between these two data points.

Let's assume that the values for Oklahoma and Pennsylvania are

(x₁,y₁) = (25k,40%) and (x₂,y₂) = (35k,60%)

respectively. Then the equation of the straight line connecting these two points is:

(y-y₁) =(y₂-y₁) / (x₂-x₁) * (x-x₁)

Substituting in the values gives:

y - 40 = (0.6 - 0.4)/(35 - 25) * (x - 25)

y - 40 = 0.02(x - 25)

y = 0.02x - 0.5

To find the value of x that corresponds to the 50% mark, we can set y = 50% and solve for x:

50 = 0.02x - 0.5

0.02x = 50.5

x = 2525

So the estimated value for x is 25.25k. Therefore, the estimated percentage of states with an average per capita income greater than 32.5k is:

scss

Copy code

100% - 40% - (10% * (32.5 - 25.25)/(30 - 25))

= 50.5%

Therefore, we estimate that about 50.5% of the states have an average per capita income greater than 32.5k.

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The answers are a) standard deviation ≈  0.02 b) probability ≈ 0.95 c) standard deviation ≈  0.031 d) probability ≈ 0.8098 e) decrease in P = 0.1402

Given: p = 75% or 0.75

n = 450

a) The sampling distribution of the sample proportion is approximately normal with mean = 0.75 and standard deviation is [tex]\sqrt \frac{p(1-p)}{n}[/tex]

= [tex]\sqrt{\frac{0.75(1-0.75)}{450} }[/tex] = 0.02

b) [tex]\^{p} - p[/tex] = 0.04

[tex]z = \frac{\^{p} - p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]

z = ±1.96(approx.)

p(-0.04 <  [tex]\^{p} - p[/tex] < 0.04)

=P(-1.96 < z < 1.96) = 1 - 2P(z < -1.96)

= 1 - 2(0.0250) = 0.95

c) The sampling distribution of the sample proportion is approximately normal with mean = 0.75 and standard deviation [tex]\sqrt \frac{p(1-p)}{n}[/tex]

= [tex]\sqrt{\frac{0.75(1-0.75)}{200} }[/tex] = 0.031

d) [tex]\^{p} - p[/tex] = 0.04

[tex]z = \frac{\^{p} - p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]

z = ±1.31(approx.)

p(-0.04 <  [tex]\^{p} - p[/tex] < 0.04)

=P(-1.31 < z < 1.31) = 1 - 2P(z < -1.31)

= 1 - 2(0.0951) = 0.8098

e) Determine the difference in probabilities (of part b) and part d))

The loss in precision by decreasing the sample size 0.9500 - 0.8098 = 0.1402

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Complete question is:

In 2008 the Better Business Bureau settled 75% of complaints they received. Suppose you have been hired by the Better Business Bureau to investigate the complaints they received this year involving new car dealers. You plan to select a sample of new car dealer complaints to estimate the proportion of complaints the Better Business Bureau is able to settle. Assume the population proportion of complaints settled for new car dealers is 0.75, the same as the overall proportion of complaints settled in 2008. a) Suppose you select a sample of 450 complaints involving new car dealers. Show the sampling distribution of [tex]\overline{p}[/tex].b) Based upon a sample of 450 complaints, what is the probability that the sample proportion will be within .04 of the population proportion? c) Suppose you select a sample of 200 complaints involving new car dealers. Show the sampling distribution of [tex]\overline{p}[/tex] . d) Based upon the smaller sample of only 200 complaints, what is the probability that the sample proportion will be within .04 of the population proportion? e) As measured by the increase in probability, how much do you gain in precision by taking the larger sample in part (b)?

Answer:

a)  See the attachment for the completed Venn diagram.

b)  The number of people who liked to watch television only is 20.

c)  The total number of people who took part in the survey was 200.

Step-by-step explanation:

Draw a Venn diagram with two overlapping circles.

Label one circle "Radio" and the other circle "TV".

Given that 50 people like to listen to the radio but not like to watch television, place the number 50 in the part of the radio circle that does not overlap the TV circle.

Given that 120 people like to listen to the radio, and 50 people like to listen to the radio but not like to watch television, then the number of people who like to listen to the radio and watch tv is:

Therefore, place the number 70 in the part where the two circles overlap.

Given that 110 people don't like to watch television, and 50 people like to listen to the radio but not like to watch television, then the number of people who don't like to listen to the radio or watch television is:

Therefore, place the number 60 in the area outside the two circles.

Given that 80 people don't like to listen to the radio, and 60 people don't like to listen to the radio or watch television, then the number of people who like to watch the television only is:

Therefore, place the number 20 in the part of the TV circle that does not overlap the radio circle.

Now the Venn diagram has been completed, we can find the total number of people who took part in the survey by adding all the numbers in the Venn diagram:

Therefore, there was a total of 200 people who took part in the survey.

To prove QR ~ SR, Use SAS to show triangle PRQ is congruent to

triangle PRS.

We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.

Given,  PR bisects ZQPS, PQ = 12 units, and PS = 12 units

Now, The two triangles formed PQR and PSR share the same side PR.

Also m∠SPR = m∠QPR, Therefore these two triangles are congruent, and hence QR ~ SR

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Option A, which is 4 x 15 + 1 - 5 x 4 x 1, is the correct expression that is equal to 45 x 4 + 5.

To show this, we can simplify the expression as follows:

4 x 51 + 1 - 5 x 4 x 1

= 204 + 1 - 20

= 205 - 20

= 184

Then, we can check if 185 is equal to 45 x 4 + 5:

45 x 4 + 5

= 180 + 5

= 185

Since 185 is equal to 185, it is concluded that an expression that is "equal to" 45 x 4 + 5, is held by option A.

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A. The probability of no nap is 0.390625, one nap is 0.234375 and two naps is 0.156250. B. The probability of zero naps is 0.152587890625, one nap is 0.3076171875, and two naps is 0.146484375. C. The probability of no nap is 0.02734375, one nap is 0.14453125, and two naps is 0.271484375. D. The probability of no naps decreases as the mean number of naps increases.

A. We can calculate the probability of no nap, one nap, and two naps by using the Poisson Distribution formula. The mean number of naps (λ) is four, so the probability of no nap (x=0) is 0.390625, one nap (x=1) is 0.234375, and two naps (x=2) is 0.156250.

B. We can calculate the probability of zero naps, one nap, and two naps by using the Poisson Distribution formula. The mean number of naps (λ) is four, so the probability of zero naps (x=0) is 0.152587890625, one nap (x=1) is 0.3076171875, and two naps (x=2) is 0.146484375.

C. We can calculate the probability of no nap, one nap, and two naps by using the Poisson Distribution formula. The mean number of naps (λ) is eight, so the probability of no nap (x=0) is 0.02734375, one nap (x=1) is 0.14453125, and two naps (x=2) is 0.271484375.

D. We can see from the answers in (b) and (c) that the probability of no naps decreases as the mean number of naps increases, suggesting that a Poisson random variable follows a decreasing probability distribution.

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The area of the given figure is 12 square meters

The given figure is a parallelogram

Parallelogram is a geometric figure that has both pair of opposites parallel sides and opposite sides are equal . Number of vertices and edges are four

The height of the parallelogram = 2 meters

The base length of the parallelogram = 6 meters

The area of the parallelogram = The height of the parallelogram × The base length of the parallelogram

Substitute the values in the equation

The area of the parallelogram = 2 × 6

Multiply the numbers

= 12 square meters

Therefore, the area is 12 square meters

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I have solved the question in general , as the given question is incomplete

The complete question is :

What is the area of the figure ?

Answer:

[tex]g(3) = 11[/tex]

Step-by-step explanation:

Greetings!!!

The given function

[tex] g(x) = x {}^{2} + 2[/tex]

What we are looking now is what will be the value when 3 is substituted in the variable x.

[tex]g(3) = (3) {}^{2} + 2[/tex]

Solve the expression

[tex]g(3) = 9 + 2[/tex]

Add the numbers

[tex]g(3) = 11[/tex]

Thus, the value of g(3)= 11

Hope it helps!!!

The experimental probability that the number rolled was odd is

23 over 60.

What is experimental probability?

Actual experiments and sufficient documentation of the occurrence of occurrences serve as the foundation for experimental probability, sometimes referred to as empirical probability. A trial is a repeating of an experiment that is performed a certain number of times.

We are given a table showing he frequency of each number rolled.

We know that the odd number outcomes are 1, 3 and 5.

So,

P (x = 1) = 8/60

P (x = 3) = 6/60

P (x = 5) = 9/60

So, the experimental probability that the number rolled was odd is

⇒P ( x is odd) = P (x = 1) + P (x = 3) + P (x = 5)

⇒P ( x is odd) = 8/60 + 6/60 + 9/60

⇒P ( x is odd) = 23/60

Hence, the experimental probability that the number rolled was odd is 23 over 60.

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