2. The table below shows the lengths of four earthworms found by the lake. Earthworm A B C D Length (cm) 10.2 3 9- 4 9.23 9/²/2 2 Write the lengths in order from shortest to longest.​

For two populations for which μ₁ = 31,σ₁ = 2, μ₂ = 27, and σ₂ = 4. The shape of the distribution is approximately normal. So, the correct choice for answer is option (b). The mean of normal distribution is equals to 4.

In statistics, the collected data distribution shape sometimes normal and sometimes non-normal. In testing of hypothesis, to use the test statistics we have to check whether data is normally or not. Here we have, two populations. In first population : mean μ₁ = 31,

standard deviations,σ₁ = 2,

sample size, n₁ = 49

In case of second sample, mean, μ₂ = 27,

standard deviations, σ₂ = 4.

Sample size, n₂ = 59

Since, population standard deviation are known and sample sizes are greater than 30, therefore the shape of the sampling distribution of the difference of sample means is approximately normal. The shape of the distribution is approximately normal. Mean of the sampling distribution of [tex] \bar x_1 - \bar x_2[/tex] are

[tex]\mu_{ \bar x_1 - \bar x_2} = \mu_1 - \mu_2 [/tex]

= 31 - 27 = 4

Hence, Mean of the distribution is 4.

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Complete question:

Consider two populations for which μ₁ = 31,σ₁ = 2, μ₂ = 27, and σ₂ = 4. Suppose that two independent random samples of sizes n₁ = 49 and n₂ = 59 are selected. Describe the approximate sampling distribution of x₁ bar - x₂ bar (center, spread, and shape). What is the shape of the distribution?

a) The distribution would be non-normal.

b) The distribution is approximately normal.

c) The shape cannot be determined.

What is the mean of the distribution?

70% of the population prefers coca-cola over pepsi, the probability that both prefer coca-cola is 0.49.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means.

Probability is a way to gauge how likely something is to happen. Several things are difficult to forecast with absolute confidence. With it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can vary from 0 to 1, with 0 being an impossibility and 1 denoting a certainty. For pupils in Class 10, probability is a crucial subject since it teaches all the fundamental ideas of the subject. One is the probability of every event in a sample space.

70% of the population prefers Coca-Cola over Pepsi,

that is 0.7

The probability of the Pepsi is 30% = 0.3

The probability that both prefers coca cola is 0.7 x 0.7 = 0.49.

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The measures of diabetes mellitus, coronary artery disease, and renal disease in study subjects represent the nominal level of measurement. This is because these measures are categorical in nature and cannot be ranked or ordered.

Nominal level of measurement is the simplest form of measurement which assigns a name or number to an attribute. The attributes can be classified into different categories or classes without any ranking.

Nominal level of measurement is commonly used in research to represent things like gender, race, marital status, religion, and so on. In this case, the attributes being measured are the different chronic diseases. These are categorical and cannot be ranked.

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The final price of the pen is $1.76 after adding the markup percentages by both the wholesaler and the retailer.

The final price is the total amount of money that a customer pays to purchase a product or service. It includes the cost of the product or service plus any additional fees or charges, such as taxes or shipping costs.

The final price of the pen can be found by adding the markup percentages to the original price of $0.50.

Markup by the wholesaler = 60% of $0.50 = $0.30

Price after markup by wholesaler = $0.50 + $0.30 = $0.80

Markup by the retailer = 120% of $0.80 = $0.96

Final price of the pen = $0.80 + $0.96 = $1.76

Therefore, the final price of the pen is $1.76 after adding the markup percentages by both the wholesaler and the retailer.

For example, if a product costs $50 and there is a 10% sales tax, the final price would be $55 (50 + 5). Similarly, if a service costs $100 and there is a $10 delivery fee, the final price would be $110 (100 + 10).

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Answer:

√9797

The result can be shown in multiple forms.

Exact Form:√9797

Decimal Form:9.84885780…

Answer:

the answer for the equations is

[tex]x = - 11[/tex]

The probability that exactly 5 of the next 7 patients survive the operation is approximately 0.123, or 12.3%.

To find the probability that exactly 5 out of the next 7 patients survive the operation, we can use the binomial probability formula, which is:
[tex]P(X=k) = C(n, k) * p^k * (1-p)^(n-k)[/tex]
where:
- P(X=k) represents the probability of exactly k successes (survivals) in n trials (operations)
- C(n, k) is the number of combinations of n items taken k at a time
- n is the number of trials (in this case, 7 patients)
- k is the number of successful outcomes (5 patients surviving)
- p is the probability of a successful outcome (0.9 for a patient surviving the operation)
Applying the formula, we have:
[tex]P(X=5) = C(7, 5) * 0.9^5 * (1-0.9)^(7-5)[/tex]
First, let's calculate the number of combinations C(7, 5):
C(7, 5) = 7! / (5! * (7-5)!)
C(7, 5) = 7! / (5! * 2!)
C(7, 5) = (7 * 6 * 5 * 4 * 3 * 2 * 1) / (5 * 4 * 3 * 2 * 1 * 2 * 1)
C(7, 5) = 21
Now, we can plug this into the binomial probability formula:
[tex]P(X=5) = 21 * 0.9^5 * 0.1^2[/tex]
P(X=5) = 21 * 0.59049 * 0.01
P(X=5) ≈ 0.1232019.

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The measure of ZL in parallelogram JKLM is 14x - 5.

A parallelogram is a quadrilateral with two pairs of parallel sides. That is, opposite sides are parallel and congruent. Parallelograms have several properties that make them useful in geometry and other fields.

In a parallelogram, opposite sides are parallel and congruent. Therefore, we can set up an equation that relates the measures of the opposite sides of parallelogram JKLM:

KL = MJ

We can use this equation to solve for x, and then find the measure of ZL.

Starting with KL, we have:

KL = 15x - 12

Now, for MJ, we need to notice that MJKL is a rectangle because it has a right angle at K. In a rectangle, opposite sides are congruent. Therefore, we have:

MJ = KL = 15x - 12

Now we can use the given expression for MJ to set up an equation for JL in terms of x:

JL = 14x - 5

We can use the fact that JKLM is a parallelogram to set up another equation that relates JL and ZL:

JL = ZL

Putting the two equations together, we get:

JL = JL

14x - 5 = JL = ZL

Therefore, ZL = 14x - 5.

We can substitute the expression we found earlier for JL into this equation to get:

ZL = 14x - 5 = JL = 14x - 5

Simplifying, we get:

ZL = 14x - 5

Therefore, the measure of ZL in parallelogram JKLM is 14x - 5.

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1. The perimeter is approximately 24.16 units.

2. Determining the height of this triangle was different from the previous activities because we had to first find the length of one side of the triangle and then find the corresponding height that intersects that side at a right angle. In previous activities, the height was either given or easily determined from the given information.

The special two-item character sequence that represents special characters like \n is known as an Escape Sequence. So the option B is correct.

An escape sequence is a sequence of characters that does not represent itself when used inside a character or string literal, but is translated into another character or a sequence of characters. It is used to signal an alternative interpretation of a series of characters. Common examples are the escape sequences used in C/C++ and other programming languages, such as "\n" for newline, "\t" for tab, and "\\" for a backslash. So the option B is correct.

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The complete question is:

The special two-item character sequence that represents special characters like \n is known as a(n) ?

a. backslash code

b. escape sequence

c. Unicode spec

d. literal character

When measuring the effects of a new diuretic medication, hourly urine output represents the ratio level of measurement.

What is ratio level of measurement?

Ratio level of measurement is a type of measurement that features a true zero point, meaning that the value 0 represents the absence of the characteristic being measured.

Some examples of ratio level measurements include weight, height, length, distance, speed, and many others. In this case, the hourly urine output of subjects is measured to determine the effects of a new diuretic medication.

The hourly urine output is a ratio measurement because it has a true zero point, which is the absence of urine output. In other words, if there is no urine output, the value would be 0, which represents the absence of the characteristic being measured.

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the adult population in millions in 2015 was 197.37 million

The student question is asking about the adult population in millions, given that the Bureau of Labor Statistics announced that 141.13 million were employed, 16.59 million were unemployed, and 39.65 million were not in the labor force in 2015.

To find the adult population, we need to add the number of employed, unemployed, and not in the labor force adults. This can be done as follows:

Adult population = Employed + Unemployed + Not in the labor force

= 141.13 million + 16.59 million + 39.65 million= 197.37 million

Therefore, the adult population in millions in 2015 was 197.37 million (rounded to two decimal places).

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The statistical test to run in this scenario is a paired t-test.

A paired t-test is appropriate in this situation because it is used to compare the means of two related groups. In this case, the related groups are the same patients measured at two different time points (2 weeks and 6 months after being prescribed a new medication). The paired t-test assumes that the differences between the two time points are normally distributed.

To conduct the test, we would calculate the mean difference between the two time points and the standard deviation of the differences. We would then calculate the t-statistic and compare it to the critical value from the t-distribution with n-1 degrees of freedom. If the calculated t-value exceeds the critical value, we would reject the null hypothesis that there is no difference between the two time points.

Therefore, a paired t-test is the appropriate statistical test to determine whether there is a significant difference in medication adherence between the two time points

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For supplementary angles 13x + 14 = A, 11x + 28= B​ and A is parallel B, A=B

Therefore x=7

A and B's corresponding angles are congruent if A and B are parallel. As a result, we may equalize the formulas for the respective angles and find x:

13x + 14 = 11x + 28

2x = 14

x = 7

Consequently, we must fix x equal to 7 in order to make A and B parallel. When we insert this value into the formulas for A and B, we obtain:

A = 13(7) + 14 = 105

B = 11(7) + 28 = 105

The corresponding angles of A and B are now congruent, and A and B are equal and parallel.

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part B:  In student A's verification the two trigonometric identities are

                             i)  sin²x+cos²x=1 [ Pythagorean trigonometric identity]

                             ii) cot x= cos x/ sin x  [ Ratio trigonometric identities]

                                 tan x= sin x/ cos x

And the identities appeared in step 3 and 6.

What is trigonometric identities?

Trigonometric Identities are being needed whenever trigonometric functions are involved in an expression.  Geometrically, these identities involve  trigonometric functions for example sine, cosine, tangent, cotangent of one or more angles.

Here first trigonometric identity showed in step 3

1 is replaced by sin²x+cos²x.

Based on Pythagorean trigonometric identities if Ф is an acute angle of a right angled triangle then sin²Ф+ cos²Ф = 1.

Another trigonometric identity used in step 6

cot x= cos x/ sin x  

tan x= sin x/ cos x

These are called ratio trigonometric identities.

Hence, In student A's verification the two trigonometric identities are

                             i)  sin²x+cos²x=1 [ Pythagorean trigonometric identity]

                             ii) cot x= cos x/ sin x  [ Ratio trigonometric identities]

                                 tan x= sin x/ cos x

And the identities appeared in step 3 and 6.

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The equation of ellipse will be  [tex]\frac{(x-4)^{2} }{16 } + \frac{(y-5)^{2} }{9 } =1[/tex]

An ellipse is the locus of all those points in a plane such that the sum of their distances from two fixed points , which is a constant. Those fixed points are known as the foci in singular term focus. The fixed line is known as directrix and the constant ratio is called the eccentricity of ellipse.

The ellipse with vertices (0, 5) and (8, 5) and minor axis of length 6.

Now the midpoint is( [tex]\frac{0+8}{2}[/tex] , [tex]\frac{5+5}{2}[/tex] )

                                 ( 4, 5)

So the center is (4, 5)

The equation  of the ellipse is

[tex]\frac{(x-h)^{2} }{b^{2} } + \frac{(y-k)^{2} }{a^{2} } =1[/tex]   where b is the semi major axis and a is the semi minor axis.

where (h, k) is the center. Here it is ( 4, 5)

Here 2a= 6 and 2b=8

Hence, the equation of ellipse will be

 [tex]\frac{(x-4)^{2} }{16 } + \frac{(y-5)^{2} }{9 } =1[/tex]

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Approximately 58.33% of the workers in the group are making over $25 an hour. The percentage was obtained by finding the area under the uniform distribution curve above the value of $25.

Since the hourly wages of the workers are uniformly distributed on the interval [20, 32], the probability density function is constant on this interval. The area under the probability density function between any two points a and b gives the probability that a randomly chosen worker's wage will be between a and b. Therefore, the probability that a worker's wage is above $25 is given by the area under the probability density function from 25 to 32, which is (32-25)/(32-20) = 7/12 or approximately 58.33%. Thus, approximately 58.33% of the workers are making over $25 an hour.

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Answer:

STAN BTS

Step-by-step explanation:

The patient will reach a level of Ibuprofen of only 10 mg between the 6th and 7th hour after taking the 200 mg dose.

A logarithm is a mathematical function that measures the relationship between two quantities, by expressing one quantity in terms of another. More specifically, a logarithm is the power to which a base must be raised to produce a given number.

To model the decay of Ibuprofen in the patient's system, we can use the equation:

A = A0 * [tex]e^(-kt)[/tex]

where A is the amount of Ibuprofen in the patient's system after t hours, A0 is the initial amount of Ibuprofen (200 mg in this case), and k is the decay constant.

To find k, we can use the fact that after one hour, the amount of Ibuprofen in the patient's system has decayed to 136 mg:

136 = 200 * [tex]e^(-k)[/tex]

Solving for k, we get k = ln(5/7) ≈ -0.3365.

Now we can use the equation A = 10 mg and solve for t:

10 = 200 * [tex]e^(-0.3365t)[/tex]

Dividing both sides by 200 and taking the natural logarithm of both sides, we get:

ln(0.05) = -0.3365t

Solving for t, we get t ≈ 6.8 hours.

Therefore, the patient will reach a level of Ibuprofen of only 10 mg between the 6th and 7th hour after taking the 200 mg dose. Answer: C.

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Answer:

a.  a = 144, b = 67

Step-by-step explanation:

a + 36 = 180  they are consecutive interior angles, so they add up to 180

a = 180 - 36 = 144

b + 113 = 180  they are consecutive interior angles, so they add up to 180

b = 180 - 113 = 67

Comparing using volume , The party store can 27 more smaller party hats on the shelf than larger party hats.

A cone is a three-dimensional geometric shape that tapers smoothly from a circular base to a point called the apex or vertex. It has a curved surface that extends from the base to the vertex and a circular base that is perpendicular to the axis of the cone.

We need to compare the number of smaller party hats that can fit on the shelf to the number of larger party hats that can fit on the same shelf. Since the hats are in the shape of cones, we need to use the formula for the volume of a cone to calculate their sizes.

The volume of a cone can be calculated using the formula:

[tex]V = \frac{1}{3}\pi r^2h[/tex]

where V is the volume, r is the radius of the base, h is the height of the cone, and π is the mathematical constant pi (approximately equal to 3.14).

Let's assume that the larger party hats have a radius of 1.5 feet and a height of 3 feet, while the smaller party hats have a radius of 1 foot and a height of 2 feet.

The volume of a larger party hat is:

[tex]V_1 = \frac{1}{3}\times\pi\times (1.5 ft)^2\times(3 ft) =3.14 ft^3[/tex]

The volume of a smaller party hat is:

[tex]V_2 = \frac{1}{3}\times\pi\times (1 ft)^2\times(2 ft) =0.21 ft^3[/tex]

The total volume of the shelf is 6 feet long and its cross-section is a rectangle, so its volume is:

[tex]V_{shelf} = (6 ft)\times(1 ft)\times(1 ft) = 6 ft^3[/tex]

To find out how many larger party hats can fit on the shelf, we need to divide the volume of the shelf by the volume of a single large party hat:

[tex]n_1 =\frac{ V_{shelf}} { V_1} = 1.91[/tex]

To find out how many smaller party hats can fit on the shelf, we need to divide the volume of the shelf by the volume of a single small party hat:

[tex]n_2 =\frac{ V_{shelf}}{ V2} = 28.57[/tex]

Rounding to the nearest whole number, we get:

n1 = 2

n2 = 29

Therefore, the party store can fit 29 - 2 = 27 more smaller party hats on the shelf than larger party hats.

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Answer: so there are two party hats, one is smaller with a radius of 4 inches and a volume of 100.5 cubic inches. The other one is larger with a radius of 6 inches and a volume of 209.4 cubic inches.

First, let's find out how many of the larger party hats can fit on the shelf. The shelf is 6 feet long, which is 72 inches long. We're gonna divide the length of the shelf by the length of the larger party hat.

So, for the larger party hat, the height is 6 inches, and the radius is 6 inches. The formula to find the volume of a cone is V = (1/3) * π * r^2 * h. Plugging in the values, we get V = (1/3) * 3.14 * 6^2 * 6 = 452.16 cubic inches.

To find out how many of the larger party hats can fit on the shelf, we'll divide the length of the shelf by the length of the larger party hat. 72 inches divided by 6 inches gives us 12.

So, 12 of the larger party hats can fit on the shelf.

Now, let's do the same for the smaller party hat. The height is 8 inches, and the radius is 4 inches. Using the same formula, V = (1/3) * 3.14 * 4^2 * 8 = 134.19 cubic inches.

To find out how many of the smaller party hats can fit on the shelf, we'll divide the length of the shelf by the length of the smaller party hat. 72 inches divided by 8 inches gives us 9.

So, 9 of the smaller party hats can fit on the shelf.

Now, to find out how many more of the smaller party hats can fit on the shelf than the larger party hats, we subtract the number of larger party hats from the number of smaller party hats. 9 minus 12 gives us -3.

The result is negative, which means that we can't fit more smaller party hats than the larger ones. In fact, we can fit 3 fewer smaller party hats on the shelf than the larger ones.

Step-by-step explanation: I hope this helps.

The total cost to operate his car for the year is then the sum of his fixed costs and his variable costs, or $10,018.00.

Annual variable is measured or observed over a 12-month period.

The annual variable costs for Anwar Mabak is $7,200.00. This can be calculated by multiplying the total number of miles driven (22,500) by the cost per mile ($0.32).

Annual Variable Costs = 22,500 x $0.32

      = $7,200.00

The total cost to operate his car for the year is then the sum of his fixed costs and his variable costs, or $10,018.00.

Total Costs = Fixed Costs + Variable Costs

    = $2,818.00 + $7,200.00

    = $10,018.00

Anwar Mabak's variable costs are a direct result of the number of miles he drives during the year, since he pays a certain amount for each mile he drives. This is why his variable costs increase or decrease depending on the number of miles he drives.

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The missing frequency in the given table is 24.

What is frequency?

To find the missing frequency, we need to use the information given in the histogram and the frequency table.

We can see from the histogram that the missing class interval is 26-28.

The total frequency for all class intervals is the sum of the frequencies in the table:

110 + 36 + 180 + f = 326 + f

We also know that the total frequency is the number of phones recorded by the manufacturer, so we can assume that the total frequency is a whole number.

Since the sum of the frequencies in the table is 326, the missing frequency must be:

f = total frequency - sum of the other frequencies

f = 350 - 326

f = 24

Therefore, the missing frequency is 24.

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Answer:

The distance between points A and D is 9 units.

The distance between points E and F is approximately 7.28 units.

Step-by-step explanation:

The probability that a rental car delivered to the firm needs a tune-up is 0.0000308, or approximately 0.0031%. The probability that a car comes from agency 2 needs a tune-up is 0.0234, or approximately 2.34%.

The probability that an event will occur or a claim will be true is measured by probability theory, a branch of mathematics. The probability of an occurrence is a number from 0 as well as 1, where around 0 represents how likely the occurrence would be to occur while 1 represents certainty. A probability is just a numeric illustration of the possibility that a specific occurrence will take place. Probabilities can also be expressed as percentages ranging between 0% to 100% or even from 0 to 1. the ratio of the number of outcomes to the proportion of occurrence in a whole set of equally probable options that lead to a specific occurrence.

given,

(a) Let's denote the event that a car comes from agency i as Ai and the event that a car needs a tune-up as T. We want to find the probability that a rental car delivered to the firm will need a tune-up, which can be written as P(T).

P(T) = P(T|A1)P(A1) + P(T|A2)P(A2) + P(T|A3)P(A3)

Substituting the given probabilities, we get:

P(T) = 0.05% * 0.36% + 0.02% * 0.06% + 0.02% * 0.58%

P(T) = 0.000018 + 0.0000012 + 0.0000116

P(T) = 0.0000308

Therefore, the probability that a rental car delivered to the firm will need a tune-up is 0.0000308, or approximately 0.0031%.

(b) Let's denote the event that a car comes from agency 2 as A2. We want to find the probability that a car comes from agency 2 given that it needs a tune-up, which can be written as P(A2|T).

P(A2|T) = P(T|A2)P(A2) / P(T)

Substituting the given probabilities, we get:

P(A2|T) = 0.02% * 0.06% / 0.0000308

P(A2|T) = 0.00000072 / 0.0000308

P(A2|T) = 0.0234

Therefore, the probability that a rental car delivered to the firm needs a tune-up and came from agency 2 is 0.0234, or approximately 2.34%.

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Answer: 12 yards

Step-by-step explanation:

Melanie bought 12 yards of ribbon.

(1 yard = 3 feet)

Answer:

Square: [tex]A = s^{2}[/tex]

Parallelogram: [tex]A = b x h[/tex]

Trapezoid: [tex]A = \frac{1}{2} xh x (base_{1} +base_{2})[/tex]

Triangle: [tex]A = \frac{1}{2} x b x h[/tex]

Answer:     Square:

    Parallelogram:

Square:

Parallelogram:

Trapezoid:

Triangle:

    Trapezoid:

       Triangle:

Step-by-step explanation:

The standard error of the mean (SEM) in statistics is a measure of the variability or dispersion of a sample mean.

The standard error of M in statistics is the standard deviation of the distribution of sample means. It is a measure of the standard distance between the sample means and the actual population mean.

It indicates the degree of sampling variability of a sample mean. It is a very important tool in inferential statistics that allows the determination of the margin of error in a statistical estimation.

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Answer:

A = 3 1/4 + 2 1/4 = 5 2/4 = 5 1/2

B = 2 1/4 + 1 1/2 = 2 1/4 + 1 2/4 = 3 3/4

C = A + B = 5 1/2 + 3 3/4 = 5 2/4 + 3 3/4 =

8 5/4 = 9 1/4

Answer:

1.5 × 4.5 × 6 = 40.5 cubic meters