The inside portion of a cylindrical tank is being filled by one of these three gases: carbon dioxide, helium, or chlorine. Explain which gas results in the heaviest weight possible and by how many kilograms.

Answer:

the distance between the two points are √89 or 9.43398113

Answer:

15 9/12

Step-by-step explanation:

convert the denominator 2 into 12 and do the same for the 1/3 then multiply the number by the amount it took you to get the denominator of 12

Answer:

\( AB=2\sqrt{29}\)

Step-by-step explanation:

Hope it helps you in your learning process.

When the relationship between two variables is explained by a third, unmeasured factor, it is referred to as a spurious relationship.

A spurious relationship occurs when there appears to be a causal relationship between two variables, but in reality, the relationship is not genuine.

Instead, the observed relationship is due to the effect of a third variable, which is not being measured or controlled for.

For example, a researcher finds that there is a strong correlation between ice cream sales and the number of drownings at a beach.

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A: The height of the street sign is obtained by indirect measurement method as 15 feet.

B: The two proportions Betsy can use is 5/1.5 = x/4.5 and 5/.x = 1.5/4.5

C: Using both the proportions height of the street sign is obtained as 15 feet.

What is indirect measurement?

A mathematical technique called as an indirect measurement is used to discover unknown measures of items that are challenging to measure. A direct measurement is something that can easily be measured, like a toddler's height.

The height of Betsy is h = 5 feet.

The shadow of Betsy is h' = 1.5 feet.

The height of the street sign is H = x feet.

The height of the shadow of street sign is H' = 4.5 feet.

The two proportions are -

h/h' = H/H' and h/H = h'/H'

These two can be used to find the measurement of the street sign.

To find the height of the street sign use the method of indirect measurement -

h/h' = H/H'     h/H = h'/H'

Substitute the values in the given equation -

5/1.5 = x/4.5            5/x = 1.5/4.5  

1.5 × x = 5 × 4.5      5 × 4.5 = 1.5 × x

1.5x = 22.5              22.5 = 1.5x

Simplify the equation further -

x = 22.5/1.5             x = 22.5/1.5

x = 15                       x = 15

Therefore, the value of the x is obtained as 15 feet.

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Answer:

x: represents the number of reward miles

traded in and is always an integer value.

f(x): represents the value of the reward in

dollars.

Tristan and Delaney are tasked with testing

the system and made the following reward

redemptions.

• Tristan traded in 1500 miles for a $290

Answer:

The vertices of the image are D' (40, 20), E' (10, 30), F' (15, 5)

Step-by-step explanation:

If the point (x, y) dilated by a scale factor k using the origin as a center of dilation, then its image is (kx, ky)

Let us use this rule to solve our question

∵ The vertices of ΔDEF are D (8, 4), E (2, 6), and F (3, 1)

∵ ΔDEF dilated by a scale factor 5

∴ k = 5

∵ The origin as the center of dilation

→ That means, multiply the coordinates of every point by 5

∴ D' = (8 × 5, 4 × 5)

∴ D' = (40, 20)

∴ E' = (2 × 5, 6 × 5)

∴ E' = (10, 30)

∴ F' = (3 × 5, 1 × 5)

∴ D' = (15, 5)

∴ The vertices of the image are D' (40, 20), E' (10, 30), F' (15, 5)

Answer:

9xx2401x=21609x

Step-by-step explanation: 3x3=9. 40x40=1600, 40x9=360x2 because there are 2 of the same problem because the number is the same. 9x9=81.

Now we add them up. 1600+720+81=2401. 2401x9=21609

But don't forget to add the x at the end or the answer is wrong!!!

Answer:

total surface area  = 298.45105 m2

lateral surface area = 141.37155 m2

top surface area = 78.53975 m2

bottom surface area = 78.53975 m2

Step-by-step explanation:

Joanna will need approximately 298.3 square inches of frosting to cover the entire cake.

To calculate the amount of frosting Joanna will need for the entire cake, we first need to find the surface area of the cylindrical cake.

The formula for the surface area of a cylinder is given by:

Surface Area = 2πr² + 2πrh

Where r is the radius of the base and h is the height of the cylinder.

Given that the diameter of the cake is 10 inches, we can find the radius by dividing it by 2: r = 10/2 = 5 inches.

Plugging in the values, we have:

Surface Area = 2π(5)² + 2π(5)(4.5)

Simplifying the equation:

Surface Area = 2π(25) + 2π(22.5)

Surface Area = 50π + 45π

Surface Area = 95π

To find the actual numerical value, we can approximate π as 3.14:

Surface Area ≈ 95 * 3.14

Surface Area ≈ 298.3 square inches

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The given expression, \(d(n)d(n)d(n)\), represents the duration in seconds for Hailey to run her \(n^{th}\) lap. The specific values provided, 333, 777, 999, correspond to the durations of the 3rd, 7th, and 9th laps, respectively. The values 858585, 999999, and 110110110 are unrelated and do not provide any additional information about lap durations.

The expression \(d(n)d(n)d(n)\) suggests that each lap duration is represented by the function \(d(n)\), where \(n\) denotes the lap number. The specific values given (333, 777, 999) correspond to the 3rd, 7th, and 9th laps, respectively. However, the remaining values (858585, 999999, 110110110) do not appear to have a direct connection to the lap durations or the function \(d(n)\).

Without further information or a specific pattern, it is difficult to interpret the significance of the remaining values. It's important to note that more context or information about the pattern or relationship between the values would be necessary to provide a more detailed explanation or analysis.

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Answer:

No solution

Step-by-step explanation:

To solve this, we subtract 7x from both sides to get 2=-3. Since 2 does not equal to negative 3, there is no solution.

Answer:

260 miles

Step-by-step explanation:

set up a proportion:

6.5/d = 1/40

cross-multiply:

d = 40(6.5) which equals 260 miles

Answer:

26mm

Step-by-step explanation:

w+10 + w+ 20 = 144/3

3w+30 = 48

3w = 18

w=6

longest side is 6+20 = 26

Referring to exhibit 8-2, we can see that the sample size is 400, and the population standard deviation is 10.

Based on these values, we can use the formula for the margin of error:
Margin of error = Z * (σ/√n)
Where Z is the Z-score for the desired level of confidence (in this case, 0.95), σ is the population standard deviation, and n is the sample size. Using a Z-score of 1.96 (which corresponds to a 0.95 confidence level), we can plug in the values:
Margin of error = 1.96 * (10/√400)
Simplifying this equation, we get:
Margin of error = 1.96 * (10/20) = 0.98
Therefore, with a 0.95 probability, the sample mean will provide a margin of error of approximately 0.98.
Based on Exhibit 8-2, with a 0.95 probability, the sample mean will provide a margin of error of "X" (please insert the value provided in the exhibit). This means that we can be 95% confident that the true population mean lies within the sample mean ± X.

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The carnival committee should expect to pay $218.70 for prizes at the booth.

We can start by calculating the expected number of students who win each prize:

Stuffed toy: 22% of 150 students = 0.22 x 150 = 33 students

Jump rope: 16% of 150 students = 0.16 x 150 = 24 students

T-shirt: 6% of 150 students = 0.06 x 150 = 9 students

No prize: 100% - (22% + 16% + 6%) = 56% of 150 students = 0.56 x 150 = 84 students

Next, we can calculate the total amount of money that the carnival committee should expect to pay for prizes at the booth:

Stuffed toy: 33 students x $3.60 per toy = $118.80

Jump rope: 24 students x $1.20 per rope = $28.80

T-shirt: 9 students x $7.90 per shirt = $71.10

Total cost of prizes = $118.80 + $28.80 + $71.10 = $218.70

Therefore, the carnival committee should expect to pay $218.70 for prizes at the booth.

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Answer:

(0,3)

Step-by-step explanation:

Answer:0,3

Step-by-step explanation:

Answer:

43%

Step-by-step explanation:

There are 39 girls. 21 of them like biology. 11 out of 34 who like chemistry are girls.

No. of girls who prefer biology = 21

There are (100-39) boys. 16 of them like physics. (34-11) of them like chemistry.

No. of boys who prefer biology = 100-39-16-34+11

                                                    = 22

Percentage of students who prefer biology = \(\frac{21+22}{100}\) × 100%

                                                                        = \(\frac{43}{100}\) × 100%

                                                                        = 43%

when the minute hand rotated through 1260° time will became 5:30 PM

Complete angle:-

                             A complete angle is a type of angle that measures 360°.A complete angle deals with one full rotation measuring 360°.

      In an hour or in 60 minute, minute hand covers a 360° angle.

   According to question,

                              initially it is 2:00PM,that is minute hand at 12 and hour hand at 2

       it is given that minute hand has rotated through 1260°

                        1260° = 3 x 360° + 180°

                                                             which means minute hand will have three complete rotation and one half rotation.

            when minute hand rotated through 360° angle then hour hand will move from 2 to 3.

              And again in second rotation, when minute hand rotated through 360° angle then hour hand will move from 3 to 4.

             Again in third rotation, when minute hand rotated through 360° angle then hour hand will move from 4 to 5.

           As of now, minute hand have taken three complete rotation and so hour hand reached at 5

                 Now, when minute hand rotated through 180° (one half rotation),minute hand will reach at 6 from 12.

           So, right now the position of hour hand is between 5 and 6 and the position of minute hand at 6.

            hence,  time will be 5:30 PM

                            Option A is correct

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Answer:

7.2

Step-by-step explanation:

good luck hope it helps

Step-by-step explanation:

To find 9% of 80 you multiply 80 and 0.09(I converted 9% to 0.09).

80x0.09=7.2

Hope it helps!

Binding constraints directly influence the optimal solution in a linear Programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution.

binding constraints and positive slack in the context of linear programming. In a linear programming problem, we aim to find the optimal solution for an objective function, given a set of constraints. The terms "binding constraints" and "positive slack" are related to these constraints.

1. Binding constraints: These are constraints that directly impact the optimal solution of the problem. In other words, they "bind" the feasible region (the area where all the constraints are satisfied) and affect the maximum or minimum value of the objective function. Binding constraints are active constraints, as they influence the final solution.

2. Positive slack: Slack is the difference between the left-hand side and right-hand side of a constraint when the constraint is satisfied. If this difference is positive, it means that there is some "extra" or "unused" resource in that constraint. Positive slack indicates that the constraint is non-binding, meaning it does not directly impact the optimal solution. It shows that there is some room for the constraint to be further tightened without affecting the final outcome.

In summary, binding constraints directly influence the optimal solution in a linear programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution. Knowing the difference between these terms can help you better understand and analyze linear programming problems.

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The expected standard deviation for a sample of size 14 with a percentage of success of 25%, assuming data follows a binomial distribution, is approximately 1.62 (option b).

To calculate the expected standard deviation, we can use the formula for the standard deviation of a binomial distribution:

SD = sqrt(npq)

where n is the sample size, p is the percentage of success, and q is the percentage of failure (q = 1 - p).

Substituting the values given, we get:

SD = sqrt(14 x 0.25 x 0.75)

SD = sqrt(2.625)

SD ≈ 1.62

Therefore, the expected standard deviation for a sample of size 14 with a percentage of success of 25%, assuming data follows a binomial distribution, is approximately 1.62. This means that the actual values of success in the sample are likely to vary from the expected value of 3.5 (14 x 0.25) by about 1.62 units.

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Answer:

(a) 1416

(b) 2 × 2 × 2 × 3 × 59

Step-by-step explanation:

The prime numbers between 0 and 10 are 2, 3, 5,7 (1 is not considered prime)
Therefore m = 2357

The square numbers between 0 and 10 are  1, 4, 9 and in descending order 9,4.1so n = 941

m - n = 2357 - 941 = 1416

Unique prime factors of 1416 are 2,3,59

1416 as a product of prime factors = 2 × 2 × 2 × 3 × 59

we can solve the equation using the inverse of A:\(\[x = A^{-1}v = \begin{bmatrix} -1 & 2 & -5 \\ 5 & -9 & 20 \\ -1 & 2 & -4 \end{bmatrix} \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix} = \begin{bmatrix} -4 \\ 16 \\ -3 \end{bmatrix}\]Therefore, the four vectors:\[u_1 = \begin{bmatrix} 1 \\ -1 \\ 2 \end{bmatrix} , \; u_2 = \begin{bmatrix} 2 \\ 1 \\ 0 \end{bmatrix} , \; u_3 = \begin{bmatrix} -1 \\ 3 \\ -1 \end{bmatrix} , \; v = \begin{bmatrix} -4 \\ 16 \\ -3 \end{bmatrix}\]\)form a basis of .

To do that, we will solve the equation:\[Ax = v\]where x is a column vector of three unknowns. We want v to be linearly independent from the columns of A, so we need the equation to have a unique solution. We can achieve that by taking v to be any vector that is not in the column space of A. For example, we can take:\\([v = \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix}\]\)Then, we can solve the equation using the inverse of A:\(\[x = A^{-1}v = \begin{bmatrix} -1 & 2 & -5 \\ 5 & -9 & 20 \\ -1 & 2 & -4 \end{bmatrix} \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix} = \begin{bmatrix} -4 \\ 16 \\ -3 \end{bmatrix}\]Therefore, the four vectors:\[u_1 = \begin{bmatrix} 1 \\ -1 \\ 2 \end{bmatrix} , \; u_2 = \begin{bmatrix} 2 \\ 1 \\ 0 \end{bmatrix} , \; u_3 = \begin{bmatrix} -1 \\ 3 \\ -1 \end{bmatrix} , \; v = \begin{bmatrix} -4 \\ 16 \\ -3 \end{bmatrix}\]\)form basis of .

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The congruence relation mod n is transitive.

The congruence relation mod n is reflexive.

The congruence relation mod n is symmetric.

How to prove the relation

To prove that the congruence relation mod n is transitive, reflexive, and symmetric

Transitivity: If a≡ n b and b≡ n c, then a≡ n c.

Reflexivity: For any natural number a, a≡ n a.

Symmetry: If a≡ n b, then b≡ n a.

To prove transitivity, assume that a≡ n b and b≡ n c. This means that there exist natural numbers k and j such that b-a=nk and c-b=nj. Adding these two equations

c-a = (c-b) + (b-a) = nj + nk = n(j+k)

Since j and k are natural numbers, j+k is also a natural number. Therefore, n divides c-a, which means that a≡ n c.

Thus, the congruence relation mod n is transitive.

Similarly, to prove reflexivity, we need to show that for any natural number a, a≡ n a. This is true because a-a=0 is divisible by any natural number, including n.

Hence, the congruence relation mod n is reflexive.

To prove symmetry, assume that a≡ n b. This means that there exists a natural number k such that b-a=nk. Dividing both sides by -n,

a-b = (-k)n

Since -k is also a natural number, n divides a-b, which means that b≡ n a.

Therefore, the congruence relation mod n is symmetric.

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Congruence mod n is reflexive, transitive, and symmetric.

In the previous question, we proved that n divides a - a or a - a = 0.

Therefore a ≡ a (mod n) is true and we have n divides 0, i.e.,  ∃k:Nvnk=∣a−a∣ = 0.

Thus, congruence mod n is reflexive.

Let a ≡ n b and b ≡ n c such that n divides b - a and n divides c - b.

Therefore, there exist two natural numbers p and q such that b - a = pn and c - b = qn.

Adding the two equations, we have c - a = (p + q)n. Since p and q are natural numbers, p + q is also a natural number. Therefore, n divides c - a.

Hence, congruence mod n is transitive.

Now, let's prove that congruence mod n is symmetric.

Suppose a ≡ n b. This means that n divides b - a. Then there exists a natural number k such that b - a = kn. Dividing both sides by -1, we get a - b = -kn. Since k is a natural number, -k is also a natural number.

Hence, n divides a - b. Therefore, b ≡ n a. Thus, congruence mod n is symmetric.

Therefore, congruence mod n is reflexive, transitive, and symmetric.

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Answer:

A= 30 years old

B= 20 years old

Step-by-step explanation:

Let the present age of A be x years old.

Since the sum of the present ages of A and B is 60 years,

present age of B= (60-x) years old

In 5 years

A= x +5

B= 60 -x +5= 65-x

Since the ratio of A:B= 4:3,

A would represent 4 units and B would represent 3 units.

Thus \(\frac{3}{4}\)A=B

\(\frac{3}{4}\)(x+5)= 65 -x

\( \frac{3}{4} x + \frac{15}{4} = 65 - x \\ \frac{3}{4} x + x = 65 - \frac{15}{4} \\ \frac{7}{4} x = 61.25 \\ 7x = 61.25 \times 4 \\ 7x = 245 \\ x = 245 \div 7 \\ x = 35\)

Thus, present age of A

= x

= 35 years old

present age of B

= 60 -x

= 60 -35

= 25 years old

5 years ago

A= 35 -5= 30 years old

B= 25 -5= 20 years old

* under the section in 5 years, \(\frac{3}{4} A=B\) because both would be equal to 3 units each. Since B is 3 units and A is 4 units, in order to make both value the same, we divide the 4 units of A by 4 then multiply by 3 to get 3 units. Thus, \(\frac{3}{4}\) of A is equal to B.

Answer:

To find the mean height of the sample, we need to sum up all the values and divide them by the total number of values.

Sum of values = 59+61+62+63+63+64+65+65+66+67+67+67+67+69+73 = 964

Total number of values = 15

Mean height = sum of values / total number of values = 964/15 = 64.2666... ≈ 65.2

Therefore, the mean height, in inches, of this sample is approximately 65.2.

The answer is B.

Answer:

Hope this helps you.

Step-by-step explanation:

I plugged in x for t, but it is the same graph.

Notice that the blue object seems to have no beginning nor end; therefore, it is a line.

Furthermore, we can define a line by identifying two points on it. Thus, the blue line can be named as EA, AE, AD, DA, ED, or DE.

Hence, the answer is option c. line, AE