Home Heating Repair Stewart's home is heated by hot water circulating in pipes. Recently, the system developed a sm leak. It loses 2(1)/(2) milliliters every 10 minutes. Use this complex fraction to find the change of the amount of water in the system per minute.

Step-by-step explanation:

To find the Highest Common Factor (H.C.F.) of 567 and 255 using Euclid's division lemma, we can follow these steps:

Step 1: Apply Euclid's division lemma:

Divide the larger number, 567, by the smaller number, 255, and find the remainder.

567 ÷ 255 = 2 remainder 57

Step 2: Apply Euclid's division lemma again:

Now, divide the previous divisor, 255, by the remainder, 57, and find the new remainder.

255 ÷ 57 = 4 remainder 27

Step 3: Repeat the process:

Next, divide the previous divisor, 57, by the remainder, 27, and find the new remainder.

57 ÷ 27 = 2 remainder 3

Step 4: Continue until we obtain a remainder of 0:

Now, divide the previous divisor, 27, by the remainder, 3, and find the new remainder.

27 ÷ 3 = 9 remainder 0

Since we have obtained a remainder of 0, the process ends here.

Step 5: The H.C.F. is the last non-zero remainder:

The H.C.F. of 567 and 255 is the last non-zero remainder obtained in the previous step, which is 3.

Therefore, the H.C.F. of 567 and 255 is 3.

The probability of selecting a T or a P on the second draw, given that an F was selected on the first draw is 0.39.

The probability of selecting a T or a P on the second draw, given that an F was selected on the first draw, can be calculated using conditional probability.

P(A|B) = P(A and B) / P(B)

P(A and B) = P(T or P on second draw and F on first draw) = P(T on second draw and F on first draw) + P(P on second draw and F on first draw)

= (3/9) x (4/10) + (2/9) x (4/10) = 14/90

To find P(B), we know that it is 0.4.

Therefore, the conditional probability of selecting a T or a P on the second draw, given that an F was selected on the first draw, is:

P(A|B) = P(A and B) / P(B) = (14/90) / 0.4 ≈ 0.39

So the probability of selecting a T or a P on the second draw, given that an F was selected on the first draw, is approximately 0.39.

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As a result, it will take roughly 10.24 years for the account to reach $20,000 in value.

As a quarter of 100, a number can be expressed as a percentage. It is frequently used to describe distinctions or express changes in numbers. The symbol for percentages is %, and they are frequently utilized to describe ratios, rates, and certain other numerical connections. An 80 percent score on a test, for instance, indicates that the student correctly answered 80 of the 100 questions. Similar to this, if a retailer were offering a 20% discount on a $100 item, the sale price would be $80.

given

With P = 10000, r = 0.08 (8% stated as a decimal), n = 12 (compound monthly), and t to be found when A = 20000, the situation is as follows.

When these values are added to the formula, we obtain:

\(20000 = 10000(1 + 0.08/12)^(12t) (12t)\)

By multiplying both sides by 1000, we obtain:

\(2 = (1 + 0.08/12)^(12t) (12t)\)

When we take the natural logarithm of both sides, we obtain:

ln(2) = 12t ln(1 + 0.08/12)

When we multiply both sides by 12 ln(1 + 0.08/12), we obtain:

t = ln(2) / (12 ln(1 + 0.08/12))

Calculating the answer, we discover:

10.24 years is t.

As a result, it will take roughly 10.24 years for the account to reach $20,000 in value.

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Answer: c. det(PAP^-1) = det(A)

To show that det(PAP-1) = det(P)det(A)det(P^-1), we can use the following properties of determinants:

1. det(AB) = det(A)det(B) for any matrices A and B

2. det(A^-1) = 1/det(A) for any invertible matrix A

Starting with det(PAP^-1), we can apply property 1 to get:

det(PAP^-1) = det(P)det(A)det(P^-1)

Then, we can use property 2 to rewrite det(P^-1) as:

det(PAP^-1) = det(P)det(A)(1/det(P))

Simplifying this expression gives:

det(PAP^-1) = det(A)

Therefore, det(PAP^-1) = det(P)det(A)det(P^-1) is equivalent to det(PAP^-1) = det(A).

So, the correct answer is:

c. det(PAP^-1) = det(A)

The symbolization of the given English sentences into Modal Logic and then translate it back into natural language.

1. My pizza does not have onions, but if it has cheese on it, then it necessarily cannot be vegan.
2. If it is possible for my pizza to be vegan, then it is not necessary for it to have cheese and onions.
3. It is necessarily true that if my pizza is vegan, then it has neither cheese nor sausage.
4. If my pizza is necessarily vegan, then it necessarily does not have cheese or sausage.
5. My pizza has onions on it and does not have cheese on it. However, it is possible that it has cheese on it.

The symbolization of the given English sentences into Modal Logic and then translate it back into natural language.
1. ¬O ∧ (C → □¬P)
Translation: My pizza doesn't have onions, and if it has cheese on it, then it is necessarily not vegan.
2. ◊P → ¬(□(C ∧ O))
Translation: If it's possible that my pizza is vegan, then it's not necessary that my pizza has both cheese and onions.
3. □(P → (¬C ∧ ¬S))
Translation: Necessarily, if my pizza is vegan, then it has neither cheese nor sausage.
4. □P → □(¬C ∧ ¬S)
Translation: If my pizza is necessarily vegan, then it necessarily has neither cheese nor sausage.
5. O ∧ ¬C ∧ ◊C
Translation: My pizza has onions on it, it doesn't have cheese on it, but it's possible that it has cheese on it.
6. DS V O(C∧O)
Translation: My pizza has sausage and onions, or it has cheese and onions.
7. (◊S → ◊¬P)
Translation: If it's possible that my pizza has sausage, then it's possible that it's not vegan.
8. POP
Translation: My pizza is vegan, and it's possible that my pizza is vegan.

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Answer:

A and D

Step-by-step explanation:

so sorry im in school

x+y=4

 -y.  -y

x=4-y

4-y-y=2

4-2y=2

-4      -4

-2y= -2

/-2.   /-2

y=1

x+1=4

  -1 -1

x=3

so A and D is correct

Answer:

What may I answer for you? Put iedit if you just forgot to add it?

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

1. Just input the x value with -180:

24 (+) -180 / 12 = answer

2. Follow PEMDAS to solve, which in this case division comes before addition:

24 + (-180 / 12)

24 + (-15)

3. Addition

24 + (-15) or 24 - 15

= 9

Therefore, 24 (+) -180 / 12 equals 9.

Answer:

x=5+1/2

Step-by-step explanation:

3(2x-5)-2x=7

We move all terms to the left:

3(2x-5)-2x-(7)=0

We add all the numbers together, and all the variables

-2x+3(2x-5)-7=0

We multiply parentheses

-2x+6x-15-7=0

We add all the numbers together, and all the variables

4x-22=0

We move all terms containing x to the left, all other terms to the right

4x=22

x=22/4

x=5+1/2

Step-by-step explanation:

3(2x-5)-2x=7

We move all terms to the left:

3(2x-5)-2x-(7)=0

We add all the numbers together, and all the variables

-2x+3(2x-5)-7=0

We multiply parentheses

-2x+6x-15-7=0

We add all the numbers together, and all the variables

4x-22=0

We move all terms containing x to the left, all other terms to the right

4x=22

x=22/4

x=5+1/2

Answer:  45

Step-by-step explanation:

We can label 5/9 of 81 as Numerator/Denominator of a whole number.

To solve the problem, we multiply the Numerator by the whole number and leave the Denominator as is:

(5 x 81) / 9 = 405/9 = 45

Therefore, the answer to 5/9 of 81 in its lowest form is:

Answer:

17

Step-by-step explanation:

3m-(m + 5)

Distribute the minus sign

3m -m -5

Combine like terms

2m -5

Let m =11

2*11 -5

22-5

17

Answer:

\(17\)

Step-by-step explanation:

\(3m-(m + 5)\)

\(m= 11\)

Plug m as 11 in the expression.

\(3(11)-(11+5)\)

Evaluate.

\(33-16\)

\(=17\)

The conclusion that more than 60% of residents in the population supported candidate A cannot be made based on the given information and analysis. The correct statements are i, ii, and iv.

In order to determine whether more than 60% of residents supported candidate A, a hypothesis test needs to be conducted. The null hypothesis (H0) assumes that the population proportion (p) is greater than 0.6, while the alternative hypothesis (Ha) assumes that p is equal to or less than 0.6.

Statement i is correct as it calculates the proportion of residents who supported candidate A based on the given sample, which is (100 - 22 - 14) / 100 = 0.64, or 64%.

Statement ii is correct in describing the null and alternative hypotheses. The null hypothesis assumes p > 0.6, while the alternative hypothesis assumes p ≤ 0.6.

Statement iii is incorrect. The rejection region for a hypothesis test with a significance level (α) of 0.05 should be based on the critical value of the z-statistic. For a one-tailed test (as implied by the alternative hypothesis), the critical value is approximately 1.645.

Statement iv is correct in calculating the z-statistic using the given sample proportion, the assumed population proportion, and the sample size. However, the calculated z-value is incorrect. The correct calculation is (0.64 - 0.6) / √(0.6 * 0.4 / 100) = 0.2357.

Statement v is incorrect. The p-value is the probability of obtaining a test statistic as extreme as the observed value, assuming the null hypothesis is true. In this case, the p-value is P(z > 0.2357) ≈ 0.4098, which is greater than the significance level of 0.05. Therefore, we fail to reject the null hypothesis. The correct conclusion is that there is insufficient evidence to conclude that more than 60% of residents support candidate A.

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Answer:

Step-by-step explanation:

Select one or more rows and columns

Or click on any cell in the row and then press Shift + Space. To select non-adjacent rows or columns, hold Ctrl and select the row or column numbers.

The required system of equation is given as y = 3x + 12 and y=x³+4x²+3x+12.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

Given equation,
y=x³+4x²+3x+12

To determine the x-intercept put equation y = 0

0 = x³+4x²+3x+12

Factorize the above equation

0=(x²+3)(x+4)

One of the factors from above is given as

x+4=0  

x = -4

The x-intercept is (-4,0)

For the y-intercepts, x=0 and solve.

y = 12

y = 12

The y-intercept is (0,12)

Now equation of the line passing these points is given as.

m = (y₂ - y₁) /  (x₂ - x₁)
m = 12/3
m = 3

C, we already have C=12

So the equation of the line is
y = mx + c
y=3x+12

Thus, the required system of equation is given as y = 3x + 12 and y=x³+4x²+3x+12.

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If all conditions for inference were met, does the interval provide convincing statistical evidence, at a level of significance of  95%, that the mean number of hours of community service performed last year was indeed different from the recommended 24 hours.

To determine if the 95% confidence interval provides convincing statistical evidence at a level of significance that the mean number of hours of community service performed last year was different from the recommended 24 hours, we'll analyze the constructed interval (20.37, 23.49).
1. First, observe the given confidence interval: (20.37, 23.49)
2. Identify the recommended average of 24 hours by the president.
3. Check if the recommended average is within the confidence interval.
Since 24 hours is not within the interval (20.37, 23.49), it provides convincing statistical evidence, at a level of significance of 95%, that the mean number of hours of community service performed last year was indeed different from the recommended 24 hours.

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Answer:

Let the smaller integer be x and greater integer be (x+1)

x+(x+1)=91

2x+1=91

2x=91-1=90

x=90/2

x=45

Answer:

The integers are 45 and 46.

Step-by-step explanation:

Let the two consecutive integers be x and therefore the other will be x+1.

Given that the sum of the integers is 91.

So ATP,

Solving for first number i.e. x,

Hence,the first number is 45.

\(\rule{225pt}{2pt}\)

Solving for second number,i.e. x+1:

It can easily be obtained by substituting the value of x we got.

Hence,the second number is 46.

\(\rule{225pt}2pt\)

The density of the liquid substance Y can be determined by using the conversion factor 1 atm = 41.5 ft⁻Y and the density of the liquid substance Y is approximately 19.68 ft⁻Y.

Conversion factor: 1 atm = 41.5 ft⁻Y

The "feet of liquid substance - Y" unit is defined as the pressure equivalent to the pressure that exists one foot below the surface of substance Y. In other words, if we go one foot below the surface of substance Y, the pressure will be equivalent to 1 ft⁻Y.

Since pressure is directly related to the density of a liquid, we can equate the pressure in units of atm to the pressure in units of ft⁻Y.

Therefore, we can say:

1 atm = 41.5 ft⁻Y

From this equation, we can conclude that the conversion factor for pressure between atm and ft⁻Y is 41.5.

we can calculate the conversion factor from "feet of liquid substance - Y" (ft⁻Y) to atm.

To convert from ft⁻Y to atm, we can use the inverse of the given conversion factor:

Conversion factor: 1 atm = 41.5 ft⁻Y

Taking the reciprocal of both sides:

1 / 1 atm = 1 / 41.5 ft⁻Y

Simplifying the equation:

1 atm⁻¹ = 0.024096 ft⁻Y⁻¹

Now, to find the density of the liquid substance Y in units of ft⁻Y, we can multiply the given density in g/cm³ by the conversion factor:

Density in ft⁻Y = 816.55 g/cm³ * 0.024096 ft⁻Y⁻¹

Calculating the density in ft⁻Y:

Density in ft⁻Y ≈ 19.68 ft⁻Y

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Answer:

60° and 67°

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

(49)

17x + 8 is an exterior angle of the triangle, thus

17x + 8 = 50 + 10x ( subtract 10x from both sides )

7x + 8 = 50 ( subtract 8 from both sides )

7x = 42 ( divide both sides by 7 )

x = 6

Thus

∠ C = 10x = 10(6) = 60°

(50)

99° is an exterior angle of the triangle, thus

2x + 10 + 6x + 1 = 99 , that is

8x + 11 = 99 ( subtract 11 from both sides )

8x = 88 ( divide both sides by 8 )

x = 11

Thus

∠ T = 6x + 1 = 6(11) + 1 = 66 + 1 = 67°

A manufacturer of compact fluorescent light bulbs advertises have a standard deviation of 1,000 hours so the values are:

A normal distribution with,

μ = 9000

σ = 1000

a) The standardized score is the value x decreased by the mean and then divided by the standard deviation.

x = 105000 - 9000 / 1000 ≈ 1.50

Determine the corresponding probability using the normal probability table in appendix,

P(X>10500) = P(Z>1.50) = 1 - P(Z<1.50)

= 1 - 0.9332 = 0.0668.

b) n = 15

The sampling distribution of the mean weight is approximately normal, because the population distribution is approximately normal.

The sampling distribution of the sample mean has mean μ and standard deviation σ/√n

μ = 1000/√15 = 258.19

c) The sampling distribution of the sample mean has mean μ and standard deviation σ/√n

The z-value is the sample mean decreased by the population mean, divided by the standard deviation:

z = x-u/σ/√n = 10500-9000/1000√15 = 5.81

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Answer:

$15.25

Step-by-step explanation:

Given that

Sadie has 142 spools of thread,61 balls of yam and 35 bottles of paint.

Capacity and price of a rack = 60 spools of thread, $14.99

Capacity and price of a basket = 20 balls of yam, $15

Capacity and price of a paint storage rack = 81 bottles of pain, $49

Money already saved = $32

To find:

Money to be saved each week for having all the necessary storage in 2 months.

Solution:

It can be analyzed that to store 142 spools of thread,61 balls of yam and 35 bottles of paint and as per the storage capacity:

Number of racks required to store thread = \(\frac{142}{60} > 2 =3\)

Number of baskets required to store balls of yam = \(\frac{61}{20} > 3 =4\)

Number of paint racks required to store bottles of paint = \(\frac{35}{81} < 1 = 1\)

Total money required for the storage = \(3\times 14.99 +4\times 15+1\times 49=\$153.97\)

Money already saved = $32

More Money to be saved = $153.97 - $32 = $121.97

There are 8 weeks in 2 months, so money to be saved every week = \(\frac{121.97}{8}\approx \bold{\$15.25}\)

Answer: 11,500 grams

Step-by-step explanation: 920/8=115 115*100= 11,500

The lines to use to solve the equation are y = –3x – 2  and y = 2x + 8

The graph of the line is attached

From the question, we have the following parameters that can be used in our computation:

–3x – 2 = 2x + 8

The above equation can be splitted by introducing the variable y

using the above as a guide, we have the following:

y = –3x – 2

y = 2x + 8

This means that the lines to use to solve the equation are y = –3x – 2  and y = 2x + 8

The graph of the line is added as an attachment

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Answer:

The price of the item is now $26.4

Step-by-step explanation:

Answer:

The price after the reduction is $26.40

Step-by-step explanation:

Good luck on the test!

The surface area of the figure for the given condition is 391.2 cm²

The pentahedron Triangular Prism contains nine different nets. The bases' vertices and edges are connected by means of their three rectangular sides. The rectangular sides of the triangular prism are joined to one another side by side.

Given the triangular prism,

which consist of two triangles and  3 rectangles,

the surface area of the figure is the sum of the area of  triangles and  3 rectangles,

given sides of triangle is 6cm x 6cm x 6cm

area of equilateral triangle = √3/4(a²)

area of equilateral triangle = 6²*(√3/4)

area of equilateral triangle = 15.6 cm²

and dimensions of the rectangle is 6cm x 20 cm

area of rectangle = l x b

area of rectangle = 6*20

area of rectangle = 120 cm²

area of shape = 2(area of triangle) + 3(area of rectangle)

area of shape = 2*15.6 + 3*120

area of shape = 31.2 + 360

area of shape = 391.2 cm²

Hence the area is 391.2 cm².

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The constant that the car must drive is 112.84 km/hr.

Average speed measures how fast an object is moving with respect to time. Average speed is the ratio of total distance to total time.

Average speed  = distance / time

Distance = speed x time

Distance  travelled = 2 h 45 minutes x 106

= 2.75 x 106 = 291.5 km

Speed that must be travelled in 2 hour 35 minutes = 291. 5 / 2h 35m

291.5 / 2.583 = 112.84 km/hr

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The hypotheses can be written as:

H0: p = 0.28

Ha: p ≠ 0.28

The null hypothesis (H0) is that the proportion of students who smoke regularly today (p) is equal to the proportion of students who smoked regularly last year (0.28). The alternative hypothesis (Ha) is that the proportion of students who smoke regularly today is different from 0.28.

This is a two-tailed test, as we are looking for a difference in either direction from the proportion found last year. A significance level (α) should be chosen in advance to determine the level of risk that we are willing to accept of rejecting the null hypothesis when it is actually true. Typically, a significance level of 0.05 is used, which means that we are willing to accept a 5% chance of making a type I error (rejecting the null hypothesis when it is actually true).

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Answer:

Let ac=ab=5

With this, bc= 5√2

Step-by-step explanation:

So to find ad, Let ad be x

5√2=(2)(x)

(5√2/2)= x

This proves that bc=2ad

Total attempt = 90

Successful throws = 81

Unsuccessful = Total attempt - Successful

= 90 - 81

=> 9

To calculate the percentage of unsuccessful, we will use the formula:

To convert the division algorithm Y=X/(-2) into a multiplication algorithm, multiply both sides of the equation by -2 to get X = -2Y.

To convert the division algorithm Y=X/(-2) into a multiplication algorithm, we can manipulate the equation by multiplying both sides by -2. By doing so, we get -2Y = X. This equation represents the multiplication algorithm equivalent to the given division algorithm.

Multiplying both sides by -2 allows us to eliminate the division by -2 on the right side of the equation. The negative sign in front of the 2 is included to maintain the equality between the two sides of the equation. As a result, the equation X = -2Y represents the multiplication algorithm that is equivalent to the division algorithm Y = X/(-2). Now, instead of dividing by -2, we can multiply by -2 to achieve the same result.

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