if terri were to paint her living room alone, it would take 3 hours. her sister angela could do the job in 4 hours. how many hours would it take them working together?

Leo has 48 toy soldiers.

What is the key concept is used to solve the question ?

This problem involves finding a number that satisfies certain conditions related to division with remainders. Specifically, the number must be divisible by 4 with no remainder, must leave a remainder of 6 when divided by 7, and must leave a remainder of 3 when divided by 5.

Calculating the number of toy soldiers :

Let's start by using the first condition to narrow down the possibilities for the number of toy soldiers. We know that the number must be divisible by 4 with no remainder, and it must be between 27 and 54. The multiples of 4 in this range are 28, 32, 36, 40, 44, 48, and 52.

Next, we can use the second condition to eliminate some of these possibilities. If we divide each of these numbers by 7, we get the following remainders:

28 ÷ 7 = 4 remainder 0

32 ÷ 7 = 4 remainder 4

36 ÷ 7 = 5 remainder 1

40 ÷ 7 = 5 remainder 5

44 ÷ 7 = 6 remainder 2

48 ÷ 7 = 6 remainder 6

52 ÷ 7 = 7 remainder 3

The only number in our list that leaves a remainder of 6 when divided by 7 is 48, so we can tentatively conclude that this is the number of toy soldiers.

Finally, we can check the third condition to make sure that 48 leaves a remainder of 3 when divided by 5. Indeed, 48 ÷ 5 = 9 remainder 3, so all of the conditions are satisfied.

Therefore, we can confidently say that Leo has 48 toy soldiers.

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The two remaining angles are 58°, and the length of the third side of the triangle is 6.5 inch.

In order to determine the other two angles of each triangle as well as the length of the third side, we need to use the Cosine Rule. According to the Cosine Rule, for any triangle with sides of length a, b, and c, and angles of A, B, and C, the following equation holds:

[tex]c^2 = a^2 + b^2 - 2ab cos(C)[/tex]

For the first triangle, we are given that the side of length 5 is adjacent to an angle of 61°. Therefore, a = 5, C = 61°. Using the information provided, we can also determine that b = 4.8. Substituting these values into the Cosine Rule equation, we get:

[tex]c^2 = (5)^2 + (4.8)^2 - 2(5)(4.8) cos(61°)[/tex]

We can solve this equation to get c = 6.5. Therefore, the length of the third side in the first triangle is 6.5. Additionally, we can use the Triangle Angle Sum theorem to determine the other two angles. According to this theorem, the sum of the three angles of a triangle is 180°. Therefore, for the first triangle, the two remaining angles are 180 - 61 - (180 - 61) = 58°.

For the second triangle, we use the same process, but with the given side lengths reversed. That is, we set a = 4.8, b = 5, and C = 61°. Again, substituting these values into the Cosine Rule equation, we get:

[tex]c^2 = (4.8)^2 + (5)^2 - 2(4.8)(5) cos(61°)[/tex]

We can solve this equation to get c = 6.5. Therefore, the length of the third side in the second triangle is also 6.5. We can use the Triangle Angle Sum theorem again to determine the other two angles. Again, for the second triangle, the two remaining angles are 180 - 61 - (180 - 61) = 58°.

In conclusion, for each triangle, the two remaining angles are 58°, and the length of the third side is 6.5 inch.

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999 divided by 42 is equal to 23 with a remainder of 33.

What is division?

Division is a basic arithmetic operation that involves splitting a number into equal parts or groups. It is the inverse operation of multiplication, and is used to find out how many times one number (the divisor) can be divided into another number (the dividend) without leaving a remainder. The result of division is called the quotient.

To simplify the division of 999 by 42, we can use the fact that 42 is a divisor of 84, which is a multiple of 42. We can write:

999 ÷ 42 = (42 × 23) + 33

= 966 + 33

= 999

Therefore, 999 divided by 42 is equal to 23 with a remainder of 33, or in other words, 999 ÷ 42 = 23 33/42.

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As per the unitary method, Arun's mother would be 36 years old if Arun is 3 years old.

Let Arun's age be m years.

Let Arun's mother's age be n years.

From the problem statement, we know that n = 4m + 6. This means that Arun's mother's age is directly proportional to Arun's age, with a constant ratio of 4 and a constant difference of 6.

To solve for n, we can use the unitary method. We can set up a proportionality between the two ages as follows:

n / m = (4m + 6) / m

To solve for n, we can cross-multiply to get:

n = m x (4m + 6)

Expanding the right-hand side of the equation, we get:

n = 4m² + 6m

Therefore, Arun's mother's age is 4m² + 6m years. We can simplify this expression by factoring out 2m:

n = 2m(2m + 3)

This gives us a simpler form of the equation for Arun's mother's age. To find her age, we simply substitute Arun's age (m) into this expression and simplify.

If Arun is 3 years old (m = 15), then his mother's age would be:

n = 2m(2m + 3) = 2(3)(2(3) + 3) = 2(3)(6) = 36

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Answer:

Step-by-step explanation:

9m = 7m + 4

9m - 7m = 4

2m = 4

m = 2

----------------------------------

check

9 x 2 = 7 x 2 + 4

18 = 18

this answer is good

n + 6 = 2n - 1

n + 7 = 2n

7 = n

-----------------------------------

7 + 6 = 2 x 7 - 1

13 = 13

this answer is good

If all other factors are held constant, decreasing the significance level results in an increase in the probability of a type II error. This is true. we can say that the probability of making a type II error increases when the significance level is lowered.

What is a type II error? In hypothesis testing, a type II error occurs when a false null hypothesis is not rejected. When there is a real effect and the null hypothesis is false, this happens. It's a mistake that occurs when a researcher fails to reject a false null hypothesis.

A false negative is another term for a type II error. The power of the test, the size of the sample, the confidence level, and the effect size are all factors that influence the probability of making a type II error. Only if we decrease the significance level can the probability of a type II error be increased.

What is the significance level? The significance level is also known as alpha. It is the probability of rejecting a null hypothesis when it is true. It is represented by α. It is usually set at 0.05 or 0.01 in most studies. When the significance level is lowered, the probability of making a type I error decreases, but the probability of making a type II error increases. Therefore, we can say that the probability of making a type II error increases when the significance level is lowered.

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On the material was used, the 100-meter flex of 14 AWA wire's entirety would range. If the silver and copper cable are in 0.0013 and 0.0014, aluminum spans 0.002 and 0.004, and iron is between 0.007 and 0.008

A force that works to slow something down or halt its progress: The air/wind drag slowed the vehicle down. the extent to which a material obstructs an electric charge from passing through it: There is little reluctance in copper.

The resistance (R) of a wire is given by the formula:

R = (ρ x L) / A

where:

ρ is the resistivity of the material

L is the length of the wire

A is the wire's cross-sectional size.

The cross-sectional area (A) of a wire with diameter d is given by the formula:

A = π x (d/2)²

where pi is a number in mathematics. (approximately equal to 3.14).

For a 100-meter length of 14 AWA wire with diameter 0.163 cm, we first need to convert the diameter to meters:

d = 0.163 cm = 0.00163 m

The cross-sectional area of the wire is then:

A = π x (0.00163/2)² = 2.087 x 10⁻⁶ m²

Using this value of A and the given resistivities, we can calculate the resistance for each material:

For copper:

R_copper = (1.67 x 10⁻⁸ O•m x 100 m) / (2.087 x 10⁻⁶ m²) = 0.00134 Ω

For silver:

R_silver = (1.59 x 10⁻⁸ O•m x 100 m) / (2.087 x 10⁻⁶ m²) = 0.00128 Ω

For aluminum:

R_aluminum = (2.65 x 10⁻⁸ O•m x 100 m) / (2.087 x 10⁶ m²) = 0.00199 Ω

For iron:

R_iron = (9.71 x 10⁻⁸ O•m x 100 m) / (2.087 x 10⁻⁶ m²) = 0.00735 Ω

Therefore, the overall resistance of the 100-meter length of 14 AWA wire made of these materials would depend on which material was used. If copper or silver were used, the resistance would be relatively low, around 0.0013-0.0014 Ω. If aluminum were used, the resistance would be higher, around 0.002 Ω. If iron were used, the resistance would be much higher, around 0.007 Ω.

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Answer:

436g

Step-by-step explanation:

1kg=1000g

3kg=3000g

3000+52=3052

3052÷7=436

Answer:

18 times bigger

Step-by-step explanation:

After the time of seven hours, the cream pie would have approximately 768 S. aureus cells after 7 hours with a generation time of 60 minutes.

Six S. aureus cells have been accidentally inoculated into a cream pie. S. aureus has a generation time of 60 minutes. S. aureus is a pathogenic bacterium found in the environment, as well as on the skin, and in the upper respiratory tract.

The generation time of this bacterium is 60 minutes, meaning that a single bacterium can produce two new cells in 60 minutes.

If there are 6 S. aureus cells in a cream pie, the number of bacteria will continue to increase as time passes.

The number of generations (n) in seven hours is calculated as:

n = t/g

n = 7 hours × 60 minutes/hour/60 minutes/generation = 7 generations

The number of cells in the cream pie after 7 hours is calculated as :

N = N₀ × 2ⁿ

N = 6 cells × 2⁷

N = 768 cells

Therefore, after seven hours, the cream pie would have approximately 768 S. aureus cells.

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According to the given information Ling has enough string to produce at least 20 bracelets.

Numbers serve the purpose of counting, measuring, organising, indexing, and other purposes. Natural numbers, whole numbers, rational and irrational numbers, integers, actual values, complex numbers, even and odd numbers, and so on are all distinct forms of numbers.

A number is really a numerical value that is used to express quantity. As a consequence, a number seems to be a mathematical idea that may be used to count, measure, and name objects. As little more than a result, numbers are the foundation of mathematics. Here is one butterfly, and here are four butterflies.

Each bracelet requires 7 1/2 inches of string. So, the total length of string required to make 20 bracelets is:

20 × 7 1/2 = 150 inches

Therefore, Ling needs to buy at least 150 inches of string.

We can write the inequality to represent this situation as:

length of string ≥ 150

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Answer:

576 books.

Step-by-step explanation:

134+254+188=576 books in total.

Hopefully this helps!

The multiplicity of a root r of the characteristic equation of A is called the algebraic multiplicity of r as an eigenvalue of A.

The above statement is True.

Eigenvalue:

An eigenvalue is a special set of scalar values ​​associated with the most probable system of linear equations in a matrix equation. Eigenvectors are also called eigenvalues. It is a non-zero vector which can be modified by at most its scalar factor after applying a linear transformation.

According to the Question:

If the geometric multiple of the eigenvalues ​​is greater than or equal to 2, the linearly independent set of eigenvectors is no longer unique to the multiple as before. For example, for the diagonal matrix A=[3003], one could also choose the eigenvectors [11] and [1−1], or any pair of two linearly independent vectors.

Sometimes vectors are simply expanded to vector times matrix. If this happens, this vector is called the eigenvector of the matrix and the "stretch factor" is called the eigenvalue. Example: Given a square matrix A, λ is the eigenvalue of A, and the corresponding eigenvector x is

Ax = λx.

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Answer:15 percent

Step-by-step explanation:

Answer:

Let's call the number "x".

Then, we can write the equation:

7 + 2x = 35

To solve for x, we need to isolate x on one side of the equation.

Subtracting 7 from both sides:

2x = 28

Dividing both sides by 2:

x = 14

Therefore, the number is 14.

Step-by-step explanation:

a. The distribution of the arrival time of the first guest X is exponential(λ). b. The distribution of arrival time of the second guest Y is Gamma(2, λ).

a) The time between events is exponentially distributed. Therefore, in this case, the number of guests arriving at a bank during the time interval [0,t) follows a Poisson(λt). Denote by X the arrival time of the first guest. This means that we want to know how long we have to wait until the first guest arrives. The waiting time until the first arrival in a Poisson process is an exponential distribution with a rate parameter of λ. Therefore, the distribution of X is exponential(λ).

b) Denote by Y the arrival time of the second guest. The waiting time for the first arrival is an exponential distribution with a rate parameter of λ, as we saw above. After the first arrival, the waiting time for the second arrival is also exponentially distributed with a rate parameter of λ. Therefore, the distribution of the time between the first and second arrivals is the minimum of two independent exponential distributions with a rate parameter of λ. This is equivalent to a Gamma distribution with parameters α =2 and β =λ. Therefore, the distribution of Y is Gamma(2, λ).

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The monthly payment required to pay off a loan of $140,000 at 7% interest would be $776.89 is the correct statement(A).

The statement given is describing a function that relates the monthly payment R of a 25-year variable-rate mortgage loan to the loan amount A and the current interest rate i.

The given values are R = $776.89 and A = $140,000, with an interest rate of 7%. This means that the monthly payment required to pay off a loan of $140,000 at 7% interest would be $776.89.

However, the other statements are incorrect interpretations. For instance, the statement "For a loan of $140,000 at 7.7689% interest, 700 monthly payments would be required to pay off the loan" is incorrect.

This is because the number of payments required to pay off a loan depends not only on the loan amount and interest rate, but also on the term of the loan.

Similarly, the statement "For a loan of $140,000 at 7% interest, 776.89 monthly payments would be required to pay off the loan" is also incorrect, as the number of payments required would be determined by the term of the loan.

Finally, the statement "For a loan of $140,000 at 7.7689% interest, the monthly payment is $700" is also incorrect. This is because, for the given loan amount and interest rate, the monthly payment required would be $776.89, as calculated above.

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Answer:

She will draw 120 times for a red marble

Step-by-step explanation:

The solution for X in equation 30=5(X+5)X is X= 1.

To solve the equation, we can start by distributing the 5 on the right-hand side of the equation, which gives us:

30 = 5X + 25X

Combining like terms, we get:

30 = 30X

Dividing both sides by 30, we get:

X = 1

However, we need to check whether this value satisfies the original equation. Plugging X=1 into the equation gives us:

30 = 5(1+5)(1)

30 = 5(6)

30 = 30

Therefore, the only valid solution is X=1.

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The equations of straight lines are \hat{y} = 2h, \hat{y} = 23r + 4 and \hat{y}= 2s + 3t. Option(A),(B) and (F) are correct.

A line in the coordinate plane can be described with the help of a linear equation, that is, an equation that has a first-degree expression, like y = 2x – 3.

There are many ways to put the equation of a line in the form y = mx + b,

where m is the slope and

b is the y-intercept,

but they all require the use of algebraic properties of equations, such as addition, subtraction, multiplication, division, and substitution.

The equations of straight lines among the following are:  \hat{y} = 2h,  \hat{y} = 23r + 4 and \hat{y}= 2s + 3t

Hence, the correct options are:Option A: \hat{y} = 2h , Option B: \hat{y} = 23r + 4  and Option F: \hat{y}= 2s + 3t.

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The length of the arc is approximately 5.51 meters when a circle with a radius of 21 meters is subtended by a central angle of 15 degrees.

The length of an arc of a circle with radius 21m that subtends a central angle of 15° can be calculated using the formula:

Arc length = (central angle/360°) x 2πr

where r is the radius of the circle, and π is the mathematical constant pi.

Substituting the given values, we get:

Arc length = (15/360) x 2π x 21

Arc length = (1/24) x 2 x 3.14 x 21

Arc length = (1/12) x 3.14 x 21

Arc length = 5.51 meters (rounded to two decimal places).

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We need to apply the  formula to determine the length of a circle's arc: (Central angle / 360°) x (2 x x radius) is the formula for arc length. the radius is  distance from the circle center to any point on its perimeter,

and the central angle is the angle subtended by the arc at its center. The radius in this instance is stated as 21 meters, while the arc's center angle is provided as 15 degrees. When these values are added to the formula, we obtain: arc length is equal to (15°/360°) x (2x x 21m) 3.68 m. As a result, the arc measures around 3.68 meters in length. As a result, the radius is the distance from the circle's center to any point on its perimeter, if we were to sketch an arc of The arc's length would be around 3.68 meters for a circle with a radius of 21 meters and a center angle of 15 degrees.

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If A = [tex]PDP^{-1}[/tex], Then [tex]A^{k}[/tex] = [tex](PDP^{-1}) ^{k}[/tex] = [tex]PDP^{-1}[/tex][tex]PDP^{-1}[/tex] .....[tex]PDP^{-1}[/tex] = [tex]PD^{k} P^{-1}[/tex]since [tex]P^{-1}[/tex] P = I, the identity matrix.

Further, the representation can be made as in the following attachment.

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Answer: 25

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

As per the points A, B, and C are colinear points and the point C lies between points A and B on the line.

Let's begin by finding the distance between points A and B. Using the distance formula equation, we can substitute the values of the x and y coordinates of A and B:

AB = √((0 - 5)² + (5 - (-5))²)

= √(25 + 100)

= √125

= 5√5

Therefore, the distance between points A and B is 5√5.

Similarly, we can find the distance between points B and C:

BC = √((2 - 0)² + (1 - 5)²)

= √4 + 16

= √20

= 2√5

Finally, we can find the distance between points A and C:

AC = √((2 - 5)² + (1 - (-5))²)

= √9 + 36

= √45

= 3√5

Alternatively, we can use the equation of the line passing through any two of these points and check if the third point lies on that line.

Let's use the points A and B to find the equation of the line passing through them:

y - (-5) = ((5 - (-5)) / (0 - 5))(x - 5)

y + 5 = (10 / (-5))(x - 5)

y + 5 = -2(x - 5)

y + 5 = -2x + 10

y = -2x + 5

Now, let's check if point C lies on this line by substituting its coordinates into the equation:

1 = -2(2) + 5

1 = 1

Since the equation is true, we can conclude that points A, B, and C are collinear. Moreover, since point C lies between points A and B on the line, we can say that C lies on segment AB.

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Complete Question:

Given points A, B, and C. Find AB, BC, and AC. Are A, B, and C collinear? If so, which point lies between the other two? A(5, −5), B(0,5), C(2, 1)

Answer:

2916 cm^2

Step-by-step explanation:

Area = side x side = 54 x 54 or 54^2 = 2916 cm^2

Answer:

The other guy is right, 2916 cm^2 is the answer

Step-by-step explanation:

Do you need help with any other questions, if so I'm available to help you.

A reasonable estimate for the number of green marbles in the bag would be around 250, since the marbles are split evenly between green and yellow. This means that for each student selecting 10 marbles, on average 5 of them should be green.

To estimate the number of green marbles in the bag, we can use the fact that the marbles are split evenly between green and yellow. This means that for each student selecting 10 marbles, on average 5 of them should be green. This means that, with 20 students selecting 10 marbles each, we can expect to have at least 100 green marbles. We can then multiply this number by two to get a reasonable estimate of 200 green marbles. Since this is a slightly conservative estimate, we can round up to 250 green marbles for our reasonable estimate.

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The area is 49 square yards.

The equation in standard form for the circle with center (5,0) passing through (5, 9/2) is 4x² + 4y² - 40x + 19 = 0

Given that

Center = (5, 0)

Point on the circle = (5. 9/2)

The equation of a circle can be expressed as

(x - a)² + (y - b)² = r²

Where

Center = (a, b)

Radius = r

So, we have

(x - 5)² + (y - 0)² = r²

Calculating the radius, we have

(5 - 5)² + (9/2 - 0)² = r²

Evaluate

r = 9/2

So, we have

(x - 5)² + (y - 0)² = (9/2)²

Expand

x² - 10x + 25 + y² = 81/4

Multiply through by 4

4x² - 40x + 100 + 4y² = 81

So, we have

4x² + 4y² - 40x + 19 = 0

Hence, the equation is 4x² + 4y² - 40x + 19 = 0

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a. To approximate the change in alcohol level from 3 to 3.2 hours and the correct expression is OC: A'(3).

For this we need to calculate the difference between the values of A(t) at t = 3.2 and t = 3. The expression that correctly approximates this change is given by: A'(3) * 0.2, where A'(t) is the derivative of A(t) with respect to t. Therefore, the correct expression is OC: A'(3).

b. Similarly, to approximate the change in alcohol level from 4 to 4.2 hours, we need to calculate the difference between the values of A(t) at t = 4.2 and t = 4. The expression that correctly approximates this change is again given by: A'(4) * 0.2. Therefore, the correct expression is also OC: A'(4).

To calculate the approximate changes in alcohol level, we need to find the derivative of A(t) with respect to t:

A'(t) = 0.03746 + 0.20242t

a. The approximate change in alcohol level from 3 to 3.2 hours is:

A'(3) * 0.2 = (0.03746 + 0.20242(3)) * 0.2 ≈ 0.118

Therefore, the approximate change in alcohol level from 3 to 3.2 hours is 0.118.

b. The approximate change in alcohol level from 4 to 4.2 hours is:

A'(4) * 0.2 = (0.03746 + 0.20242(4)) * 0.2 ≈ 0.149

Therefore, the approximate change in alcohol level from 4 to 4.2 hours is 0.149.

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