Please simplify the following expression while performing the given operation.
(-3+i)+(-4-i)

Answer: 45min

Step-by-step explanation:

3x60=180

2x60=120

120+15=135min

180-135=45min

The equations that arise when the steps of the Euclidean algorithm are reversed to express the greatest common divisor of each of these pairs of integers as a linear combination of these integers are:

1 = 10 - 3.3, 1 = 37.10 - 3.123, and 1 = 37.2347-706 - 123.

The Euclidean algorithm is a recursive method for finding the greatest common divisor (GCD) of two positive integers. When we divide the larger number by the smaller number, we obtain the remainder. The smaller number and the remainder are then passed on as input to the next round. The process continues until the remainder is zero, at which point the GCD is obtained.

The solution to the given problem is as follows:

We will use the Euclidean algorithm to compute gcd(123, 2347).

123 ÷ 2347 = 0 remainder 123.2347 ÷ 123 = 19 remainder 106.123 ÷ 106 = 1 remainder 17.106 ÷ 17 = 6 remainder 4.17 ÷ 4 = 4 remainder 1.4 ÷ 1 = 4 remainder 0.The last nonzero remainder we get is 1.

Therefore, the greatest common divisor (GCD)(123, 2347) = 1.

The greatest common divisor of 123 and 2347 can be expressed as a linear combination of the two numbers in the following ways:1 = 10 - 3.3, 1 = 37.10 - 3.123, and 1 = 37.2347-706 - 123.

Thus, the equations arising when the steps of the Euclidean algorithm are reversed to express the greatest common divisor of each of these pairs of integers as a linear combination of these integers are:

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Answer: Its Slope

Step-by-step explanation: in the given graph both lines a parallel .meaning they both should have the same slope

The most appropriate statistical test to assess whether a correlation exists between the Wong-Baker FACES pain rating scale and a previously validated visual analog scale is the (C) Spearman rank correlation.

Correlation refers to the connection between two variables in which a modification in one variable is linked to a modification in the other variable. Correlation can be positive or negative.

Spearman rank correlation- A non-parametric approach to test the statistical correlation between two variables is Spearman rank correlation, also known as Spearman's rho or Spearman's rank correlation coefficient. This is based on the ranks of the values rather than the values themselves. The results are denoted by the letter "r".

The formula for Spearman's rank correlation coefficient:

Rs = 1 - {6Σd₂}/{n(n₂-1)}

Where, Σd₂ = the sum of the squared differences between ranks.

n = sample size

Thus, the most appropriate statistical test to assess whether a correlation exists between these two measurements is the (C) Spearman rank correlation.

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Answer:

120 km/h.

Step-by-step explanation:

480 km / 4h

Divide top and bottom by 4 to get the desired km/h.

We have 120 km/h.

Hope this helps!

Answer:$2.60

Step-by-step explanation:40*0.065

Answer:42.06

Step-by-step explanation:

The Objective Function in the linear programming problem given in the above-stated scenario is:

B. S = 3x + 5y

Linear programming is a statistical technique used to find a maximum or minimum value of an equation in order to find a solution to a problem. It is used to calculate how much to produce to maximize profits, how to allocate resources, and determine which investments to make.

Linear programming problems include an objective function, which is the equation to be maximized or minimized, and constraints that must be followed. Linear programming problems can be solved graphically or algebraically. In order to solve a linear programming problem, we first need to identify the objective function and constraints.

Objective Function in the linear programming problem:

The score of the student is to be maximized in the given time frame by answering the maximum number of questions of both types.

Therefore, the objective function is: S = 3x + 5y

Answer: B. S = 3x + 5y

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Answer:

A ,B ,C

Step-by-step explanation:

2+2+2+2 equals 8

4x2 equals 8 and

1x8 equals 8

Answer:

A) 2 + 2 + 2 + 2

B) 4 × 2

C) 1 × 8

Hope this helps!

Step-by-step explanation:

A = 4 + 4 = 8

B = 8

C = 8

D = 16

E = 16

Answer: y = -192

Step-by-step explanation:

The equation given is:

-24 = y/8

To solve for y, we need to isolate the variable y on one side of the equation. We can do this by multiplying both sides by 8:

-24 x 8 = y

Simplifying the left side:

-192 = y

Therefore, the solution is y = -192.

Answer: I hope this helped!

Step-by-step explanation:

.

The distance from points A(-2, 2) to B (4, -2)​ is equal to √52 units.

Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using the following mathematical expression:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represents the data points (coordinates) on a cartesian coordinate.

Substituting the given points into the distance formula, we have the following;

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance = √[(4 - (-2))² + (-2 - 2)²]

Distance = √[(6)² + (-4)²]

Distance = √(36 + 16)

Distance = √52 units.

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Answer: 105:210

Step-by-step explanation:

1:2 = ?:210

? = 210/2 = 105

1:2 = 105:210

Answer: The person paid $396.

Step-by-step explanation:

1. Since we need to find 60% of 360, we can do 360 x 60/100.

2. We are now left with 216.

3. Now we have to add the total together.

4. 216 + (15x12) = 396.

5. The person paid $396.

The smallest number of batteries in the package for the probability to exceed 1% is a) 17. This can be calculated using the binomial distribution with parameters n=17 and b)p=0.2927 and number of batteries is c)4. (Where p is the probability from part a).

a) The probability that a battery does not reach the significant milestone after 8 hours of usage is 0.2927.

This can be calculated using the cumulative normal distribution function. The parameters are μ=7.36, σ=0.29, and x=8.

b) The probability that at least 10 batteries will last more than 7.5 hours is 0.7012.

This can be calculated using the binomial distribution with parameters n=12 and p=0.2927 (where p is the probability from part a).

c) The number of batteries should be in package is μ*4.2/7.5 = 4.

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Answer:

n > 10

Step-by-step explanation:

2n > 20

2n/2 > 20/2

n > 10

Answer:

To sketch the given region on the Argand diagram, we need to find the intersection of the three conditions:

-3i < Im(z) < 3i (the imaginary part of z lies between -3 and 3 on the vertical axis)

1 < Re(z) ≤ 6 (the real part of z lies between 1 and 6 on the horizontal axis)

|z - 4| ≥ 1 (the distance between z and 4 is greater than or equal to 1, which means z is outside or on the boundary of the circle centered at 4 with radius 1)

The first two conditions define a rectangle in the complex plane with vertices at (1,-3i), (1,3i), (6,3i), and (6,-3i). The third condition excludes the inside of a circle centered at 4 with radius 1, which means the region we want is the rectangle with a circular hole in the middle.

To find the area of this region, we can subtract the area of the circle from the area of the rectangle. The area of the rectangle is:

A_rect = length x width = (6 - 1) x (3i - (-3i)) = 30i

The area of the circle is:

A_circle = πr^2 = π(1)^2 = π

Therefore, the area of the region is:

A_region = A_rect - A_circle = 30i - π

So the area of the region is 30i - π, written in terms of π.

Answer:

To use an area model to determine the quotient of 556 and 16, we can divide a rectangle of area 556 into 16 equal parts. Each part will have an area of 556/16.

We can start by dividing 556 into 16 groups of 10 (160), and then into 16 groups of 3 (48). That leaves us with a remainder of 4.

So we have:

556 = 16 x 34 + 48 + 4

This shows that 556 can be written as 16 times some whole number (34) plus a remainder of 48 + 4/16.

Simplifying the remainder, we have:

48 + 4/16 = 48 + 1/4 = 48.25

Therefore, the quotient of 556 and 16 is:

556/16 = 34 1/4

The quotient of 556 and 16 using an area model can be determined by producing a rectangle with the total area of 556 and one side of 16. The length of the other side will be the quotient. In this case, the quotient is 34 3/4.

When asked to determine the quotient of 556 and 16 using the area model, one way to think of this is making a rectangle. The total area is 556 and one side is 16. The length of the other side will be the quotient.

Start by first estimating how many times 16 could fit into 556. Let's take 30 as an estimate, because 30*16 = 480, which is relatively close to 556. Draw a rectangle with the width of 16 and the length of 30.

Find the difference between the rectangle's area and 556. So, 556 - 480 = 76. Now, 76 is our remaining area to fill. 16 goes into 76 four more times, adding up to 64.

There is still a leftover area, which is 76-64 = 12. This is smaller than our width of 16. So, your final answer is 34 12/16 or 34 3/4 in simplest form.

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The formula for the nth term of the series will be (11+n)*(n+1).

A series in mathematics is essentially the process of adding an infinite number of quantities, one after the other, to a specified starting quantity. A significant component of calculus and its extension, mathematical analysis, is the study of series. The fundamental concepts in mathematics are series and sequence. A series is the total of all elements, whereas a sequence is an ordered group of elements in which repeats of any kind are permitted. One of the typical instances of a series or a sequence is an arithmetic progression.

In this the pattern of the series is

24=12*2

39=13*3

54=14*4

hence The formula for the nth term of the series will be (11+n)*(n+1).

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The second segment on the left, which is equal to the price per bag of lemons (X) times the quantity of bags of lemons, represents the cost of the lemons (7).

A way for resolving proportionality issues is the unitary method. Finding the value of one unit and then using that value to determine the value of another unit in relation to the first is what this process entails. If we already know that three pens cost $6, for instance, we can use the unitary technique to get the price of five pens as follows: 1 pen costs $6, 3 pens cost $2. Five pens cost $10, or $5 multiplied by $2.

given

The arrow on the right in the diagram above, which is equal to $29.12, represents the total cost of the cookies and lemons.

The first segment on the left, which is $2.66, represents the price of the cookies.

The second segment on the left, which is equal to the price per bag of lemons (X) times the quantity of bags of lemons, represents the cost of the lemons (7).

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From the construction of the triangle ABC we get that the measure length of BC is approximately 4.22cm

To construct triangle ABC, we can follow these steps:

To measure the length of BC in triangle ABC, we can use the law of sines.

The law of sines states that in any triangle ABC:

a / sin(A) = b / sin(B) = c / sin(C)

Where a, b, and c are the lengths of the sides of the triangle opposite to the angles A, B, and C, respectively.

In our triangle ABC, we know AB = 6 cm, angle BAC = 96 degrees and angle ABC = 35 degrees. We can find the measure of angle ACB by using the fact that the sum of the angles in a triangle is 180 degrees:

angle ACB = 180 - angle BAC - angle ABC

= 180 - 96 - 35 = 49 degrees

Now, we can apply the law of sines to find the length of BC:

BC / sin(35) = 6 / sin(96)

BC = 6 × sin(35) / sin(96)

Using a calculator, we can evaluate this expression to get:

BC ≈ 4.22 cm

Therefore, the length of BC in triangle ABC is approximately 4.22 cm.

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The probability of the given event is 11/13.

A card is drawn randomly from a deck of 52 cards.

The probability that the card drawn is neither an ace nor a king is a question that can be answered with probability.

We know that there are 4 aces and 4 kings in a deck of 52 cards.

The probability of drawing an ace or a king is P(Ace or King) = 4/52 + 4/52 = 8/52 = 2/13

There are four of each card rank in a deck of 52 cards, and there are a total of 52 cards. A player must choose one of the 52 cards at random.

The probability of drawing an ace or a king is P(Ace or King) = 4/52 + 4/52 = 8/52 = 2/13

The probability of at drawing neither an ace nor a king is:

P(Not Ace and Not King) = 1 - P(Ace or King) = 1 - 2/13 = 11/13

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The distance Mrs. Smith covers is 3520 yards during the duration of the week by Friday morning.

One week has seven days in total.

Mrs. Smith walks half a mile each day after work, she walks a total of

0.5 miles/ day × 7 days/ week = 3.5 miles/ week

Now, if we calculate the distance on Friday morning, she must have walked four times till Friday morning since she has to walk after her work.

Therefore,

0.5 miles/ day × 4 days = 2 miles

To convert miles to yards, we can use the fact that there are 1760 yards in one mile:

2 miles/week × 1760 yards/mile = 3520 yards/week

Therefore, by Friday morning, Mrs. Smith will have walked 3520 yards.

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Answer is X=2.

1. Collect like terms

(x) + 4 + 9 = 17 - x

2. Add the numbers

x + (13) = 17 - x

3. Move the variable to the left-hand side and change its sign

x + 13 (+x) = 17

Move the constant to the right-hand side and change its sign

x + x = 17 - 13

4. Collect like terms

2x = 17 - 13

Subtract the numbers

2x = 4

5. Divide both sides of the equation by 2

Therefore, you get your solution: X=2.

Using the properties of equality, the steps for solving the equation is explained below.

To solve an equation, we would apply the properties of equalities where necessary to isolate the variable in the equation to one side.

Step 1: [tex]3x + 4 - 2x + 9 = 17 - x[/tex] [given]

Step 2: [tex]x + 13 = 17 - x[/tex] [Combine like terms]

Step 3: Add x to both sides of the equation

[tex]x + 13 + x = 17 - x + x[/tex] [addition property of equality]

Step 4: [tex]2x + 13 = 17[/tex] [simplify]

Step 5: Subtract 13 from both sides

[tex]2x + 13 - 13 = 17 - 13[/tex] [subtraction property of equality]

Step 6: [tex]2x = 4[/tex] [simplify]

Step 7: [tex]x = 2[/tex] [division property of equality]

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Answer:

35 passengers produce the maximum revenue for the bus company.

Step-by-step explanation:

Define the variables:

If there are 30 or fewer passengers, each passenger will be charged $80. Therefore, the equation for the total revenue for 30 or fewer passengers is:

[tex]y = 80x,\quad x \leq 30[/tex]

If there are more than 30 passengers, each passenger will be charged $80 minus $2 for every passenger over 30. Therefore, the equation for the total revenue for more than 30 passengers is:

[tex]y = [80 - 2(x - 30)]x, \quad x > 30[/tex]

This simplifies to:

[tex]y = [80 - 2x + 60]x, \quad x > 30[/tex]

[tex]y = [140 - 2x]x, \quad x > 30[/tex]

[tex]y = 140x - 2x^2, \quad x > 30[/tex]

To maximize revenue, we need to find the value of x that maximizes the above equation.

Since this is a quadratic function, the maximum value occurs at the vertex of the parabola.

The x-value of the vertex of a parabola in the form y = ax² + bx + c is when x = - b/2a. Therefore, the x-value of the vertex is:

[tex]\implies x_{\sf vertex}=\dfrac{-140}{2(-2)}=\dfrac{-140}{-4}=35[/tex]

Therefore, the number of passengers that produce the maximum revenue for the bus company is 35.

In order to solve this problem, we need to begin by examining the graph of Amir's altitude relative to sea level. We can see that the graph starts at an altitude of 700 meters and ends at an altitude of 400 meters.

We can also see that the slope of the graph is negative, which means that the altitude is decreasing over time. This means that it will take Amir some amount of time to reach sea level (which is 0 meters).

To calculate how long it took Amir to reach sea level, we can use the following equation:

Time = (Altitude Final - Altitude Initial) / (Rate of Change)

In this equation, the Rate of Change is the slope of the graph, which can be determined by examining the graph.

Plugging in our values, we get:

Time = (400 - 700) / (-6) = 100 / (-6) = -16.67 minutes

Therefore, it took Amir 16.67 minutes to reach sea level.

Answer: 9, 10, and 11

Step-by-step explanation:

If the sum of three consecutive natural numbers is 30, then we can represent the smallest of the three numbers as x. The next two consecutive natural numbers would be x+1 and x+2. Therefore, we can form the equation:

x + (x+1) + (x+2) = 30

Simplifying the left-hand side, we get:

3x + 3 = 30

Subtracting 3 from both sides, we get:

3x = 27

Dividing by 3, we get:

x = 9

Therefore, the three consecutive natural numbers are 9, 10, and 11.

She should navigate at angle 76.86° to go to Island C.

The cosine rule is for solving triangles which are not right-angled in which two sides and the included angle are given. The following are cosine rule formula:

cosA = (b²  +  c² - a²)/2bc

where a, b and c are the lengths and A, B and C are the angles for the islands respectively

Using the formula:

cosA = (b²  +  c² - a²)/2bc

cosA = (13²  +  11² - 15²)/(2*13*11)

cosA = 5/22

A = arc cos(5/22)

A = 76.86°

Thus, θ = 76.86

Therefore, she should navigate at angle 76.86° to go to Island C.

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