The diagram shows a square with a perimeter of 20 cm.
Not drawn
accurately
Eight of these squares fit together to make a rectangle.
Not drawnaccurately
What is the perimeter of the rectangle?​

The sum of the measures of the exterior angles of any polygon, including a triangle, is always 360 degrees.

We have,

An exterior angle of a polygon is formed by extending one of its sides outward.

In the case of a triangle, when we extend each side, we create three exterior angles.

These exterior angles are located outside the triangle.

The key concept to understand is that the sum of the exterior angles of any polygon is always 360 degrees.

This property holds true for all polygons, regardless of their shape or size.

To visualize this, imagine starting at any vertex of a triangle and moving along its sides while measuring the exterior angles.

As you move around the triangle, the sum of the exterior angles will always add up to 360 degrees.

This is because, at each vertex, the exterior angle supplements the interior angle to form a straight angle of 180 degrees.

In a triangle, each interior angle measures less than 180 degrees.

So, when we extend each side to create the exterior angles, they collectively compensate for the deficiency of the interior angles, resulting in a sum of 360 degrees.

Therefore,

The sum of the measures of the exterior angles of a triangle is always 360 degrees.

This principle holds true for all polygons, making it a fundamental property of geometry.

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Answer:

Step-by-step explanation:

x + 2 + 57 = 90

x + 59 = 90

x = 31°

x + 2 = 33°

Answer:

x=31

Step-by-step explanation: Since we know Angle A and Angle B are complementary and complementary angles add up to 90 we can set up an equation:

x+2+57=90

x+59=90

x=31

Hope this helps :)

The median is the middle value when the data is arranged in ascending or descending order. The mode is the value that appears most frequently in the data set.

The range is the difference between the maximum and minimum values in the data set.

To find the median, mode, and range of a data set, we need to analyze the values within the set.

To find the median, mode, and range of a data set, follow these steps:

Arrange the data set in ascending or descending order.

Find the median by identifying the middle value. If the data set has an odd number of values, the median is the middle value. If the data set has an even number of values, the median is the average of the two middle values.

Identify the mode by determining the value(s) that appear most frequently in the data set.

Calculate the range by subtracting the minimum value from the maximum value in the data set.

By following these steps, you can determine the median, mode, and range of a given data set. Remember to round to the nearest tenth if necessary.

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Answer:

3rd quadrant.

Step-by-step explanation:

We know that

4x + 7 < -3

5 - 3*y ≥ 11

We should isolate both of the variables in these inequalities:

for the first one we get:

4x + 7 < - 3

4x < -3 - 7

4x < -10

x < -10/4

So x is smaller than a negative number, then we know that x is negative, from this we already know that the point will be on quadrants 2 or 3.

For the other inequality we get:

5 - 3*y ≥ 11

5 - 11 ≥ 3y

-6 ≥ 3y

-6/3 ≥ y

-2 ≥  y

So we can see that y is equal to or smaller than a negative number, then y is a negative number.

So both values, x and y, are negatives.

This means that the point P(x, y) is in the 3rd quadrant.

Answer:

(x+4)(3x-2)(x+1)

Step-by-step explanation:

Great Grains of Canada has made a wheat purchase of 4,000 tonnes from Gateway Grains in Malta at a rate of 130 euros per tonne, with payment due in one year. The current spot exchange rate between the Canadian dollar (CAD) and the euro (EUR) is 1.6750 CAD/EUR.

The spot exchange rate of 1.6750 CAD/EUR indicates that 1 Canadian dollar is equivalent to 1.6750 euros. Since the wheat purchase is denominated in euros, Great Grains of Canada will need to convert the payment amount from Canadian dollars to euros at the prevailing exchange rate.

To calculate the total payment in Canadian dollars, we multiply the number of tonnes (4,000) by the price per tonne (130 euros) to get the payment in euros. The total payment can be calculated as 4,000 tonnes * 130 euros/tonne = 520,000 euros.

To determine the equivalent payment in Canadian dollars, we multiply the payment in euros by the spot exchange rate. In this case, the payment in Canadian dollars would be 520,000 euros * 1.6750 CAD/EUR = 871,000 CAD.

It's important to note that the given information does not mention the 1-year forward rate, so we cannot determine the forward exchange rate or the amount Great Grains of Canada would pay in Canadian dollars at the forward rate. However, if the 1-year forward rate were provided, it could be used to estimate the payment in Canadian dollars based on the forward exchange rate and the payment amount in euros.

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Answer:

ans: The line passes through the point (0,13)

Step-by-step explanation:

(0,13) is Y-intercept

Answer:

The answer is C the line passes through (0,13)

Step-by-step explanation:

The probability of selecting a score between 75 and 90 with a mean of 70 and a standard deviation of 10 is 0.2857.

The formula for calculating the probability of selecting a score between 75 and 90 with a mean of 70 and a standard deviation of 10 is P(X>75 and \(X < 90)= P(X < 90)-P(X < 75)\).

To calculate P(X<90) we use the z-score formula and calculate the z-score for 90, which is \((90-70)/10=2\).

Using the z-table, we look up the probability of scores lower than 2, which is 0.9772.

Similarly, to calculate P(X<75), we calculate the z-score for 75, which is (75-70)/10=0.5.

Using the z-table, we look up the probability of scores lower than 0.5 which is 0.6915.

Therefore, the probability of selecting a score between 75 and 90 is 0.9772-0.6915= 0.2857.

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Answer:

22,3

Step-by-step explanation:

It should be that

Answer:

x = 2 and x = -1

Step-by-step explanation:

The zeroes of the function are found by setting g(x) equal to 0:

g(x) = (x - 2)(3x + 3) = 0

By the Zero Product Property, in order for this equation to be equal to 0, each of (x - 2) or (3x + 3) or both has to equal 0. So, set each equal:

x - 2 = 0

x = 2

3x + 3 = 0

3x = -3

x = -3/3 = -1

The zeroes are thus x = 2 and x = -1.

~ an aesthetics lover

Answer:

x=2 x=(-1)

Step-by-step:

Solve: (x-2)(3x+3)=0

= x-2=0                   3x+3=0

=x-2(+2)=0(+2)       =3x-3(-3)=0(-3)

=x=2                      =3x=(-3)

                              =3x/3=(-3)/3

                              =x=(-1)

The given function's difference quotient is -1 / (x^2 + xh), which measures the average rate of change of the function over a specific interval.

The difference quotient is a formula that measures the average rate of change of a function over a specific interval. It is commonly used in calculus to find the slope of a tangent line to a curve at a specific point. The formula for the difference quotient is:

Difference quotient = (f(x + h) - f(x)) / h

In this case, the function f(x) is given as 1 / f(x) - f(5). To evaluate the difference quotient, we need to substitute the values of x and h into the formula and simplify the result. Here are the steps:

1. Substitute the values of x and h into the formula:

Difference quotient = (1 / (x + h) - f(5) - (1 / x - f(5))) / h

2. Simplify the numerator:

Difference quotient = (1 / (x + h) - 1 / x) / h

3. Find a common denominator for the fractions in the numerator:

Difference quotient = ((x - (x + h)) / (x * (x + h))) / h

4. Simplify the numerator:

Difference quotient = (-h / (x * (x + h))) / h

5. Simplify the denominator:

Difference quotient = -h / (h * x * (x + h))

6. Cancel out the h terms:

Difference quotient = -1 / (x * (x + h))

7. Simplify the denominator:

Difference quotient = -1 / (x^2 + xh)

This is the simplified result of the difference quotient for the given function.

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Answer:

66m*2

Step-by-step explanation:

2(20m + 13m)

= 66m*2

Answer:

66 m

Step-by-step explanation:

Since you are adding all the sides, you multiply 20x2 because there are two sides. Then you multiply 13x2 because 6 plus the missing number in the bottom right corner is equal to 7. The answer that you get from the multiplications, you add them and you have your perimeter.

Answer:

  100 local calls

Step-by-step explanation:

You want to know the number of local calls Jennifer made when her telephone bill for $63.50 includes a $30 monthly charge, $18.50 in long distance charges, and local calls at $0.15 each.

For n local calls, Jennifer's bill is ...

  total bill = monthly charge + long distance charge + $0.15n

Filling in the given values, we have ...

  63.50 = 30 +18.50 +0.15n

  15.00 = 0.15n . . . . . . . subtract 48.50

  100 = n . . . . . . . . divide by 0.15

Jennifer made 100 local calls.

Answer:

\(thank \: you\)

Answer:

27

Step-by-step explanation:

The answer is x=27

In this exercise, we are given two functions f and g, and an interval [a, b]. We are asked to find the area between the graphs of f and g from x=a to x=b using definite integrals and the Fundamental Theorem of Calculus. The process involves finding the antiderivatives of the functions f and g, and then subtracting the values of the antiderivatives at a and b.

In particular, for this problem, we have f(x) = 8(x) = 6 - |x - 2| and the interval [3, 7). We can split the interval into two parts: [3, 5) and [5, 7). On the first part, the function f(x) is equal to 8(x) = 6 - (2 - x) = x + 4. On the second part, the function f(x) is equal to 8(x) = 6 - (x - 2) = 8 - x. Therefore, we can write the integral for the area between the graphs of f and g as follows:

∫[3,5) [f(x) - g(x)] dx + ∫[5,7) [f(x) - g(x)] dx

Substituting the functions f and g, we get:

∫[3,5) [(x+4) - 3] dx + ∫[5,7) [(8-x) - 3] dx

Evaluating the integrals, we get:

[(1/2)x^2 + 4x - 3x] from 3 to 5 + [(8x - (1/2)x^2) - 15] from 5 to 7

Simplifying, we get:

8

Therefore, the exact area between the graphs of f and g from x=3 to x=7 is 8 square units.

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Answer:

42.64 mph

Step-by-step explanation:

5 1/3 / 7 1/2 = m/60

see attached for explanation

The production level that will maximize profit is 550 units.

To find the production level that maximizes profit, we first need to find the revenue and cost functions.

The revenue function is given by:

R(q) = pq = (13 - q/600)q = 13q - q²/600

The cost function is given by:

C(q) = 670 + 2q + 0.01q²

The profit function is given by:

P(q) = R(q) - C(q) = (13q - q²/600) - (670 + 2q + 0.01q²) = -0.01q² + 11q - 670

To find the production level that maximizes profit, we need to take the derivative of the profit function with respect to q and set it equal to zero

P'(q) = -0.02q + 11 = 0

Solving for q, we get

q = 550

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The noise in the medium is also a Gaussian distributed random variable with a mean of 0 and standard deviation of 7 (square root of 49). The probability of X being greater than 10 is very small, less than 0.001%.

In this communication system, the signal Θ is a Gaussian distributed random variable with a mean of 0 and standard deviation of 1. The noise in the medium is also a Gaussian distributed random variable with a mean of 0 and standard deviation of 7 (square root of 49).

The receiver observes X, which is the sum of 2Θ and W. Since Θ and W are independent, we can calculate the mean and variance of X as follows:

E[X] = E[2Θ + W] = 2E[Θ] + E[W] = 0 + 0 = 0

Var[X] = Var[2Θ + W] = 4Var[Θ] + Var[W] = 4(1) + 49 = 53

Therefore, X is also a Gaussian distributed random variable with a mean of 0 and standard deviation of √53 = 7.2801.

To find the probability of X taking a certain value, we can use the formula for the Gaussian probability density function:

f(x) = (1/√(2πσ^2)) * e^(-(x-μ)^2/(2σ^2))

where μ is the mean and σ is the standard deviation. For example, the probability that X is equal to 0 can be calculated as:

f(0) = (1/√(2π*53)) * e^(-(0-0)^2/(2*53)) = 0.0494

To find the probability of X being greater than a certain value, we can use the cumulative distribution function (CDF) of the Gaussian distribution. For example, the probability that X is greater than 10 can be calculated as:

P(X > 10) = 1 - Φ((10 - μ)/σ)

where Φ is the standard normal CDF. Substituting the values for μ and σ, we get:

P(X > 10) = 1 - Φ((10 - 0)/7.2801) = 0.00002

So the probability of X being greater than 10 is very small, less than 0.001%.
In the given communication system with Gaussian noise, the signal Θ is a Gaussian distributed random variable Θ∼N(0,1), and the noise W is also a Gaussian distributed random variable W∼N(0,49), independent of the signal. The receiver observes X = 2Θ + W. To provide accurate information, answers should be given to at least 4 decimal places.

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A triangle is a polygon. The total area of the figure can be represented by 12a, (6a+b), and 2b cm².

A triangle is a polygon with 3 sides and 3 vertices.

Since the area of a single triangle is a cm², and the shape is formed of 12 triangles, therefore, the area of the 12 triangles will be equal to,

\(\text{Area of the complete figure} = 12 \times a = 12a\rm \ cm^2\)

Given that the area of the complete dark portion is b cm², therefore, the area of the 6 triangles with a cm² of area each, and the black portion can be written as,

\(\text{Area of the complete figure} = (6 \times a)+b = (6a+b)\rm \ cm^2\)

As the dark portion also consists of 6 triangles with an area of a cm² each and the total sum of this dark area is b cm². Also, the light portion consists of 6 triangles with an area of a cm². Therefore, the total area can be written as,

\(\text{Total area} = 6a+6a = b+b = 2b\rm\ cm^2\)

Thus, the total area of the figure can be represented by 12a, (6a+b), and 2b cm².

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Answer:

Coordinate Q is (0.8, 0.7)

Step-by-step explanation:

We are told that the coordinates of point Pare (0.6,0.1).

This means that along the x-axis, x = 0.6 and along the y-axis, y = 0.1.

Now, by inspection of the graph, we can see that when we count boxes from the origin to the point P, we have 6 boxes. Thus, each box corresponds to 0.1. So, for point Q, from the origin to that point, on the x-axis, we have 8 boxes. Since one box = 0.1, then the x - value of Coordinate Q is 0.8.

On the y - axis, we see that we have one box from the origin up for the corresponding y-value of coordinate P.

This means that one box is 0.1.

For coordinate Q, we will count 7 boxes. Thus, y-value of coordinate Q is 0.7.

Thus,coordinate Q is (0.8, 0.7)

Answer:

74 Degrees

Step-by-step explanation:

Mistakes were made when i said 37

Answer:

\(\Huge\boxed{74}\)

Step-by-step explanation:

Hello There!

First things first, we need to find the value of x

If you didn't know the measures of supplementary angles add up to equal 180 so we can use this equation to solve for x

180 = 2x + 3x - 5

step 1 combine like terms

2x + 3x = 5x

now we have

180 = 5x - 5 step 2 add 5 to each side

-5 + 5 cancels out

180 + 5 = 185

now we have 185 = 5x

step 3 divide each side by 5

5x/5=x

185/5=37

we're left with x = 37

Now we want to plug in 37 into x for angle A

angle a = 2(37)

2*37=74

so we can conclude that angle A = 74

There are approximately 3.72 x 10⁴¹ ways that Anna can hand out 1 treat to each of the 36 children who come to her door.

Anna has 2 dozen Rollo bars, which is equivalent to 2 x 12 = 24 Rollo bars.

She also has 1 dozen apples, which is equivalent to 1 x 12 = 12 apples.

So, Anna has a total of 24 + 12 = 36 treats to hand out.

Now, she needs to hand out 1 treat to each of the 36 children who come to her door.

This can be thought of as selecting 1 treat from the total of 36 treats for each child, without replacement, as each child can only receive 1 treat.

The number of ways to do this is given by the concept of permutations, denoted by "nPr", which is calculated as;

nPr = n! / (n - r)!

where n is the total number of items (treats) to choose from, and r is the number of items (treats) to choose.

In this case, n = 36 (total number of treats) and r = 36 (number of children).

Plugging in the values, we get;

36P36 = 36! / (36 - 36)! = 36! / 0! = 36!

Since 0! (0 factorial) is equal to 1, we can simplify further:

36! / 1 = 36!

36! ≈ 3.72 x 10⁴¹

So, there are 3.72 x 10⁴¹ ways that Anna can hand out 1 treat to each of the 36 children who come to her door.

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Answer: (i) The upper bound for the length of the rod can be found by rounding up to the nearest decimal place. Since the length of the rod is 2.9 m, correct to 1 decimal place, we round up to 3.0 m. Therefore, the upper bound for the length of the rod is 3.0 m.

(ii) Without knowing the dimensions of the box, it is not possible to determine if the rod will fit completely inside it. The length of the box, as well as the width and height, would need to be known in order to determine if the rod will fit.

Step-by-step explanation:

The required simplified solution of the given expression is given as x = -8.

Given that,
An expression is given we have to determine the simplified solution of the given expression x + 6 = -2.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression,
x + 6 = -2
simplify

x + 6 = -2
x = -2 - 6
x = -8

Thus, the required simplified solution of the given expression is given as x = -8.

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Answer:

Hi! The answer to your question is \(g = 0\)

Step-by-step explanation:

In the equation there is no g so g is nonexistant so it equals 0

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