a circular table is painted yellow with a red square in the middle. the radious of the tabletop is 6x. the side length of the red square is 3x. what is the area of the yellow part of the tabletop.

The solution to the equation is (a) x = ln(7/5) - 2

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

4 + 5e^(x + 2) = 11

Evaluate the like terms in the equation

So, we have the following representation

5e^(x + 2) = 7

Divide through the equation by 5

This gives

e^(x + 2) = 7/5

Take the natural logarithm of both sides

x + 2 = ln(7/5)

So, we have

x = ln(7/5) - 2

Hence, the solution is x = ln(7/5) - 2

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Answer:

alternate exterior angles

Step-by-step explanation:

congruent alternete exterior angles

If on the following Tuesday, Terry fills out scale again and receives a score of 28 , then Terry's scores on the Self-Monitoring Scale do not appear to be Reliable .

The Terry's scores on the Self-Monitoring Scale do not appear to be reliable, because there is a significant difference between his score on Friday and his score on the following Tuesday.

The Reliability is defined as the consistency of measurement over time or across different conditions.

In this case, if Terry's scores on the Self-Monitoring Scale were reliable, we would expect them to be consistent or stable over time.

However, his score on Tuesday is significantly lower than his score on Friday suggests that there may be some inconsistency in his responses .

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Using combinatorics, there are 1926 ways to distribute 9 different computer games among Wendy, Jim, and Hannah so that each person receives an odd number of games.

If each person receives an odd number of games, then the number of games must be 1, 3, 5, or 7. There are four odd numbers to choose from.

We can use combinatorics to find the odd number in each turn.

Let's consider each odd number in turn.

If each person gets 1 game, then we are looking for the number of ways to choose 3 games out of 9 to distribute. This is simply the number of combinations of 3 things taken from a set of 9 things, which is 9C3, or (9!)/(3!6!) = 84.

If each person gets 3 games, then we are looking for the number of ways to choose 3 games out of 9 to distribute to one person. Once those games have been chosen, we are left with 6 games to distribute to the other two people. The number of ways to choose 3 games out of 9 is again 84, but we must multiply this by the number of ways to choose 3 games out of the remaining 6. This is 6C3, or (6!)/(3!3!) = 20. Therefore, the total number of ways to distribute 9 games with each person getting 3 games is 84*20 = 1680.

If each person gets 5 games, then we are looking for the number of ways to choose 5 games out of 9 to distribute to one person. Once those games have been chosen, we are left with 4 games to distribute to the other two people. The number of ways to choose 5 games out of 9 is 126, and the number of ways to choose 4 games out of the remaining 4 is 1. Therefore, the total number of ways to distribute 9 games with each person getting 5 games is 126*1 = 126.

If each person gets 7 games, then we are looking for the number of ways to choose 7 games out of 9 to distribute to one person. Once those games have been chosen, we are left with 2 games to distribute to the other two people. The number of ways to choose 7 games out of 9 is 36, and the number of ways to choose 2 games out of the remaining 2 is 1. Therefore, the total number of ways to distribute 9 games with each person getting 7 games is 36*1 = 36.

Adding up the number of ways to distribute the games in each case, we get 84 + 1680 + 126 + 36 = 1926.

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The angle corresponding to each other of the different triangles are equal. The correct option is D.

"Similar triangles are triangles that have the same shape but differ in size. Similar objects include all equilateral triangles and squares with any side length. In other words, if two triangles are similar, their corresponding angles and sides are congruent and in equal proportion ".

Here given, ΔJGR is similar to a triangle ΔMST

So, from the definition of a similar triangle,

angle J ≅ angle M

angle G ≅ angle S

angle R ≅ angle T

Hence, option D is correct.

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Answer:

5

Step-by-step explanation:

5.4772

To round to the nearest whole number, look at the number to the right of it (4)     if     5 or greater round the 5 up to '6'    o/w   leave it as '5'

The measure of the angle x in the figure is 55 degrees

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

The polygon and the external angles

The sum of the exterior angles of a polygon is 360°.

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

5 * x + x + 30 = 360

Evaluate the like terms

So, we have

6x = 330

Divide by 6

x = 55

Hence, the value of x is 55

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Option A i.e. the first and the third service will be provided by a full-service broker but not by a discount broker.

What is meant by a broker?

An impartial party whose services are often used in several businesses is a broker. The main duty of a broker is to connect buyers and sellers; as a result, the broker acts as a neutral intermediary between a buyer and a seller.

The services which will be provided by a full-service broker but not by a discount broker are

Option I. Research of potential investment opportunities

Option III. Recommendation of investments

For any form of investment, research and recommendations are key and important components. Before you make any investments, you should conduct adequate research.

Hence, option A i.e. the first and the third service will be provided by a full-service broker but not by a discount broker.

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The value of k in the exponential function is -3.

Taking the natural logarithm of both sides of the equation, we have:

ln [ (1 + 65/x)^(3x) ] = ln(e^k)

Using the properties of logarithms, we can simplify the left side of the equation:

3x ln(1 + 65/x) = k

Taking the limit as x approaches infinity, we have:

lim (x → ∞) 3x ln(1 + 65/x)

= lim (x → ∞) [ln(1 + 65/x) / (1/x)] × 3

Using L'Hopital's rule, we can evaluate the limit:

lim (x → ∞) [ln(1 + 65/x) / (1/x)]

= lim (x → ∞) [-65 / (x(1+65/x))]

= -65/65

= -1

Therefore, we have:

lim (x → ∞) 3x ln(1 + 65/x)

= lim (x → ∞) [ln(1 + 65/x) / (1/x)] × 3

= -3

Thus, the exponential equation simplifies to:

-3 = k

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We have the expression:

[tex]\displaystyle{\lim_{x\to \infty} \left(1+\dfrac{65}{x}\right)^{3x} = e^k} \\[/tex]

As [tex]\displaystyle{x\to \infty} \\[/tex], the term [tex]\displaystyle{\dfrac{65}{x}} \\[/tex] approaches 0. Therefore, we can rewrite the expression as:

[tex]\displaystyle{\lim_{x\to \infty} \left(1+\dfrac{65}{x}\right)^{x \cdot \dfrac{3x}{65}} = e^k} \\[/tex]

Simplifying the exponent, we get:

[tex]\displaystyle{\lim_{x\to \infty} \left(1+\dfrac{65}{x}\right)^{\dfrac{3x^2}{65}} = e^k} \\[/tex]

Now, as [tex]\displaystyle{x\to \infty} \\[/tex], the expression [tex]\displaystyle{\left(1+\dfrac{65}{x}\right)^{\dfrac{3x^2}{65}}} \\[/tex] approaches [tex]\displaystyle{e^{-3}} \\[/tex].

Therefore, we have:

[tex]\displaystyle{e^k = e^{-3}} \\[/tex]

Comparing the exponents, we can conclude that:

[tex]\displaystyle{k = -3} \\[/tex]

Hence, the correct value of k is indeed -3.

You slept for 9 hours in those three days, calculated by multiplying 12.5% of the total hours (72) by 72, which equals 9.

To calculate the number of hours slept in three days, we first need to determine how many hours there are in three days.

As given, 1 day has 24 hours. So, three days will have 3 x 24 = 72 hours.

Now, we are told that you slept for 12.5% of those 72 hours. To calculate this, we multiply the percentage by the total number of hours:

12.5% x 72 hours = (12.5/100) x 72 = 0.125 x 72 = 9 hours

Therefore, you slept for 9 hours in those three days.

Percentage is a way to express a proportion or ratio as a fraction of 100. The sign "%" is widely used to represent it. For example, if you had 20 apples and you ate 5 of them, you would have consumed 25% of the apples (5 out of 20).

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It is important to note that this calculation provides the value of tan(x) in terms of the cosine of the angle x, which is dependent on the specific triangle that is being considered.

Given the triangle with sides ZY = 48, ZX = 50, and XY = 14, we can use trigonometry to find the value of tan(x).

First, we can use the Pythagorean theorem to find the value of YX, the length of the side opposite angle x:

[tex]YX = \sqrt{(ZY^2 + ZX^2 - 2 * ZY * ZX * cos(x))[/tex]

We know that ZY = 48 and ZX = 50, so we can substitute these values into the equation:

[tex]YX = \sqrt{(48^2 + 50^2 - 2 * 48 * 50 * cos(x))[/tex]

[tex]YX = \sqrt{(2304 + 2500 - 2400 * cos(x))[/tex]

Next, we can use the definition of tangent to find the value of tan(x):

[tex]tan(x) = YX/ZX = \sqrt{(2304 + 2500 - 2400 * cos(x)) / 50[/tex]

It is important to note that this calculation provides the value of tan(x) in terms of the cosine of the angle x, which is dependent on the specific triangle that is being considered. The exact value of tan(x) will depend on the specific angle x in the triangle.

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The solution of the quadratic equation for y is given as follows:

y = 0.17 and y = 1.69.

The quadratic equation for this problem is defined as follows:

7y² - 13y + 2 = 0.

The coefficients are given as follows:

a = 7, b = -13 and c = 2.

Hence the discriminant is of:

D = (-13)² - 4 x 7 x 2

D = 113.

The first root is of:

y = (13 + sqrt(113))/14

y = 1.69.

The second root is of:

y = (13 - sqrt(113))/14

y = 0.17.

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By using a system of equations of two variables we concluded that the first number was 6

Let the numbers be x and y and their sum gives z

The equation for the sum of 2 numbers:

                                             x + y = z    -(1)

We know, z = 30 and y = 4 times x = 4x

Putting values of y and z in equation (1), we get

                                             x + 4x = 30

Solving for x, we get

                                                  5x = 30

                                         x = 30/5 = 6

To get the value of y, put the value of x in y = 4x and we get

                                          y = 4 x 6 = 24

So the real equation was

                                              6 + 24 = 30

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For removing all the perfect squares of √(39y^9), we need to factor out any perfect squares from the expression under the square root.

To get rid of all the perfect squares in (39y9), factor out any perfect squares in the expression under the square root.

First, by factoring 39 and y9, we can simplify the expression under the square root:

[tex]√(39y^9) = √(313y^8y) = √(313*(y^4)^2*y)[/tex]

Because (y4)2 is a perfect square, we can take it out from under the square root:

[tex]√(39y^9) = √(313(y^4)^2y) = (y^4)√(313*y)[/tex]

By removing all of the perfect squares from (39y9), we get:

[tex](y^4)√(313y)[/tex]

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Pair of ratios can form a true proportion I would usually give 45 points but i have 35 soo ye 25/20, 16/21.

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Answer:

B. (-7, -1)

C. (5, 12)

Step-by-step explanation:

A function can only have one output for a specific input

In math terminology that means if y = f(x) is a function of x then the mapping from x to y is 1:1

Or,

For a specific value of x, there can be one and only one value for y

This is often referred to as a vertical line test; if a vertical line parallel to the y-axis is drawn for any x value it should intersect the function graph at one and only one point

g(x) includes all the ordered pairs of f(x) therefore the ordered pairs of g(x) are:
{ ( -18, -31), (-9, -23), (4, 2), (11, 5), (14, 12) }

Looking at the answer choices:
A. (-9, 11) will violate the 1:1 correspondence between x and y since (-9, -23) is already a pair

B. (-7, -1) is OK. There is no other entry with x = -7

C. (5, 12) is OK. There is no other entry with x = 5

D. (4, 15) will violate; there is already an entry for x = 4: (4, 2)

E.  (14,20). This will also violate the properties of a function since there exists an entry for x = 14, namely (14, 20)

The x has a value of 36. The line's two points are (-12, 1) and (36, 7).

The slope of a line frequently represents the steepness and direction of the line. The slope of a straight line between the two locations, (x1,y1) and (x2,y2), can be easily determined by calculating the difference between their coordinates.

We can apply the slope formula to determine the value of x:

m is the slope and (x1, y1) and (x2, y2) are two points on the line, with m = (y2 - y1) / (x2 - x1).

We are given the point (x1, y1) = (-12, 1) and the slope m = 1/8. We are also given the y-coordinate of the other point as y2 = 7.

Plugging in the known values, we get:

1/8 = (7 - 1) / (x - (-12))

Simplifying and solving for x, we get:

1/8 = 6 / (x + 12)

1 = 48 / (x + 12)

x + 12 = 48

x = 36

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Answer:

131,072 Zombies:

the equation: 32 x 4^6 = 131,072

the equation in scientific notation form: 3.2 x 4^7 = 131,072

Step-by-step explanation:

The amount of zombies starts at 32. It quadruples per hour, so we need to multiply the amount by 4 six times(once for every hour).

We can use an exponent to represent this in an equation:

32 x 4^6 = 131,072

Or, if we put it in scientific notation,

3.2 X 4^7 = 131,072.

The equation which represents the number of zombies is;

= [tex]1.31072[/tex]×[tex]10^{5}[/tex]

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

Given that

The amount of zombies = 32.

And It quadruples per hour,

Therefore,

Multiply the amount by 4 six times (as it occurs once for every hour).

The the exponent form to represent this equation:

32 x 4^6 = 131,072

Hence, in scientific notation the equation is,

= [tex]1.31072[/tex]×[tex]10^{5}[/tex]

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Answer:

x = 3

Step-by-step explanation:

2.5/x = 10/12

Multiply both sides by x

2.5 = 10/12x

Divide both sides by 10/12

3 = x

The cost per pound of a house blend of coffee is $ 5 per pound.

What is the cost price?

The precise value that corresponds to the unit price paid is represented by the cost price. In some stock market theories, this value is utilized to establish the value of stock holdings and is used as a key determinant of profitability.

Here, we have

Weight of Central American coffee = 10 lb

Cost of Central American coffee = $7 per pound

Total value of Central American coffee = weight × cost = 10 ×7 = $ 70

Weight of South American coffee = 40 lb

Cost of South American coffee =  $ 4.50 per pound

Total value of Central American coffee = weight × cost = 40 ×4.50 = $ 180

Total weight of house blend coffee = Weight of Central American coffee + weight of South American coffee

= 10 +40 = 50 lb

The total value of house blend coffee = value of Central American coffee + value of South American coffee

= $ 70 + $ 180 = $ 250

Cost per pound of house blend coffee = ( total value of house blend coffee) / (total weight of house blend coffee)

= 250 / 50 = $ 5 per pound

Hence, the cost per pound of a house blend of coffee is $ 5 per pound.

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Answer:

3 and 7/8 gallons remaining

Step-by-step explanation:

You did not give the container options, but hopefully this will help

Answer:

Step-by-step explanation:

multiply all numbers together

2 x 6 x 3 = 36

The required number of markers does Gerald has 56 markers.

Let's represent the number of markers that Gerald has with the variable "m", and the number of pens he has with the variable "p". We can set up two equations based on the information given:

m + p = 78 (equation 1)

(m + 11) + (p + 11) = 78 (equation 2)

In equation 2, we add 11 to both the number of markers and the number of pens, since Gerald has 11 more of each. We can simplify equation 2 by combining like terms:

m + p + 22 = 78

m + p = 56 (equation 3)

Now we have two equations with two variables. We can use either substitution or elimination to solve for one of the variables. Let's use substitution and solve for "m" in terms of "p" using equation 1:

m + p = 78

m = 78 - p

Now we can substitute this expression for "m" into equation 3:

m + p = 56

(78 - p) + p = 56

Simplifying the equation, we get:

78 - p + p = 56

78 = 56 + p

p = 22

Therefore, Gerald has 22 pens. To find the number of markers he has, we can substitute this value of "p" into equation 1:

m + 22 = 78

m = 56

So, Gerald has 56 markers.

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It will take 50 seconds for the person to travel from one end to the other at the current speed.

We know that the person travels 28 feet in 7 seconds, remember that speed is defined as the quotient between distance and time, then the person's speed is:

s = 28ft/7s = 4ft/s

Now we want to find the time T that it takes for the person to travel the 200 feet of the sidewalk, then we need to solve:

(4ft/s)*T = 200ft

T= 200ft/(4 ft/s) = 50s

It takes 50 seconds.

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Answer:

I think a is the right answer

The total surface area of the rectangular prism is 24 * 2 + 36 * 2 + 6 * 2 = 72 + 72 + 12 = 156 square yards.

The surface area of a rectangular prism is given by the sum of the areas of its six faces. To find the surface area of a rectangular prism that is 3 yards long, 2 yards wide, and 12 yards high, we need to find the area of each of its four rectangular faces and then add these areas together.

First, we find the area of the two faces that are 2 yards wide and 12 yards high. Each of these faces has an area of 2 * 12 = 24 square yards.

Next, we find the area of the two faces that are 3 yards long and 12 yards high. Each of these faces has an area of 3 * 12 = 36 square yards.

Finally, we find the area of the two faces that are 3 yards long and 2 yards wide. Each of these faces has an area of 3 * 2 = 6 square yards.

So, the total surface area of the rectangular prism is 24 * 2 + 36 * 2 + 6 * 2 = 72 + 72 + 12 = 156 square yards.

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In a case whereby there are 7213 applicants for the astronaut program only one half of the applicants which is about 3607 applicants will be accepted into the program​.

The concept that will be used here is multiplication. One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical size.

The symbols for multiplication are cross (), asterisk (*), and dot (). You seem to utilize the cross a lot when you write in your notebooks. In both algebra and computer languages, the asterisk and dot are symbols (higher mathematics).

Total applicants =7213 applicants

Then one half of the applicants  = 1/2 of 7213

=7213/2

= 3607 applicants

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complete question:

There are 7213 applicants for the astronaut program only one half of the applicants which is about ______will be accepted into the program​

On solving the provided question we cans ay that The side of the square is w/2, then its area is: A = (w/2)² = w²/4

A square is an equilateral quadrilateral with four equal sides and four equal angles according to Euclidean geometry. It is also known as a rectangle with two neighboring sides that have the same length. Having all four equal sides and all four equal angles, a square is an equilateral quadrilateral. 90 degree or straight angles are square angles. In addition, the square's diagonals are equally spaced and split at a 90-degree angle. a neighboring rectangle with two equal sides. a quadrilateral with four right angles and four sides of equal length. a parallelogram having two adjacent, equal sides that form a right angle. straight-sided rhombus.

The side of the square is w/2, then its area is:

A = (w/2)² = w²/4

The darkened region represents the difference between the square's and rectangle's areas:

[tex]14w - w^2/4 = 84\\56w - w^2 = 336\\w^2 - 56w + 336 = 0[/tex]

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