14. greater than a number g is 32​

The correct answer is (C) by the pigeonhole principle, if we have 5 points, then at least two of these points will have the same parity (both odd or both even). The midpoint of the segment joining these two points will therefore have integer coordinates

The statement that at least one pair of the five distinct points with integer coordinates in the xy plane has a midpoint with integer coordinates can be proven using the pigeonhole principle.

Assume that we have five distinct points with integer coordinates, (X1, Y1), (X2, Y2), (X3, Y3), (X4, Y4), and (X5, Y5) in the xy plane. To find the midpoint of the line joining two points, we take the average of their x-coordinates and the average of their y-coordinates. Thus, the x-coordinate of the midpoint of the line joining two points (Xi, Yi) and (Xj, Yj) is (Xi + Xj)/2, and the y-coordinate is (Yi + Yj)/2.

Consider the x-coordinates of the five points. These are integer values, and there are only five of them. Therefore, at least two of them must be equal, by the pigeonhole principle. Without loss of generality, let us assume that X1 = X2.

Now, consider the midpoint of the line joining (X1, Y1) and (X2, Y2). Its x-coordinate is (X1 + X2)/2 = X1, which is an integer. Therefore, we have found a midpoint with an integer x-coordinate.

Alternatively, consider the parity (even or oddness) of the x-coordinates of the five points. There are only two possible parities, and there are five points. Therefore, at least two points must have the same parity, by the pigeonhole principle. Without loss of generality, assume that (X1, Y1) and (X2, Y2) have the same parity. Then, the midpoint of the line joining these two points has an integer x-coordinate, since the sum of two even (or two odd) integers is even.

Therefore, we have shown that at least one pair of the five distinct points with integer coordinates in the xy plane has a midpoint with integer coordinates. The correct answer is (C) by the pigeonhole principle, if we have 5 points, then at least two of these points will have the same parity (both odd or both even). The midpoint of the segment joining these two points will therefore have integer coordinates.

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The length of the base of the scale model is 20 ft.

The scale model is 10% of the size of the actual building. Since the building has a side measurement of 200 ft, we can calculate the side measurement of the scale model by multiplying 200 ft by 10% (0.1).

200 ft * 0.1 = 20 ft

Therefore, the length of the base of the scale model is 20 ft.

The scale model is a proportional representation of the actual building, where each dimension of the model is a fraction of the corresponding dimension of the building. In this case, the scale factor is 10% (0.1), which means that every length measurement of the scale model is 10% of the corresponding length measurement of the actual building. By multiplying the side measurement of the building (200 ft) by the scale factor (0.1), we can determine the corresponding side measurement of the scale model, which is 20 ft.

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As per the angle sum property of quadrilateral, then values of x is 245 and the value of y is 341

Angle sum property of quadrilateral:

The angle sum property states that the sum of all the angles of the quadrilateral is 360 degree.

Given,

The angles of the quadrilateral are 5x degrees, (4y minus 2 )degrees, (13x plus 10 )degrees, and 10y degrees.

Now we have to write and solve a system of linear equations to find the values of x and y.

While we looking into the given angles, then we get the values

=> 5x°

=> (4y - 2)°

=> (13x + 10)°

=> 10y°

We know that, the sum of all the angles of the quadrilateral is 360°.

So, it ca be written as,

=> 5x° + (4y - 2)° + (13x+ 10)° + 10y° = 360°

=> 18x° + 14y° - 8° = 360°

=> 18x° + 14y° = 354°

When we divide all of them by 2, then we get the equation as,

=> 9x° + 7y° = 177°

Now we have to rewrite the given equation as,

=> 9x° = 177° - 7y°

=> x° = (177° - 7y°)/9

Apply these value on the angles, then we get,

=> 13(177 - 7y)/9 = -10

=> 13(177 - 7y) = 90

=> -7y = -90 - 2301

=> 7y = 2391

=> 341

Then the value of x is

=> 245

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The person is required to select a three-digit number, and if they guess the right number, they will be paid $700 for each dollar they bet. Each day, there is a new winning number.

The person bets $1 each day for one year.To get the possible win or loss from the game, the following formula can be used:Expected win or loss = (Probability of winning × Amount won) − (Probability of losing × Amount lost)From the question, we know that the person is betting $1 every day for a year. Therefore, the total amount of money spent by the person in a year is: Amount spent in a year = $1 × 365 = $365Let's calculate the probability of winning: There are 1000 possible three-digit numbers that can be selected. Only one of them is the winning number.Therefore,

The probability of winning the game is:P(win) = 1/1000Let's calculate the probability of losing the game:There are 999 three-digit numbers left after selecting the winning number.  This means that the person can expect to lose about $0.299 every day. Therefore, the person can expect to lose $109.14 in a year (365 days). Answer: $109.14

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Answer:

25

Step-by-step explanation:

an absaloute value means that every number inside of that would be a positive number.

By using the unitary method and dividing the time into equal intervals, the number of bacteria doubled every 3 hours, the final total of 32,000 bacteria after 14 hours.

Unitary method involves dividing the time interval into equal parts, and calculating the growth for each unit of time before adding them all up to get the total growth.

To start, let's divide the 14 hours into 3 hour intervals. We have

=> 14 hours / 3 hours = 4 intervals.

Next, we need to calculate the growth in each 3 hour interval. Since the number of bacteria doubles every 3 hours, we can find the growth by multiplying the initial number of bacteria by 2.

Starting with the first interval, we have 2000 bacteria * 2 = 4000 bacteria.

We can now repeat this calculation for each interval, multiplying the previous total by 2 each time.

For the second interval, we have 4000 bacteria * 2 = 8000 bacteria.

For the third interval, we have 8000 bacteria * 2 = 16,000 bacteria.

Finally, for the fourth interval, we have 16,000 bacteria * 2 = 32,000 bacteria.

So, at the end of 14 hours, there will be 32,000 bacteria in the culture.

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The similarity statement that would be true for the given figure is;

A. ∆ DAB ~∆ DAC

Similar triangles are those triangles that have the same proportionate side lengths as well as related angle measurements.

here, we have,

Two triangles are said to be similar if their corresponding angles and sides have the same ratio. Similar triangles will possess the same form but may or may not have the same size.

The SAS similarity rule states that If the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle inscribed by the two sides in both the triangle are equal, then it means that the two triangles are similar.

The Side-Side-Side (SSS) similarity rule states that If all the three sides of a triangle are in proportion to the three sides of another triangle, then the two triangles are similar.

In this question, when we analyze the triangles well, it is clear that;

DA is congruent to itself by reflexive property of congruence.

Thus, we can say that ΔDAB is similar to ΔDAC,

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The sides and the angle of the right triangle are a = 10√2, b = 10√2 and B = π / 4.

In this problem we need to determine the values of two sides and an angle of the right triangle. This can be done by means of the following properties:

A + B + C = π

sin A = a / c

cos A = b / c

tan A = a / b

Where:

If we know that A = π / 4, C = π / 2 and c = 20, then the missing angle and missing sides are, respectively:

B = π - π / 4 - π / 2

B = π / 4

cos (π / 4) = b / 20

b = 20 · cos (π / 4)

b = 10√2

sin (π / 4) = a / 20

a = 20 · sin (π / 4)

a = 10√2

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Answer:

17,984,000

Step-by-step explanation:

because it is

An example of a function that includes the quantity e and a logarithm with a derivative of 0 is \($f(x) = \ln(e^x)$\). The derivative of this function is 0, which can be confirmed by differentiating it with respect to x.

The function \($f(x) = \ln(e^x)$\) satisfies the condition of having a derivative of 0.

To verify this, let's differentiate the function with respect to x:

\(f'(x) = d/dx [ln(e^x)]\)

Using the chain rule, we can rewrite the function as:

\(f'(x) = (1 / (e^x)) \cdot d/dx[e^x]\)

The derivative of \(e^x\) with respect to x is \(e^x\). Therefore, we have:

\(f'(x) = (1 / (e^x)) \cdot e^x\)

Simplifying, we find:

f'(x) = 1

As we can see, the derivative of f(x) is a constant value of 1, which means that the function has a derivative of 0.

This indicates that the function remains constant for all values of x.

The presence of \(e^x\) in the function and the logarithm ensures that the derivative is 0.

The exponential function \(e^x\) grows rapidly, but the logarithm ln(x) "undoes" the effect of the exponential, resulting in a constant function.

This demonstrates the relationship between the exponential and logarithmic functions and how they can be combined to produce a function with a derivative of 0.

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The probability that a student chosen at random plays an instrument other than the keyboard is 64/73.

To calculate the probability that a student chosen at random plays an instrument other than the keyboard, we need to consider the total number of students who play instruments other than the keyboard and divide it by the total number of students.

In the seventh grade, the number of students playing instruments other than the keyboard is 11 (Guitar) + 10 (Bass) + 12 (Drums) = 33.

In the eighth grade, the number of students playing instruments other than the keyboard is 9 (Guitar) + 8 (Bass) + 14 (Drums) = 31.

The total number of students playing instruments other than the keyboard in both grades is 33 + 31 = 64.

The total number of students in both grades is 11 (seventh grade Guitar) + 10 (seventh grade Bass) + 12 (seventh grade Drums) + 2 (seventh grade Keyboard) + 9 (eighth grade Guitar) + 8 (eighth grade Bass) + 14 (eighth grade Drums) + 7 (eighth grade Keyboard) = 73.

Converting this probability to a percentage, we get (64/73) * 100 = 87.67.

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Answer:

720 I think there is your answer from me

have a great day bye hop helps

Step-by-step explanation:

Answer:

360 cubic cm

Step-by-step explanation:

((4*9)÷2)*20 = 36/2 *20 = 18*20 = 360 cubic cm

formula: ((base*height1)÷2)*height2

Answer:

0.70104025x^ 435466207018946428

Step-by-step explanation:

We will find the values as follows:

*Discount:

So, the discount is $6.

*Sale price:

So, the sale price is $14.

The missing side of the triangle is 22.8.

Triangle is a polygon that has three angles and three sides. It is one of the basic shapes in geometry and is used in many everyday objects such as buildings, bridges, and even teacups.

In this case, we have the angle of 27° and the lengths of 20 hypo and 11 OPP.

We need to use trigonometry to find the missing side, which is adjacent to the 27° angle.

To do this, we will use the SOH-CAH-TOA acronym, which stands for sine equals Opposite over Hypotenuse, cosine equals Adjacent over Hypotenuse, and tangent equals Opposite over Adjacent.

Since we know the angle and the length of the adjacent side, we can use the cosine of the angle to solve for the missing side.

To solve, we will plug in the known values into the equation:

cos(27°) = 20 hypo/x adjacent.

x adjacent = 20 hypo/cos(27°).

x adjacent =22.75

Rounding it to the nearest tenth= 22.8.

Thus, the missing side of the triangle is 22.8.

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Answer:

7x^2−19x+10

Step-by-step explanation:

3 x 2 − 14 x + 16 + 4 x 2 − 5x − 6

Answer:

Step-by-step explanation:  will u be my friend

Answer:

how do i explain if i dont know how?

Step-by-step explanation:

^^^

Step-by-step explanation:

ΔSTR and ΔSQR are similar triangles

so TR/SR=SR/QR

--> q/14=4/q

--> q = 2\(\sqrt{14}\)

Answer:

Option B.

Step-by-step explanation:

The given function is

\(f(x)=-2\sqrt{x-7}+1\)

The above function is defined if (x-7) is greater than 0.

\(x-7\geq 0\)

Add 7 on both sides.

\(x\geq 7\)

It is means domain of the function is \([7,\infty)\). So, -6 is not in domain.

We know that

\(\sqrt{x-7}\geq 0\)

Multiply both sides by -2. So, the sign of inequality will change.

\(-2\sqrt{x-7}\leq 0\)

Add 1 on both sides.

\(-2\sqrt{x-7}+1\leq 0+1\)

\(f(x)\leq 1\)

It is means range of the function is \((-\infty,1]\). So, -6 is in Range.

Since –6 is not in the domain of f(x) but is in the range of f(x), therefore the correct option is B.

Answer:

B

Step-by-step explanation:

Answer:

48 600

Step-by-step explanation:

6(4×6) × 9(5×9)

Solve the numbers in brackets first

6(20) × 9(45)= 120 × 405

= 4 8 600

Answer:

6(20) × 9(45)= 120 × 405

= 4 8 600

Answer:

15 + -12

Step-by-step explanation:

15 + -12 = -27 any positive plus a negative would be a negative while two positives equal a positive and two negatives equal a negative

The values of a and b are 2 and π/5, respectively

The graph of the complete question is added as an attachment

The equation of the graph is given as:

y = sin(ax - b)

From the graph, we have the following points:

(π/10, 0), (3π/5, 0) and (11π/10, 0)

Substitute the above points in y = sin(ax - b)

sin(a(π/10) - b) = 0 and sin(a(3π/5) - b) = 0

Take the arc sin of both sides

a(π/10) - b = 0

a(3π/5) - b = π

Subtract the equations to eliminate b

a(π/10) - a(3π/5) = -π

Divide through by π

a(1/10) - a(3/5) = -1

Express fractions as decimals

0.1a - 0.6a = -1

Evaluate the difference

-0.5a = -1

Divide by -0.5

a = 2

Substitute a = 2 in a(3π/5) - b = π

2 * (3π/5) - b = π

Evaluate the product

6π/5 - b = π

This gives

b = 6π/5 - π

Evaluate the difference

b = π/5

Hence, the values of a and b are 2 and π/5, respectively

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A polynomial is even if each term is an even function. f ( x ) = 2 x 4 − 3 x 2 − 5 f(x)=2x^4-3x^2-5 f(x)=2x4−3x2−5. Odd

What is odd and even polynomial?

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No, there is no concrete counter example for this false statement. We are given that "Suppose that V is a finite-dimensional vector space, that S1 is a linearly independent subset of V, and that S2 is a subset of V that generates V. Then S1 cannot contain more elements than S2."

We are required to find a concrete counter example for this false statement.  Proof: Let V be a finite-dimensional vector space, S1 be a linearly independent subset of V, and S2 be a subset of V that generates V. We can always extend S1 to a basis of V, say B1. Similarly, we can always reduce S2 to a basis of V, say B2. Since S2 generates V, it follows that B2 is the same as V. Since B1 is a basis of V, it follows that it contains the same number of vectors as B2, namely the dimension of V.

Therefore, it cannot contain more elements than S2. Thus, the statement is proved. We were able to prove the statement so there is no counter example to this.

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