in how many ways can 5 men and 5 woman sit alternately in a row of 10 seats?

1 foot = 12 inches

 divide 69 by 12

69/12 = 5.75 feet

The pre-image of the point (1, 1) under the translation (x, y) -> (x+3, y-3) in a coordinate system is the point (-2, 4).

The student's question relates to a translation transformation in mathematics. A translation moves every point of a figure or a space by the same distance in a given direction. In this case, the student has provided a specific translation transformation, which is represented by the formula (x, y)
ightarrow (x+3, y-3). This transformation means that for any point with coordinates (x, y), the translated point will have coordinates where 3 is added to the x-coordinate and 3 is subtracted from the y-coordinate.

If the point (1,1) is an image under this translation, you can find its pre-image by reversing the translation. Thus, subtracting 3 from the x-coordinate of the image and adding 3 to the y-coordinate of the image gives the pre-image coordinates:

Therefore, the pre-image of the point (1, 1) under the given translation is (-2, 4).

48−32÷4×2

=48−32×24

=48−8×2 or 48−644

=48−16

=32

Answer:

32

Step-by-step explanation:

We have been given an expression [tex]48-32\div 4\cdot 2[/tex]. We are asked to find the value of our given expression.

Using order of operations (PEMDAS), we will divide or multiply from left to right.

Dividing 32 by 4:

[tex]48-8\cdot 2[/tex]

Multiplying 8 by 2:

[tex]48-16[/tex]

[tex]32[/tex]

Therefore, the value of our given expression is 32.

Answer:

1 negative x-tile and 8 positive unit tiles on the left side; 7 positive tiles and 8 negative unit tiles on the right side.

Step-by-step explanation:

Two positive integers x and y

x - y = 4

x² + y = 68

x and y

Add the two equations together.

... (x - y) + (x² + y) = (4) + (68)

... x² + x = 72

Rearrange to standard form and factor.

... x² + x - 72 = 0

... (x + 9)(x - 8) = 0

Use the zero product rule to find the solutions. That rule says the product is zero when one or more factors is zero.

... x + 9 = 0 ⇒ x = -9

... x - 8 = 0 ⇒ x = 8 . . . . . . the positive solution

Then we can find y from

... 8 - y = 4

... y = 4 . . . . . . . add y-4 to the equation

The two positive integers are 8 and 4.

To solve for the two positive integers where their difference is 4 and the sum of the smaller and the square of the larger is 68, we set up a quadratic equation and solve for n to find that the integers are 4 and 8.

The problem given is a classic algebra question where we are asked to determine two positive integers based on their relationship to each other and an additional numeric condition. We know that the difference between these two numbers is 4, and when the smaller integer is added to the square of the larger, the result is 68.

Let's denote the smaller number as n and the larger number as n+4, since there is a difference of 4 between them. Now, according to the second condition given, we can set up the following equation: n + (n+4)2 = 68.

Expanding the squared term and combining like terms, we get a quadratic equation: n2 + 8n + 16 + n = 68. Simplifying, n2 + 9n + 16 = 68. Further simplification leads to n2 + 9n - 52 = 0. Factoring this quadratic equation, we find the integers that satisfy the equation: n = 4 and n = -13. Since we are looking for positive integers, the solution is n = 4 and n+4 = 8.

Therefore, the two positive integers are 4 and 8.

The quadratic equation defined by the table is f(x) = 2.35x^2 + 4.72x -1.55

A quadratic function is represented as:

f(x) = ax^2 + bx + c

Using the table of values, we have:

a(0)^2 + b(0) + c = -1.55

This gives

c = -1.55

Also, we have:

a(2)^2 + b(2) + c = 17.29

4a + 2b -1.55 = 17.29

This gives

4a + 2b = 18.84

Divide through by 2

2a + b = 9.42 --- (2)

Also, we have:

a(4)^2 + b(4) + c = 54.93

16a + 4b -1.55 = 54.93

This gives

16a + 4b = 56.48

Divide through by 4

4a + b = 14.12 ---- (3)

Subtract (2) from (3)

2a = 4.7

Divide by 2

a = 2.35

Substitute a = 2.35 in 4a + b = 14.12

4*2.35 + b = 14.12

Evaluate

b = 4.72

Substitute values for a, b and c in f(x) = ax^2 + bx + c

f(x) = 2.35x^2 + 4.72x -1.55

Hence, the quadratic equation defined by the table is f(x) = 2.35x^2 + 4.72x -1.55

Read more about quadratic equation at:

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There are 10 integers from 1 to 700 that are divisible by 2, 5, and 7. This is calculated by finding the least common multiple (LCM) of the numbers, which is 70, and then determining how many multiples of 70 are within the given range.

The question asks to find out how many integers from 1 to 700 are divisible by 2, 5, and 7. An integer divisible by 2, 5, and 7 is also divisible by their least common multiple (LCM). The LCM of 2, 5, and 7 is 70 since 2 x 5 x 7 = 70. So, the task is to find the number of multiples of 70 between 1 and 700.

To find the number of multiples of 70 in that range, you can use the following steps:

Therefore, there are 10 integers from 1 to 700 that are divisible by 2, 5, and 7.

Answer:

Figure B appears to be a polygon under certain conditions.

Step-by-step explanation:

We are given the following information in the question:

Figure A is a hexagon with varying lengths.

Figure B is a pentagon.

Figure C is a right triangle.

Figure D is a rectangle.

We have to find which are the regular polygons.

Figure A is not regular because of varying length.

Figure B can be a regular pentagon provided it is equiangular and equilateral

Figure C cannot be a regular polygon because a right angle follows the Pythagoras theorem and all the three sides can never be equal in a right angled triangle.

Figure D cannot be a regular polygon as the length of only opposite sides are equal and not all sides are not equal.

Figure B appears to be a polygon under certain conditions.

The correlation coefficient of the given data pairs is most likely closest to 0.8694.

The correlation coefficient measures the strength and direction of the relationship between two variables. To find the correlation coefficient, you can use the formula:

r = [n(Σxy) - (Σx)(Σy)] / sqrt{[n(Σx^2) - (Σx)^2][n(Σy^2) - (Σy)^2]}

Using this formula, you can calculate the correlation coefficient for the given data pairs. The closest value to the correlation coefficient will be 0.8694, option d.

The answer closest to the correlation coefficient of the data is 0.835.

To find the correlation coefficient of the given data pairs, we can use the formula:

r = (Σxy - (Σx)(Σy)/n) / sqrt((Σx^2 - (Σx)^2/n)(Σy^2 - (Σy)^2/n))

where Σ represents the sum, n is the number of data pairs, x is the average temperature, y is the electricity cost, and xy is the product of x and y.

To calculate the correlation coefficient, we first need to find the sums and products of the data pairs:

Σx = 65 + 59 + 71 + 78 + 82 + 85 + 88 + 91 + 84 + 79 + 63 + 59 = 924
Σy = 147 + 141 + 176 + 189 + 183 + 211 + 231 + 227 + 198 + 188 + 152 + 126 = 2259
Σxy = (65*147) + (59*141) + (71*176) + (78*189) + (82*183) + (85*211) + (88*231) + (91*227) + (84*198) + (79*188) + (63*152) + (59*126) = 219907

Using these values, we can calculate the correlation coefficient:

r = (219907 - (924*2259)/12) / sqrt((Σx^2 - (Σx)^2/12)(Σy^2 - (Σy)^2/12))

Calculating the remaining sums:

Σx^2 = (65^2) + (59^2) + (71^2) + (78^2) + (82^2) + (85^2) + (88^2) + (91^2) + (84^2) + (79^2) + (63^2) + (59^2) = 73482
Σy^2 = (147^2) + (141^2) + (176^2) + (189^2) + (183^2) + (211^2) + (231^2) + (227^2) + (198^2) + (188^2) + (152^2) + (126^2) = 827259

Plugging in the values:

r = (219907 - (924*2259)/12) / sqrt((73482 - (924^2)/12)(827259 - (2259^2)/12))

After performing the calculations, the correlation coefficient is approximately 0.835.

Therefore, the answer closest to the correlation coefficient of the data is 0.835.

Bill Gates makes approximately $22,831.05 per minute, calculated by dividing his annual earnings of $12 billion by the number of minutes in a year (525,600).

To calculate how much Bill Gates makes per minute, we need to start by determining how much he makes per year. According to the question, Bill Gates makes approximately $12 billion a year. To find out how much that is per minute, we need to follow these steps:

Therefore, on average, Bill Gates makes $22,831.05 per minute.