60,488 rounded to the nearest 10,000

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:

There can be multiple possible dimensions for a garden with an area of 11 square feet depending on its shape. For example, the garden could be 1ft by 11ft, 2ft by 5.5ft, or even a square with each side measuring 3.32 ft.

The area of a garden is calculated by multiplying its length by its width. As the area of the garden is given as 11 square feet, possible dimensions for the garden could be 1 foot by 11 feet, 2 feet by 5.5 feet, or any other combinations that, when multiplied, give the result as 11 square feet.

Another way to look at it is that if you imagine the garden as a perfect square shape, each side would be approximately 3.32 feet since 3.32 multiplied by 3.32 equals roughly 11. This is because the square root of 11 is about 3.32.

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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

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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.

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.

It takes 6 minutes to print 21 more photos. It takes 10 minutes to print 35 more photos.

To determine the time it takes to print 21 more photos, we first need to calculate the rate at which the printer prints photos. We can do this by dividing the number of photos printed (28) by the time it takes to print them (8 minutes). This gives us a rate of 3.5 photos per minute.

Next, we can divide the number of additional photos (21) by the rate of photos per minute to find the time it takes to print them. This gives us 21 photos / 3.5 photos per minute = 6 minutes.

Therefore, it takes 6 minutes to print 21 more photos.

To construct a double number line diagram, we create two parallel number lines, one for the number of photos and one for the number of minutes. We mark the starting point on both lines as 0.

Next, we plot the point (28, 8) on the diagram, representing the fact that 28 photos are printed in 8 minutes.

To determine the time it takes to print 35 more photos, we can extend the number of photos line to the point (35 + 28, 8), which is (63, 8). This point represents the fact that 63 photos are printed in 8 minutes.

Finally, we can draw a vertical line from the point (63, 8) on the number of photos line to the number of minutes line. This line intersects the number of minutes line at the point (63, 8 + 10), which is (63, 18).

Therefore, it takes 10 minutes to print 35 more photos.

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.

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.

The local property tax rate is 0.051.

Given that,

Based on the above information, the calculation is as follows:

[tex]= \$2,834.58 \div \$55,580[/tex]

=0.051

Therefore we can conclude that The local property tax rate is 0.051.

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Final answer:

To express 32.043 in expanded form, break it into each digit's value based on its place: 30 (tens) + 2 (ones) + 0.04 (hundredths) + 0.003 (thousandths), resulting in 30 + 2 + 0.04 + 0.003.

Explanation:

The question asks about expressing the number 32.043 in expanded form. Expanded form is a way of writing numbers to show the value of each digit. It involves breaking down the number into each of its digits, multiplied by their respective place value. For the number 32.043:

Therefore, 32.043 in expanded form is 30 + 2 + 0.04 + 0.003.

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.

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).

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.