Now suppose that the 5 (identical) prizes will be distributed among the 8 people. a winner can receive more than one prize. in how many ways could the 5 prizes be distributed?

An infinite number of line segments can have the midpoint (2, -3) in the coordinate plane, because you can have infinite pairs of points such that their midpoint is (2, -3).

In the coordinate plane, an infinite number of line segments can have the midpoint (2, -3). The reasoning behind this is that a midpoint is the point that is equidistant from the end points of a line segment. You can have infinite pairs of points in a coordinate plane such that their midpoint is (2, -3). For instance, the points (4, -1) and (0, -5) have the midpoint (2, -3), and so do the points (2, 7) and (2, -13). This can similarly be done for an infinite number of other sets of points.

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The answer is that there are infinitely many line segments that have the midpoint (2, -3).

A midpoint of a line segment is the point that divides the segment into two equal parts.

Let's consider a Cartesian coordinate system where the midpoint is given as (2, -3).

Any line segment with the midpoint (2, -3) would have a segment bisecting it.

So, it's not just one line segment that has this midpoint, but an infinite number of line segments.

To explain this, consider any line segment in the coordinate plane.

The midpoint of AB will always be (2, -3) if the segment is positioned such that it's equally distant from (2, -3).

We can slide and rotate this line segment around the midpoint (2, -3) while keeping it the same length, and the midpoint will always remain (2, -3).

So, the answer is that there are infinitely many line segments that have the midpoint (2, -3).

Answer:

Its the first gragh

Step-by-step explanation:

Graph D is a correct choice.

We have a set of inequalities -

y > − 2x − 2

y ≤ x + 4

We have select the graph that represents the solution set of the system of inequalities.

An inequality compares two values or expressions, showing if one is less than, greater than, or simply not equal to another value.

According to the question, we have -

Let →   y = -2x - 2

Now, plot the graph of the line → y = - 2x - 2 with a Dotted line ( > is a strict inequality).

Assume a point (0,0) -

0 > - 2 x 0 - 2

0 > -2

Which is true, hence shade the area where the point (0, 0) lies.

Let →   y = x + 4

Now, plot the graph of the line → y = x + 4 on the graph.

Assume a point (0,0) -

0 ≤ 0 + 4

0 ≤ 4

Which is true, hence shade the area where the point (0, 0) lies.

Refer to the image attached for final graph - the area under the Red thick line is common to both and is the solution set of  system of inequalities.

Hence, Graph D is a correct choice.

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The solution to the given expression is x = 31.

In order to simplify an expression with exponents of the same base, we would have to apply the properties of multiplication of exponents with the same base;

[tex](k^m)\cdot(k^{n})=k^{m+n}[/tex]

Based on the properties of roots of exponents, we have the following:

[tex]\sqrt[a]{x^b} =x^{\frac{b}{a} }[/tex]

By raising both sides of the given expression to the reciprocal of the exponent, we have:

[tex](x-4)^{\frac{2}{3} }=9\\\\((x-4)^{\frac{2}{3} })^{\frac{3}{2} }=9^{\frac{3}{2} }\\\\x-4=(9^{\frac{1}{2} })^{3 }\\\\x-4=(3)^{3 }\\\\[/tex]

x - 4 = 27

x = 27 + 4

x = 31

Final answer:

Explanation of summation notation using examples and patterns for different expressions.

Explanation:

Summation notation:

First sum: The sum is calculated using the formula: Σ(-8 + 5n) from n = 0 to 15.

Second sum: The sum can be expressed as Σ(-40n) from n = 0 to ∞ (infinity).

Third sum: The sum is Σ(-40n) from n = 0 to 15.

Fourth sum: The sum is given by Σ(-8 + 5n) from n = 0 to ∞.

Answer:

5 offices had fewer than 5 desks

Step-by-step explanation:

Clearly from the scatter plot we could see that 5 offices have lesser than 5 desks.

The number of desks are represented by the horizontal axis and the number of computers are represented by the vertical axis.

so by looking at the scatter plot we could see that the five points are before 5 on the horizontal axis i.e. we have to count all those points such that the desk are less than 5 i.e. ( when the desks are 0,1,2,3 and 4).

|X+4|=4

x = 4-4 = 0

|X+4|=-4 no solution since the lines are absolute value which would be a positive number

The question does not provide enough specifics to calculate the area of the rectangle. Generally, you find a rectangle's area by multiplying its length by its width.

Unfortunately, the question seems to have provided the potential answers for the area of the rectangle, but no specifics about the rectangle itself are given. Typically, you would find the area of a rectangle by multiplying the length by the width. For example, if a rectangle had a length of 10 units and a width of 7 units, you would calculate the area by multiplying together these two figures (10 units * 7 units), which equals 70 units².

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Answer:

Integers between (-∞, 4)

Step-by-step explanation:

Negative Integer is integers whose value is less than 0 i.e. -1, -2, -3, -4,.... so on.

The expression x - 4 will be negative if x is less than 4.

For Example, if we take integers greater than 4 or equal to 4 as the value of x then,

5 - 4 = +1 which is not a negative integer

4 - 4 = 0 which is again not a negative integer.

But, if we take x as less than 4 then we get,

2 - 4 = -2 i.e. negative integer

-3 - 4 = -7 i.e. also negative integer.

So, for all value of x which is less than 4, we will get a negative integer.

Answer:   Domain=   0[tex]\leq[/tex]x[tex]\leq[/tex]20

                Range=  2.8[tex]\leq[/tex]y[tex]\leq[/tex]72.8

Step-by-step explanation:

CREDIT:ANSWER ABOVE ME,HOPE THIS HELPS. Burrgh

Finding the equation of the line, it is found that the value of b is -1.

----------------------------

The equation of a line is given by:

[tex]y = mx + b[/tex]

In which:

----------------------------

[tex]y = -2x + b[/tex]

[tex]-3 = -2(1) + b[/tex]

[tex]b = -3 + 2 = -1[/tex]

The value of b is -1.

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By substituting the values x=2 and y=4 into the given equation, we get a result of 70 which does not match with any of the provided options.

The value of the expression 4x + y-2y−x when x = 2 and y = 4 can be determined by substituting these values into the expression. By doing so, we get:

4 * 2 + 4^2 * 4 - 2 = 8 + 64 - 2 = 70

So, the correct value is 70, which is not present in the provided options (a. 2 b. 3 c.4 d.6). Maybe there is a misunderstanding or typo in the question or options. The way it's presented right now, the correct answer would be none of the above.

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There are 20 twentieths in five halves. This conversion is achieved by first converting halves to tenths (5 halves = 10 tenths) and then further converting tenths to twentieths by doubling the numerator, resulting in 20 twentieths in total.

To determine how many twentieths are in five halves, we need to convert both fractions to a common denominator. Since twentieths have a denominator of 20 and halves have a denominator of 2, we can make them compatible by expressing halves as tenths (which have a denominator of 10) and then further converting them to twentieths.

First, we can rewrite five halves as ten tenths (5/2 = 10/10). Now, we need to express tenths as twentieths, which is done by doubling the numerator. So, 10 tenths are equivalent to 20 twentieths.

Therefore, there are 20 twentieths in five halves.

In summary, when converting from halves to twentieths, we first turn halves into tenths by multiplying by 10, and then we further convert tenths to twentieths by doubling the numerator. Thus, five halves equal 20 twentieths.]

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Answer:

Step-by-step explanation:

from the graph, y=0 when x=3

so that eliminates:

g(x) = (x + 3)3

g(x) = x3 + 3

g(x) = x3 − 3

ans is g(x) = (x-3)^3

Answer:

g(x) = (x - 3)3

Step-by-step explanation:

Compare to the parent function of f(x) = x3, the displayed graph is shifted to the "left" by 3 units so it is a translation in the x-direction.

The answer is g(x) = (x - 3)3

Let us say that x is the real height of the original hut, therefore we can establish the equation:

5 : x = 1.5 : 8

5 / x = 1.5 / 8

Solving for x:

x = 5 * 8 / 1.5

x = 40 / 1.5

x = 26.67 ft

There is about 1129 feet per second on the speed of sound in the stormy day.

Find the distance in feet:

1129 * 5 = 5645 ft

Change to miles: 1 mile is equal to 5280 foot

5645 / 5280 = 1 mile