The diameter of a circle is 24 cm. Find its area to the nearest whole number.

The image of (3, -3) is (1, -1).

The image of (-4, 7) is (-12, 21).

The image of (3, 3) after a dilation by a scale factor of 5 is (15, 15).

The image of (-8,-8) is (-2, -2).

The scale factor is the size by which the shape is enlarged or reduced. It is used to increase the size of shapes like circles, triangles, squares, rectangles, etc.

To find the image of (3, -3) after a dilation by a scale factor of 1/3 centered at the origin, multiply the coordinate by 1/3. That is:

image = (1, -1)

For image of (-4, 7) after a dilation by a scale factor of 3, multiply the coordinate by 3:

image = (-12, 21)

For the image of (3, 3) after a dilation by a scale factor of 5, multiply the coordinate by 5:

image = (15, 15)

For the image of (-8,-8) after a dilation by a scale factor of 1/4, multiply the coordinate by 1/4:

image = (-2, -2)

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Complete Question

What is the image of (3, -3) after a dilation by a scale factor of 1/3 centered at the origin?

What is the image of (-8,-8) after a dilation by a scale factor of 1/4 centered at the origin?

Answer:

Goku died you I just started watching

The population of the bees when it was first measured was 500 bees

The bees are  growing by the same factor each week. The answer is yes

At the fist time the bees where measured, we have to measure from the origin of the graph.

The first point on the graph is at the population of 500

2. To get if the growth is by the same factor, we have to observe how the growth is taking place weekly

In the first week, it grew from 500 to 1000

1000 / 500 = 2

In the second week, the growth is from 2000 to 1000

2000 / 1000 = 2

In the third week. the growth is from 2000 to 4000

4000 / 2000 = 2

Hence there is a growth constant of 2 across the weeks

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[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{1}~,~\stackrel{y_1}{5})\qquad B(\stackrel{x_2}{4}~,~\stackrel{y_2}{2})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AB=\sqrt{(~~4 - 1~~)^2 + (~~2 - 5~~)^2} \implies \implies AB=\sqrt{( 3 )^2 + ( -3 )^2} \\\\\\ AB=\sqrt{ 9 + 9 } \implies AB=\sqrt{ 18 }\implies AB\approx 4.24[/tex]

now, we could do the same thing for CD,  however, notice, the y-coordinates are the same, meaning is just a horizontal line, we can just count the units off the grid, from 2 to 6, 4 units.

The measure of the major arc along the perimeter of the circle between Stanley and Frank is 264°.

A circle's arc, or circumference, is a section of the circle. The difference between an arc length and an arc measure is the angle the arc creates with the circle's center. It is possible to measure this arc in radians or degrees.

Given:

Fifteen friends are playing Duck, Duck, and Goose.

The friends sit equally spaced in a circle.

So, 360/15 = 24° is the angle measure of an arc.

There are three people between Stanley and Frank.

That means there are 11 people between Stanley and Frank.

So, 11 x 24 = 264° is the measure of the major arc.

And the perimeter of the major arc is 264°

Therefore, the perimeter of the major arc is 264°

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Using the conversion formula of converting inches to centimeters, we get 1.5 inch is 3.81 centimeters.

To convert 1.5 inches to centimeters, we can use the formula:

1 inch = 2.54 centimeters

So, 1.5 inches = 1.5 x 2.54 = 3.81 centimeters

Therefore, 1.5 inches is equal to 3.81 centimeters.

The conversion factor between inches and centimeters is based on the definition of the inch and centimeter units. The inch is a unit of length in the imperial system of measurement, while the centimeter is a unit of length in the metric system. The conversion factor between the two systems is based on the definition of the meter, which is the primary unit of length in the metric system. In summary, 1.5 inches is equal to 3.81 centimeters, and this conversion is based on the relationship between the inch and centimeter units, as well as the definition of the meter as the primary unit of length in the metric system.

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The equation of the line that has a slope of -4 and passes through the point (4, -1) is y = -4x + 15.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of a line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

Given:
An equation,

y = x/4 - 2.

The slope of the line that is perpendicular to the line y = x/4 - 2 is,

= -(1/1/4)

= -4.

The equation of the line that has a slope of -4 and passes through the point (4, -1) is,

y + 1 = -4(x - 4)

y = -4x +16 -1

y = -4x + 15

Therefore, the equation is y = -4x + 15.

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Answer:

Step-by-step explanation:

the volume of top triangular prism :

(16x21)/2x15=2520 yd^3

the volume of bottom:

22x16x15=5280 yd^3

so the volume of the figure:

2520+5280=7800 yd^3

Two different values are possible for the length of Rectangle jklm.

When we say that two rectangles are congruent, we indicate that their sides are equal. The rectangles' lengths and widths have to be comparable. It's feasible that jm will be 4 or 7 inches long given that one rectangle has dimensions of 4 and 7. Two lengths are conceivable as the solution. The length and breadth make up the rectangle shape. A rectangle has four sides, and its opposing sides are all the same length. You are given the perimeter of a rectangle. The perimeter, as you know, is the total distance along the outside of the rectangle.

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The total volume of all the tents is 1920 cubic feet

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

Number of tents = 6

Base area of the tents = 96 square ft

Height of the tent = 10 ft

The total volume of all the tents is calculated as

Volume = Number of tents * Base area of the tents * Height of the tent/3

Substitute the known values in the above equation, so, we have the following representation

Volume = 6 * 96 * 10/3

Evaluate

Volume = 1920

Hence, the volume is 1920 cubic feet

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The model [tex]p = 200.3^d[/tex] satisfies the statement, A population of cells starts at 200 and triples every day.

The formula for exponential growth is [tex]y = y_0.e^{(kt)}.[/tex]

The formula for exponential decay is [tex]y = y_0.e^{(-kt)}.[/tex]

Given, A population of cells starts at 200 and triples every day.

Where 'p' is the number of cells and 'd' is the number of days.

The situation is represented by [tex]p = 200.3^d[/tex].

Now, Three times 200 is 600 and Nine times 200 is 1800.

At d = 1.

[tex]p = 200.3^1[/tex].

[tex]p = 600[/tex].

And,

At, d = 2.

[tex]p = 200.3^2[/tex].

[tex]p = 1800[/tex].

So, The model satisfies the statement and it is true.

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Answer:

approximate number

Step-by-step explanation:

Hi this a great question. A number close to an exact value is an approximate number. That is a number that is close but not exactly equal to another number. It is the counterpart to exact numbers. There is no uncertainty in an exact number, while the definition of an approximate number is one in which uncertainty exists.

The measure of the angles given in the rhombus are given as follows:

A rhombus is a type of parallelogram with the following properties:

To obtain the following, therefore, here is the premise behind each assertion:

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According to the information, the line plots of points 6 and 7 have several values that are repeated more than once as shown in the graphs.

To make a line plot we must identify the values that we must locate on the number line. Once we know the values we must place a point or symbol above the corresponding numerical value. For each number we must put a point, so we can count the frequency of different values.

Based on the above, we can infer that the line plots of points 6 and 7 would look like this:

attached images

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Answer: Can't help I tried to figure it out, but it was wrong.

Step-by-step explanation: I'm sorry.

Answer:

There is exactly one solution: (1, 2).

Step-by-step explanation:

For this, it's already in slope intercept form so all you have to do is graph the two and see at what point do these two lines cross, which is (1, 2).

Hope this helps!

The equation of line is y= -1/4x+ 6.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

passes through the point (4, 5);

slope = -1/4

Using the slope intercept form

y = mx + b

y= -1/4x + b

As the point passes through (4, 5) then

5 = -1/4 (4) + b

5 + 1 = b

b= 6

So, the equation of line is y= -1/4x+ 6.

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Answer:

Liberty Hill

Step-by-step explanation:

To determine which hill is the steepest, calculate the absolute value of m for each hill and compare them:

|m|= |Slope (or gradient)|

    = |[tex]\frac{VerticalDistance}{HotizontalDistance}[/tex]|

The hill with the greatest absolute value of m is the steepest:

|[tex]m_{Dixie} = |\frac{40}{80}|[/tex]

            = 0.5

[tex]|m_{Bell}| =|\frac{20}{80}|[/tex]

          = 0.25

[tex]|m_{Liberty}| = |\frac{60}{80}|[/tex]

               = 0.75

Liberty Hill has the greatest absolute value of m of 0.75, therefore it is the steepest

Answer:

Step-by-step explanation:i cant see words need closer view

It is false that the probability of the union of two events can be more than the probability of the intersection of the two events occurring.

This is because when two events intersect, the intersection of the two events refers to the occurrence of both events at the same time, while the union of the two events refers to the occurrence of either event or both events at the same time. therefore, the union of two events can have a higher probability of occurring than the intersection of two events since the union includes the possibility of both events occurring, while the intersection does not.

For example, let us consider two events, A and B. Event A has a probability of 0.3, and event B has a probability of 0.4. The probability of the intersection of these two events is 0.12(0.3 X 0.4) while the probability of the union of these two events is 0.7(0.3+0.4-0.12). As seen in this example, the probability of the union of two events (0.7) is greater than the probability of the interaction of two events(0.12)

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The bedroom has a surface space of 17.4225 m² and the closet has a surface area of 2.5875 m².

In mathematics, the area is a measure of the amount of two-dimensional space taken up by a shape. It is a scalar quantity, meaning it has only magnitude and no direction. The unit of measurement used for area depends on the units used for the length of the sides of the shape. Common units used to measure area include square centimeters, square meters, square inches, and square feet. The formula for finding the area of a shape depends on the specific type of shape. For example, the area of a rectangle is given by the formula A = lw, where l is the length and w is the width of the rectangle. The area of a triangle is given by the formula A = (1/2)*bh, where b is the base and h is the height of the triangle.

Here,

area of bedroom=l*w

l=5.05 m

w=3.45 m

area of bedroom=5.05*3.45

=17.4225 m²

area of closet=l*w

l=0.75 m

w=3.45 m

area=0.75*3.45

=2.5875 m²

The area of the bedroom is 17.4225 m² and that of closet is 2.5875 m².

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1 cm is defined as 1/100 of a meter. One foot is defined as 1/3 of a yard or 12 inches in length. We know that, 1 inch = 2.54 cm and therefore, 23.5 centimeter = 9.252 inches

Centimeters :

The centimeter (cm) is the fractional part of the meter, the international standard unit of length, and equals approximately 39.37 inches. It is defined as 1/100 of a meter.

The centimeter is based on the SI unit of measurement and is equal to one hundredth of a meter as indicated by the prefix "centi". The metric prefix ranges from 10-18 to 1018 in decimal, and the base (metric in this case) has no prefix and a modulus of 1. Exploring the most commonly used metric prefixes such as kilogram, mega, giga, tera, centi, milli, micro, and nano can be useful for quickly navigating metric units.

Inch:

Inches is a unit of length or distance in several systems of measurement, including traditional American units and British Imperial units. An inch is defined as 1/12 of a foot, so 1/36 of a yard. By modern definition, 1 inch equals 25 exactly 4 mm.

The term "inch" comes from the Latin unit "uncial", equivalent to "1/12" in Roman terms. There were several standards for inches in the past and the current definition is based on international yards. One of the earliest definitions of an inch was based on a barley grain, where an inch equals the length of three dry round grains of barley laid end to end. Another version of the inch is believed to be derived from the width of a person's thumb, where length was obtained by averaging the widths of three thumbs (small, medium, and thumb).

By multiplying  the value in centimeters by the conversion factor 0.3937007874021.

So, 23.5 centimeters = 23.5 × 0.39370078740213

                                   = 9.25196850395 inches.

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So the x-coordinates of the points where the proton crosses the x-axis are x = ±√(5).

In mathematics, a function is a relation between a set of inputs (the domain) and a set of possible outputs (the codomain or range) with the property that each input is related to exactly one output. In other words, a function is a rule or a mapping that assigns a unique output value to each input value. Functions can be represented in various ways, such as equations, tables, graphs, or diagrams. They are used to describe and model a wide range of phenomena in mathematics and other fields, such as physics, engineering, economics, and social sciences. Functions are often denoted by symbols such as "f(x)", "g(x)", or "h(t)" and can be composed or combined to form new functions. They can also be classified according to various properties, such as whether they are continuous, differentiable, invertible, or periodic. In summary, in mathematics, a function is a relation between a set of inputs and a set of possible outputs that assigns a unique output value to each input value.

Here,

To find the x-coordinates of the points where the proton crosses the x-axis, we need to find the roots of the function f(x) = x⁴ - 2x² - 15. These are the values of x that make the function equal to zero, which correspond to the points where the proton crosses the x-axis.

To find the roots, we can use the factoring method or the quadratic formula. In this case, we can factor the function as follows:

f(x) = x⁴ - 2x² - 15

= (x² - 5)(x² + 3)

Setting each factor equal to zero and solving for x, we get:

x² - 5 = 0 or x² + 3 = 0

Solving for x in each equation, we get:

x = ±√(5) or x = ±i*√(3)

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The exponential equation is N ( t ) = a ( b )^t , where a = 50 and b = 3

The exponential growth or decay formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

x ( t ) is the value at time t

x₀ is the initial value at time t = 0.

r is the growth rate when r>0 or decay rate when r<0, in percent

t is the time in discrete intervals and selected time units

Given data ,

Let the number of bacteria in the culture at a given time be N ( t )

The culture increases by a factor of 2

So , the value of r = 200 % , r = 2

Now , when t = 0 , the number of bacteria in the culture N ( 0 ) = 50

So , the exponential equation is

N ( t ) = N ( 0 ) ( 1 + r )^t

Substituting the values in the equation , we get

N ( t ) = 50 ( 1 + 2 )^t

N ( t ) = 50 ( 3 )^t

On simplifying the equation , we get

N ( t ) = a ( b )^t , where a = 50 and b = 3

Hence , the exponential equation is N ( t ) = 50 ( 3 )^t

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The numerical values of x and y are 14 and 54 respectively.

The sum of angles on a straight line is equal to 180 degrees.

From the diagram, angle (9x + 2)° and angle (5x - 18)° are on a straight line,

Since the sum of angles on a straight line is equal to 180 degrees.

(9x + 2)° + (5x - 18)° = 180°

Solve for x

9x + 2 + 5x - 18 = 180

14x - 16 = 180

14x = 180 + 16

14x = 196

x = 196/14

x = 14

Now, angle (9x + 2)° and angle (2y + 20)° are corresponding angles.

Since corresponding angles are congruent.

(9x + 2)° = (2y + 20)°

Plug in x = 14 and solve for y

9( 14 ) + 2 = 2y + 20

126 + 2 = 2y + 20

128 = 2y + 20

128 - 20 = 2y

108 = 2y

2y = 108

y = 108/2

y = 54

Therefore, the value of x is 14 and y is 54.

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The second and fourth graphs represent linear functions.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

To determine which of the given graphs represents a linear function, we need to check whether the graph is a straight line.

The first graph passes through the points (-3, 0), (-1, -4), and (1, 0). We can plot these points and see that they do not lie in a straight line. Therefore, the first graph does not represent a linear function.

The second graph passes through the points (-4, 0), (0, -4), (4, 0), and (0, 4). We can plot these points and see that they do lie on a straight line. Therefore, the second graph represents a linear function.

The third graph passes through the points (-4, -2), (-4, -1), and (-4, 0). We can plot these points and see that they lie on a vertical line. Therefore, the third graph does not represent a linear function.

The fourth graph passes through the points (-4, 0), (-2, -1), and (0, -2). We can plot these points and see that they do lie on a straight line. Therefore, the fourth graph represents a linear function.

Therefore, the second and fourth graphs represent linear functions.

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Answer: It is the second one

Step-by-step explanation:

Because It makes the most sense

The plan that costs less if Hans makes 300 minutes of long distance calls is Plan A by $ 4.

The number of long distance minutes till the plans cost the same is 350 minutes.

If the time spent on long distance calls is more than this amount, the plan that costs less is Plan B.

The cost per plan can be seen on the graph. At 300 minutes of long distance calls, Plan A costs $ 24 and plan B costs $ 28 so the cheaper plan is Plan A by :

= 28 - 24

= $ 4

The number of minutes till they cost the same is 350 minutes which is where they intercept and after this, Plan B will cost less.

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The number of participants that shopped in:

- BJ's Wholesale Club only: 32
- Costco only: 22
- Sam's Club only: 27
- Exactly one of these warehouse stores: 81
- BJ's Wholesale Club and Costco: 11
- BJ's Wholesale Club and Sam's Club: 10
- Sam's Club and Costco: 7
- None of these warehouse stores: 17

To answer this question, we can use a Venn diagram to visualize the data and find the number of participants that shopped in each category.

First, we'll create a venn diagram with three circles, one for each store (BJ's Wholesale Club, Sam's Club, and Costco). Then, we'll fill in the data from the question.

1. Start with the center of the venn diagram, where all three circles overlap. This represents the 5 participants who shopped in all three stores.
2. Next, fill in the overlapping sections between two circles. These represent the participants who shopped in two of the stores, but not the third.
- BJ's Wholesale Club and Sam's Club: 15 - 5 = 10
- BJ's Wholesale Club and Costco: 16 - 5 = 11
- Sam's Club and Costco: 12 - 5 = 7
3. Finally, fill in the sections that do not overlap with any other circles. These represent the participants who shopped in only one of the stores.
- BJ's Wholesale Club only: 58 - 10 - 11 - 5 = 32
- Sam's Club only: 49 - 10 - 7 - 5 = 27
- Costco only: 45 - 11 - 7 - 5 = 22

Now, we can use the venn diagram to answer the questions:
- BJ's Wholesale Club only: 32
- Costco only: 22
- Sam's Club only: 27
- Exactly one of these warehouse stores: 32 + 22 + 27 = 81
- BJ's Wholesale Club and Costco: 11
- BJ's Wholesale Club and Sam's Club: 10
- Sam's Club and Costco: 7
- None of these warehouse stores: 17

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