Convert 2 grams into milligrams.

*Note: you must use these exact conversion factors to get this question right.
1 pound (lb) = 16 ounces (oz)
1 kilogram (kg) = 1000 grams (g)
1 ton (ton) = 2000 pounds (lb)
1 ounce (oz) = 28.35 grams (g)
1 gram (g) = 1000 milligrams (mg)
1 pound (lb) = 0.454 kilograms (kg)

Using proportions, it is found that:

a. The scale of the model is of 9:900.

b. The scale factor used was of 100.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the context of a situation using operations such as multiplication and division to find the unit rates.

The concept of proportion is followed in scale problems, as scale is the proportion of the drawn distance by the actual distance, as follows:

Scale = Drawn distance : Actual distance.

For the building, in this problem, we have that:

Applying it's formula, the scale is given by:

9 : 900

The ratio between the actual height and the drawn height is the scale factor, hence:

Scale factor = 900/9 = 100.

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Since TV and WY are parallel lines, the angles which are adjacent angles include the following: C. <VUX and <WXZ.

Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.

The vertical angles theorem is also referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other.

In Geometry, when two (2) parallel lines are cut by a transversal, the vertical angle and its adjacent angle that are formed are supplementary angles, which makes:

<VUX and <WXZ.

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Complete Question:

TV and WY are parallel lines. Which angles are adjacent angles?

<VUX and <TUX.

<VUX and <VUX.

<VUX and <WXZ.

<VUX and <YXZ.

0.8465 is the probability that the system operates if the probability that each component functions equals to 0.90, 0.99, and 0.95 respectively.

As the components are in a series system, this means that all the components have to function in order for the system to operate, and the failure of any one of the components to function will result in the system not operating.

Therefore, the probability for the system to operate is the probability that all the components c1, c2, and c3 function together

The probability of multiple events occurring together can be found by multiplying the probabilities of each event by one another.

Therefore;

Probability = 0.90 × 0.99 × 0.95

Probability = 0.84645

Rounding it off to 4 decimals as follows;

Probability = 0.84645 = 0.8465

Therefore, the probability that the system operates is calculated to be 0.8465.

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f(x) = x^2

write new equation after translation using vertex form;

(x+4)^2 - 2

simplify; convert to standard form

(x+4)(x+4) - 2

x^2 + 8x - 2

The function after translation is g(x) = x²+ 8x - 2.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Given:

f(x) = x²

Now, g is a translation left 4 units and down 2 units of the graph of f.

So, g(x)= (x+4)² - 2

Then, in the standard form

g(x) = (x+4)(x+4) - 2

g(x) = x²+ 8x - 2

Hence, the function is g(x) = x²+ 8x - 2.

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Using the definition of a midpoint and collinear points, the proof that shows that B is the midpoint of AC is explained below.

If three points are on a straight line, they are defined as being collinear points. That is, three points, A, B, and C are collinear points if they are on a straight line, and B is in the middle of points A and b.

When a segment is divided into two equal halves, the point that lies in the middle of the segment where the segment is cut into halves is called the midpoint of the line segment.

The proof that shows that B is the midpoint of line segment AC is shown below:

Statements                                  Reasons                                        

a. A, B, and C are collinear        a. Given

AB = BD, BD = BC                        

b. AB = BC                                   b. Substitution

c. AB ≅ BC                                   c. Definition of congruency

d. B is the midpoint                    d. AB ≅ BC

Thus, the proof above explains how point B is the midpoint of line segment AC in the image given.

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The amount of time it would take this object to hit the ground is 2.56 seconds.

A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable to an output variable.

The maximum value of a function can be defined as a point on the graph where the function reaches its highest point. This ultimately implies that, the maximum value of a function simply refers to its vertex on a graph.

The height (h) in meters, of this falling object is related to the time by the following function:

h = -4.9t² + d

Substituting the given parameters into the formula, we have;

0 = -4.9t² + 32

4.9t² = 32

Time, t² = 32/4.9

Time, t² = 6.53

Time, t = √6.53

Time, t = 2.56 seconds.

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Answer: x-intercept: 5/4

y-intercept: -5/3

Step-by-step explanation:

We can find the y-intercept by looking at the y = mx + b form, the y-intercept would be b in that form:

4x = 3y + 5

y = 4/3x - 5/3

Next, we plug x into that equation:

We can graph it, or find it mathematically:

Set 4/3x = 5/3

4/3x * 3/4 = 5/3 * 3/4

x = 5/4

When Rectangle A measures 9 inches by 3 inches and rectangle B is a scaled copy of Rectangle A, the possible dimensions will be:

From the information, Rectangle A measures 9 inches by 3 inches. Therefore, the ratio will be:

=Length / Width

= 9 / 3

= 3:1

Therefore, a scaled copy will have an equivalent ratio of 3:1.

This can be 3 inches by 1 inches and 6 inches by 2 inches. Their ratio is:

= 6/2 = 3:1.

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As the sample size becomes larger, the sampling distribution of the sample means approaches a sampling distribution.

Therefore, as the sample size becomes larger, the sampling distribution of the sample means approaches a sampling distribution.

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Answer: 1: 6√6 = 36

hope this helps, good luck!

Using Complete the Square method, we find out that [tex]x^{2} -5x+8[/tex] can be expressed in the form of [tex](x-a)^{2}+b[/tex] as [tex](x-\frac{5}{2}) ^{2} +\frac{7}{4}[/tex] where a and b are top-heavy fractions.

It is given to us that the expression is -

[tex]x^{2} -5x+8[/tex] ----(1)

We have to express it in the form of[tex](x-a)^{2}+b[/tex] where a and b are top-heavy fractions.

In order to achieve the required expression in the form of  [tex](x-a)^{2}+b[/tex] we have to use "Completing the Square" method.

The given expression from (1) is -

[tex]x^{2} -5x+8[/tex]

This expression is in the form of [tex]ax^{2} +bx+c[/tex]

Adding and subtracting [tex](b/2)^{2}[/tex] terms into the expression, we get

[tex]x^{2} -5x+[\frac{5}{2}] ^{2}-[\frac{5}{2}] ^{2}+8[/tex] -----(2)

Equation (2) can also be represented as -

[tex](x-\frac{5}{2}) ^{2} -[\frac{5}{2}] ^{2} +8[/tex]

[tex]= > (x-\frac{5}{2}) ^{2} -\frac{25}{4} +8\\= > (x-\frac{5}{2}) ^{2} +\frac{7}{4}[/tex]------- (3)

We see that equation (3) is in the form of [tex](x-a)^{2}+b[/tex].

So, we can derive that -

[tex]a=\frac{5}{2}[/tex]

and, [tex]b=\frac{7}{4}[/tex].

Thus, [tex]x^{2} -5x+8[/tex] can be expressed in the form of [tex](x-a)^{2}+b[/tex] through "Complete the Square" method as [tex](x-\frac{5}{2}) ^{2} +\frac{7}{4}[/tex] where a and b are top-heavy fractions.

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The expression representing height of kite from ground is Height = sin 50° × 40.

The kite, person holding the string and ground from where height is to be measured will form right angled triangle. We can use the sine function to find the height of kite from the ground. Writing the trigonometric relation -

sin theta = perpendicular ÷ hypotenuse

Keep the values in mentioned trigonometric relation to find the expression -

sin 50 = height ÷ 40

Height = sin 50° × 40

Finding the height using formed equation -

Height = 0.77 × 40

Performing multiplication

Height = 30.64 meters

Therefore, the expression to find the height of kite from ground is Height = sin 50° × 40.

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Answer:

yes

Step-by-step explanation:

Goggle

The number that Joseph is thinking of that is between 15 and 30 is 16.

The first step is to determine the squares between 15 and 30. The square of a number is the product of a number with itself. For example, 16 is a square number.

Squares between 15 and 30 = 16, 25

The next step is to determine the even number. An even number is a number that is perfectly divisible by 2. An example of an even number is 4.

The even number that is a square between 15 and 30 is 16.

The last step is to determine the composite number. A composite number is a number that has more than 2 factors.

Factors of 16 = 1, 2, 4, 8, 16

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Answer:

you'll need a graph to answer this

The Hillsdale is 8 km from the Kinsley's house

Let Kinsley's house be A

     Summerfield be B

     Hillsdale be C

The Kinsley's house due west of Summerfield be AB which is 6 km and The distance between Summerfield and Hillsdale is BC which is 10 km

Distance between Kinsley's house and Hillsdale can be calculated using Pythagoras' theorem, which states that the square of the hypotenuse is equal to the sum of the square of the other two sides.

        BC² = AB² + AC²

 We need AC, so let us rewrite this equation

        AC² = BC² - AB²

        AC²  =  10² - 6²

        AC² = 100 - 36

        AC² = 64

        AC = √64

        AC = 8 km

Therefore, Kinsley's house is due south of Hillsdale from 8 km

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A sandwich shop charges $20 for delivery of three turkey subs and $26 for delivery of four. There is no proportionality between the quantity of turkey subs delivered and the amount billed.

Given that,

A sandwich shop charges $20 for delivery of three turkey subs and $26 for delivery of four.

We have to find the relation ship between the quantity of turkey subs delivered and the amount billed.

The reciprocal of the ratio of subs to amount charges is

We get,

3/20 and 4/26

Since,  

3/20≠4/26

Therefore, There is no proportionality between the quantity of turkey subs delivered and the amount billed.

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Algebric equations which has the same solution as 4 - 2(x - 5) = (x - 19)/4 are all equations which has a solution of 55/9.

The equation given is,

4 - (2x-5) = (x - 19)/4

16 - 4(2x - 5) = (x - 19)

16 - 8x + 20 = x - 19

All terms having a variable x is taken to one side and the numerical values are kept on the other side.

16 + 20 + 19 = x + 8x

9x = 55

x = 55/9

Therefore, equation which has the same solution as 4 - 2(x - 5) = (x - 19)/4 are all equations which has a solution of 55/9.

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to get the slope of any straight line, we simply need two points off of it, let's use the ones from the picture below.

[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{(-4)}}}{\underset{run} {\underset{x_2}{0}-\underset{x_1}{(-3)}}} \implies \cfrac{4 +4}{0 +3}\implies {\Large \begin{array}{llll} \cfrac{8}{3} \end{array}}[/tex]

The perimeter is 70[tex]cm^{2}[/tex]. and x is 7

The complete circumference of a shape is referred to as its perimeter. It is the length of any geometric shape with a two-dimensional boundary or outline. Depending on their proportions, multiple figures can have equal perimeters. Think of a triangle built of an L-length wire as an example. If the length of each side is the same, the same wire can be used to create a square. Look at the illustration below, which shows the bounds of a rectangular park.

Given that :The perimeter is 70[tex]cm^{2}[/tex]. The sides are 3x-1, 3x, 4x+ 1.

3x -1 + 3x + 4x + 1 = 70

10x = 70

x = 7

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Answer:

$7.95 per visit

Step-by-step explanation:

To find the unit rate, divide dollars by number of visits.

79.5 ÷ 10 = 7.95

Answer:

It takes the kangaroo 7.5 minutes to travel 5 kilometers.

Step-by-step explanation:

It takes the kangaroo 7.5 minutes to travel 5 kilometers.

First step is to formulate

3×5/2

Second step is to determine the time by calculating the product or quotient

Time=3×5/2

Time=15/2

Time=7.5 minutes

Inconclusion how long it takes the kangaroo to travel 5 kilometers is 7.5 minutes.

Answer:

6 m

Step-by-step explanation:

First I want you to understand that distance = speed × time.Consider:

speed= 250. 300.

minutes= let it be x. x-1

distance= 250× x. 300(x-1)

=250x. 300x-300

Since distance remains the same ,250x=300x-300

hence. -50x=-300.

x= 6

The length of the race was 1500 meters.

What is Speed?

Speed is defined as the rate of change of distance travelled per unit time.

Given is an athlete who ran at a speed of 250 m/min. However, on the day of the race, he increased his average speed to 300 m/min and finished the race one minute faster than he had during training.

Assume that the length of the race is (x) meters. Suppose that the runner takes (t) minutes to to complete the race in training. Therefore, we can write -

x = 250t

During the race -

x = 300(t - 1)

Equating both, we get -

250t = 300(t - 1)

250t = 300t - 300

300 = 50t

t = 6 min

Then, the length of the race will be -  

x = 250 x 6 = 1500 meters

Therefore, the length of the race was 1500 meters.

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( 8.43 , 21.57) is ist a plausible 99% confidence interval for the new slope.

In algebra, what is an interval?

95% of confidence interval  = (10 ,20)

                                        x = 10 + 20 /2 = 15

margin of error = 20 - 10 /2 = 10/2 = 5

SE = Margin of error/2  = 5/1.96  = 2.551

99% confidence interval = x ±  z/2   * 3E

                                        =  15 ± 2.576 * 3E.

                                        = 15 ± 2.576 * 2551

                                         = 15 ± 6.571376

                                       = (15- 6.571376  ,  15 + 6.571376)

                                       = ( 8.43 , 21.57)

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The volume of air in liters that might inhale (and exhale) in 8.00 hours is 4060.8 litres.

For the given question;

The volume of air inhale (and exhale) once = 0.475 liters

Number of breathing in 1 minutes = 18 times.

Thus, the volume of air inhaled in 1 minutes is 0.47×18 = 8.46 litres.

This can be written as;

1 minutes ------- > 8.46 litres of air.

For calculating in 8 hours that is 8×60 = 480 minutes, multiply the both side by 480 in above equation;

1× 480 minutes ------- >  480×8.46 litres of air.

480 minutes --------> 4060.8 litres of air.

Therefore. the volume of air in liters that might inhale (and exhale) in 8.00 hours is 4060.8 litres.

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If 4 teenagers can clean in 6 hours, 1 teenager will take 4x more time

1 teenager will take 24 hours = k

No. of teenagers (p) is proportional to time (t):

p = k/t

3 = 24/t

t = 24/3 = 8 hours

So it will take 8 hours for 3 teenagers to clean a house.

8 hours

Step-by-step explanation:

teenagers. hours

4. 6

3. ?

it is actually direct multiplication where you multiply the upper numbers,4 × 6 ,then divide by the lower value, 3. This gives 24 /3 which gives you 8 .

Answer:

15

Step-by-step explanation:

B*3

5*3

15

Answer:

Step-by-step explanation: if b= 5 the the equation will be (5)^3 you multiply and get 15

The number of adults, high school​ students, and children not yet in high school attended this​ year are respectively; 70, 100, 120

We are told that a total of 290 people attended the high school play.

If x represents number of adults, y represents number of high school students and z represents number of children, then we have;

x +  y +  z =  290  ----  (1)

The admission prices were $14 for​ adults, $7 for high school​ students, and $3 for children not yet in high school. The ticket sales totaled $2040 . Thus;

14x + 7y + 3z = 2040  ----  (2)

The principal suggested that next year they raise prices to $17 for​ adults, $8 for high school​ students, and $4 for children not yet in high school. Total cost of $2470. Thus;

17x + 8y + 4z = 2470  ----  (3)

Solving the three equations simultaneously gives;

x = 70, y = 100, z = 120

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The value of the product -8/9 . 5/6 is -20/27. Option C

A fraction can simply be defined as the part of a whole set or element.

The several types of fractions are listed as;

Examples of proper fractions: 3/4, 5/6

Examples of improper fractions: 4/3 , 8/7

Examples of mixed fractions:  2 1/2 , 3 4/5

Examples of simple fractions: 1/2 , 1/3

Given the expression:

-8/9 . 5/6

To determine the product of the fractions, we need to follow the steps

Multiply the numerators

-40/ 9 × 6

Now, multiply the denominators

-40/57

Reduce to simplest forms by using the divisor 2, we have;

-20/ 27

Hence, the value is -20/27

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If the lengths of a certain species of crocodiles are normally distributed with a mean of 12.5 ft and a standard deviation of 2.1 ft. the probability that a randomly selected crocodile is more than 12 feet long is  0.5941.

Given :

Mean = 12.5 ft

Standard deviation = 2 .1 ft

Randomly selected crocodile = 12 ft

Hence,

First find Z value, Z = (12 – 12.5) / 2.1

Z =  - 0.5 / 2. 1

Z = - 0.238

Using Z table, we will get the probability :

Probability =  1 – 0.4059

Probability = 0.5941

Therefore we can conclude that the probability is 0.5941.

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