Although it is much larger in reality, when we
see Saturn from Earth, it looks like it has a
diameter of 20 μm. Through a telescope, the
diameter looks 9,000 um long. What
magnification scale was used?

Answer:

4x^3 (3)_/x + 10x^3 (3)_/x

Step-by-step explanation:

First lets solve the first term

When you multiply exponents you add them, so x^10 can be split into:

x^3 * x^3 * x^3 * x^1

We can then take it out.

4x^3 (3)_/x

Then for the other part we can also factor it.

2*2*2 is 8 so we can take that out and multiply it by 5 =10

You can keep x in there since you can factor it into smaller pieces.

The final answer you get when you add all of it together is :
4x^3 (3)_/x + 10x^3 (3)_/x

Answer:

13,-13 are the factors

The steps are

x²-13²=(x+13)*(x-13)

so the factors are 13,-13

calculate the total of the bills= 300+200+225+275 =1000

the average monthly bill= 1000/12 = 83.333

Total =0

for i in range(4):

  bill = float(input("Enter bill for quarter " + str (i+1) + ": "))

  total += bill

average = total / (4 * 3)

if average > 75:

  print("Average monthly bill is $" + str(average) + ". Too much water is being used")

if 25 <= average < 75:

  print("Average monthly bill is $" + str(average) + ". A typical amount of water is being used")

if average < 25:

  print("Average monthly bill is $" + str(average) + ". Thank you for conserving water")

calculate the total of the bills= 300+200+225+275 =1000

the average monthly bill= 1000/12 = 83.333

Total =0

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The margin of error at 90% confidence and its interpretation is 0.085. 90% confident that the true proportion of sophomores who will attend Homecoming is within 0.085 of the sample proportion.

The margin of error is defined as a term used in statistics to find the confidence interval. It is denoted by E.

Given, random sample of 92 .

The formula for margin of error is;

[tex]E = z(\sqrt{(p(1 - p)/n} )[/tex]

The parameters are given as;

Sample size; n = 92

Sample of success; x = 51

Sample proportion:

p = 51/92

= 0.554

z at 90% CL = 1.645

Thus;

[tex]E = 1.645(\sqrt{(0.554(1 - 0.554)/92} )[/tex]

[tex]E = 0.085[/tex]

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Answer:

See picture below

Step-by-step explanation:

Answer:

7. 2^-5= 1/2^5= 1/32

8. (4/5)^-3= (5/4)^3=125/64

9. 8^-4/8^-7=8^-4+(-7)=8^11=216

10. (1/3)^-2 x (1/3)^2=(1/3)^-2+2=(1/3)^0=1

Answer:

13

Step-by-step explanation:

Area of triangle = 0.5 × base × height

= 0.5 × 6 × 13

= 39

Area of parallelogram = 4 × Area of triangle

Note - Area of parallelogram = base × perpendicular height

Hence,

Base × perpendicular height = 4 × 39

12 × H = 156

H = 156 ÷ 12

= 13

Answer = 13

Answer:

h = 13 cm

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

here b = 6 and h = 13 , then

A = [tex]\frac{1}{2}[/tex] × 6 × 13 = 3 × 13 = 39 cm²

Then the area (A) of the parallelogram = 4 × 39 = 156 cm²

the area (A) of the parallelogram is calculated as

A = bh ( b is the base and h the height )

here b = 12 , then

12h = 156 ( divide both sides by 12 )

h = 13

Answer: A. [tex]3\sqrt{5}[/tex]

B. l=[tex]6\sqrt{5}[/tex], w=[tex]3\sqrt{5}[/tex]

Step-by-step explanation:

A. A=l*w

l=2w

A=2w*w

90=2w*w

w*w=45

w=[tex]\sqrt{45}[/tex]

w=[tex]\sqrt{9*5}[/tex]

w=[tex]3\sqrt{5}[/tex] ==> Square length and the rectangle width

B. 90=l*w

90=l*[tex]3\sqrt{5}[/tex]

30=l[tex]\sqrt{5}[/tex]

l=[tex]\frac{30}{\sqrt{5} }[/tex]

l=[tex]\frac{30\sqrt{5} }{5}[/tex]

l=[tex]6\sqrt{5}[/tex], w=[tex]3\sqrt{5}[/tex]

The correct form of the expression is 5(2x - 2)

It should be noted that the expression that is given is illustrated as:

3x-5-2x + 9x.

To solve this, collect the like terms

3x - 2x + 9x - 5

= 10x - 5

= 5(2x - 1)

The correct form of the expression is 5(2x - 1)

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Answer:

2.65 gallons

Step-by-step explanation:

He originally had 4 gallons and he used 1.05 gallons.

4 - 1.05 = 2.95

He then used another three-tenths to take another friend home.

Three-tenths is equal to 3/10 or 30/100 or 0.30

2.95 - 0.30 = 2.65 gallons

Yes, figure B is a scale copy of figure A.

As per the question statement and its reference diagram attached thereby, we are provided with two geometrical figures of same shape but different sizes.

We are required to determine if figure B is a scale copy of figure A or not.

To solve this question, we need to carefully compare the lengths of the corresponding sides from both the figures.

We can clearly see that, the dimension of every side of figure B is twice that of the corresponding side of Figure A, i.e.,

[tex](1*2)=2\\(2*2)=4\\(3*2)=6\\(4*2)=8[/tex]

Hence, it is proved that figure B is a scale copy of figure A.

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The standard form for given values is 12416.

A number has two form . First is standard form and another is expended form of numbers.

It is a form in which we write number as a whole without describing the places for the numbers.

The numbers such as 456, 17817, 9009, 32 etc all are the standard form of the numbers.

In the case of expended form we generally write number with its describe places of value or with the plus (+) symbol between them.

For example, 16 ones 24 tens 1 hundred is the expended form of numbers.

In the given question the form given is :

16 ones 24 tens 1 hundred

so, we have to place 16 at ones place , 24 at tens place and 1 at hunderedth place value .

Therefore, the standard form becomes : 12416.

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The complete question is:

Convert to standard form

16 ones 24 tens 1 hundred

Answer:

[tex]\frac{10}{3}[/tex] or 3.3333.....

Hope this helps.

Step-by-step explanation:

( negative ) * ( negative ) = ( positive )

5 *  [tex]\frac{2}{3}[/tex] = [tex]\frac{5*2}{3}[/tex] = [tex]\frac{10}{3}[/tex]

Each side of the triangle should contain four numbers whose sum is 28.

3+5+9+11=28

3+10+8+7=28

11+6+9+7=28

The pain of numbers that can be used for A and B is [5,9] The pain of numbers that can be used for C and D is [10,8] and the pain of numbers that can be used for E and f is [6,4].

The hypotenuse of a right triangle is its longest side; its "opposite" side is the one that faces the angle in question; and its "adjacent" side is the one that faces it. We use special terminology to define the sides of right triangles.

We use special terminology to define the sides of right triangles.

The side opposite the right angle is always the hypotenuse of a right triangle. It is the longest side in a right triangle.

The opposing and neighboring sides are the other two sides. The labels on these sides relate to an angle.

One side is across from another at a particular angle.

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The volume of the square frustrum, the volume of the pyramid and the volume of the obelisc are 1018791.667 ft³, 22019.625 ft³ and 1040811.292 ft³, respectively.

In this problem we must determine the volume of a obelisc, which is equal to the sum of the volumes of a square frustrum and a pyramid with a square base. First, sum the volumes of the frustrum and the pyramid:

V' = (1 / 3) · 500 · (55² + 55 · 34.5 + 34.5²)

V' = 1018791.667 ft³

V'' = (1 / 3) · (34.5)² · 55.5

V'' = 22019.625 ft³

Second, calculate the volume of the obelisc:

V = V' + V''

V = 1018791.667 ft³ + 22019.625 ft³

V = 1040811.292 ft³

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Answer:

1.7 kilograms

Step-by-step explanation:

750 + 450 + 0.5kg ( 1kg = 1000) so 0.5 would be 500g.

=1,700g (1.7kg) :)

Answer:

the tetrahedron, octahedron and icosahedron

Answer:

tetrahedron, octahedron, icosahedron

Answer:

4/45

Step-by-step explanation:

8 - 4

9   5

=  8 × 5 - 4 × 9

       9 × 5   5 × 9

=  40 - 36

       45   45

=  40 – 36

            45

=  4

      45

8/9 - 4/5

= 4/45

The approximation of -8 plus the square root of 20 is given by:

-3.5.

To round a number to the nearest tenth, it will have only one decimal digit, and the rule is as follows:

The square root of 20 is given by:

sqrt(20) = 4.47.

7 > 5, hence, rounded to the nearest tenth:

sqrt(20) = 4.5.

Then:

-8 + 4.5 = -3.5.

Which is the approximation.

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The percent of the increase in the number of yards Nicole swam will be 33.33%.

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Nicole swam 1,200 yards during the swim rookie minicamp before the break. She swam 1,600 yards after the break.

Then the percent of the increase in the number of yards Nicole swam will be

P = [(1600 - 1200) / 1200] x 100

P = (400 / 1200) x 100

P = 0.3333 x 100

P = 33.33%

The percent of the increase in the number of yards Nicole swam will be 33.33%.

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Answer:

3d-4

Step-by-step Explanation:

2d+1+d-5 Combine like terms 2d and d together which is 3d. That leaves you with 1-5 which is -4. so then you end up with 3d-4 as your answer.

The correct representation of x + 5 using algebra tiles is one green rectangle box and one small yellow box.

Algebra tiles are the tiles or square or rectangular boxes which are use to represent the polynomial expression whether of linear , monomial or quadratic.

There are three types of algebra tiles :

All of these tiles has different color to represent positive and negative value :

Square Type                      Positive color                      Negative Color

Small squares                     Yellow                                 Red

Rectangles                          Green                                  Red

Large Squares                     Blue                                    Red

For the given question, Expression is x + 5

that means, there is one Green rectangle and one Yellow small square.

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Answer:

A. 25°

Step-by-step explanation:

In triangle ABC:

<A + <B + <C = 180°

=> 45° + (2x - 15)° + 4x° = 180°

=> 6x° + 30° = 180°

=> 6x° = 150°

=> x° = 25°

Choose A.25°

Answer:

A. 25 degrees

x = 20

2(20) - 15 = 25 degrees

In the given picture there is a graph and we have to find out is that graph is one to one or not.

It is a one to one graph.

In the graph there is line.

To know is the line is one to one or not we have to check 1st that the line is a function or not.

To check the line is function or not we have to do by vertical line test.

Graphically, the vertical line test is a way to determine if a line is a function or not.

To perform the vertical line test, we pass the vertical lines arrows the graph and if it does not intersect the graph more then one point it passes the vertical line then it can say as a function.

In the given figure1 we can see the vertical lines does not touch the line in the graph more then one point so it is a function.

Now, we know the line is a function so now we have to check if the line is one to one or not.

To check the line is one to one or not we have to do by horizontal line test.

Graphically, the horizontal line test is a way to determine if a line is a one to one or not.

To perform the horizontal line test, we pass the horizontal lines arrows the graph and if it does not intersect the graph more then one point it passes the horizontal line then it can say as a one to one function.

In the given figure2 we can see the horizontal lines does not touch the line in the graph more then one point so it is a one to one function.

Therefore, The graph is a one to one function.

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Answer:

=($25×5)+($125×5)

=$125+$625

=$750

A local maximum occurs over the interval (-2,0).

A local minimum occurs over the interval (0,2).

If the graph of the function increases first and decreases after a particular point, then the function acquires a local maximum at that point.

Similarly, if the graph of the function decreases first and then increases after a point, then the function acquires a local minimum at that point.  

Here the given x and f(x) values for the continuous function f(x) are:

x        f(x)

-3       -16

-2        -1

-1         2

0         -1

1          -4

2          -1

As we can see by examining the table values, the function is increasing in the intervals (-3,2) and (-2,-1).The function acquires value f(x) = 2 at x = -1 and then it starts to decrease. So this value f(x) = 2 is the local maximum and is acquired on the interval (-2,0).

The graph is then decreasing from x = -1 to x = 1. The function has the value f(x) = -4 at x = 1. Then the function starts to increase from x = 1 to x = 2. So f(x) = -4 is the local minimum of the function and is acquired on the interval (0,2).

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Answer:

3

Step-by-step explanation:

y=mx+b

m is the slope