If a spacecraft was parked on Venus and needed to make a flight to Jupiter, how far would it need to travel? (Assume both planets are aligned with the sun and are on the same side of the sun.) Show your work and provide your answer in scientific notation.

Two hundred percent (200%) is equivalent to whole number 2.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

We have the percentage 200%.

Converting percentage to whole number,

200/100,

= 2

2 is equivalent to 200%.

Therefore, 2 is equivalent to 200%.

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Final answer:

To do twice of p minus q, multiply p by 2 and then subtract q. For example, if p is 5 and q is 3, the result would be 7 (since 2*5 - 3 equals 10 - 3 equals 7).

Explanation:

To calculate twice of p minus q, first you need to understand that 'twice of p' means 2 times p, which is written as 2p. Then, you subtract q from this result. The algebraic expression for this calculation is 2p - q.

Here is an example, if p equals 5 and q equals 3, then twice of p minus q would be calculated as follows:

Twice of p is 2 times 5, which equals 10.

Then, subtract q (which is 3) from this result: 10 - 3 equals 7.

Therefore, twice of p minus q would be 7 when p is 5 and q is 3.

The percent of change from 14 inches to 26 inches is approximately 85.71 percent, calculated by using the formula for percent of change which is [(change in quantity)/(original quantity)] × 100.

To find the percent of change from one value to another, you apply the formula [(change in quantity)/(original quantity)] × 100. In this instance, the original quantity is 14 inches and it changed to 26 inches. Therefore, the change in quantity is 26 - 14 = 12 inches.

Now, substitute these values into the formula: (12/14) × 100 = 85.71% (approximately). This means the change from 14 inches to 26 inches represents an approximately 85.71 percent increase.

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The average miles per gallon is given by the equation A = 65 miles per gallon

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the average miles per gallon be represented as A

Now , the equation will be

The total distance moped = 78 miles

The amount of gallons of gas for 78 miles = 1.2 gallons

Now , average miles per gallon = total distance moped / amount of gallons of gas for 78 miles

Substituting the values in the equation , we get

The average miles per gallon A = 78 / 1.2

The average miles per gallon A = 65 miles per gallon

Therefore , the value of A is 65 miles per gallon

Hence , the equation is A = 65 miles per gallon

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Linear function f with f(-3) = 1 and f(13) = 5 is given by   [tex]\rm f(x) = \dfrac{1}{4}x + \dfrac{7}{4}[/tex]  and this can be determined by using the given data.

Given :

f(-3) = 1 and f(13) = 5.

The generalised linear function is given by:

f(x)  = ax + b   --- (1)

Now, it is given that (f(-3) = 1) that means at (x = -3) the above function is equal to 1.

f(-3) = a(-3) + b

    1  = -3a + b

b = 1 + 3a   ---- (2)

Now, it is also given that (f(13) = 5) that means at (x = 13) the function (f(x) = ax + b) is equal to 5.

f(13) = 13a + b

5 = 13a + b

Now, put the value of 'b' in the above equation.

5 = 13a + 1 + 3a

4 = 16a

[tex]\rm a = \dfrac{1}{4}[/tex]

Now, put the value of 'a' in equation (2).

[tex]b = 1 +3\times \dfrac{1}{4}[/tex]

[tex]b = \dfrac{7}{4}[/tex]

Now, put the value of a and b in equation (1).

[tex]\rm f(x) = \dfrac{1}{4}x + \dfrac{7}{4}[/tex]

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Answer:

The vertices of image are (5,1), (2,-5) and (-4,-5).

Step-by-step explanation:

The vertices of triangle are (5,-1), (3,-5) and (-1,-5).

If a figure dilated by scale factor k centered at (a,b), then

[tex](x,y)\rightarrow (k(x-a)+a,k(y-b)+b)[/tex]

The figure after a dilation with a scale factor of 3/2 centered at (5, −5).

[tex](x,y)\rightarrow (\frac{3}{2}(x-5)+5,\frac{3}{2}(y+5)-5)[/tex]

The coordinates of image are

[tex](5,-1)\rightarrow (\frac{3}{2}(5-5)+5,\frac{3}{2}(-1+5)-5)\rightarrow (5,1)[/tex]

[tex](3,-5)\rightarrow (\frac{3}{2}(3-5)+3,\frac{3}{2}(-5+5)-5)\rightarrow (2,-5)[/tex]

[tex](-1,-5)\rightarrow (\frac{3}{2}(-1-5)+5,\frac{3}{2}(-5+5)-5)\rightarrow (-4,-5)[/tex]

Therefore vertices of image are (5,1), (2,-5) and (-4,-5).

Nathan can completely fill a bag of mixed nuts by calculating the total weight of the nuts, then dividing that total by 1.2 kg, which is the weight of nuts per bag. Any decimal in the result would be rounded down to give the number of full bags.

To determine the number of bags of mixed nuts Nathan can completely fill, you first need to calculate the total weight of all the nuts he bought. This is done by adding up the masses of all the different nuts mentioned in the table.

Let's assume that Nathan's total weight of nuts is 'T'. His plan is to fill each bag with 1.2 kg of nuts, thus the number of full bags he can make, denoted as 'B', is the total weight divided by the weight per bag. In other words, B = T / 1.2.

A key fact here is that this calculation will give a decimal if 'T' is not a multiple of 1.2. However, since he cannot create partial bags, you would round down any decimal to get the number of complete bags.

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the value of the fraction when x = 2 and y = 3 is approximately [tex]\( \frac{1}{31.6} \).[/tex]

To find the value of the fraction [tex]\( \frac{1}{2x^3 + 5.2y} \) when \( x = 2 \) and \( y = 3 \)[/tex], we substitute these values into the expression:

[tex]\[ \frac{1}{2(2)^3 + 5.2(3)} \][/tex]

[tex]\[ = \frac{1}{2(8) + 5.2(3)} \][/tex]

[tex]\[ = \frac{1}{16 + 15.6} \][/tex]

[tex]\[ = \frac{1}{31.6} \][/tex]

So, the value of the fraction when x = 2 and y = 3 is approximately [tex]\( \frac{1}{31.6} \).[/tex]

The probable question maybe:

What is the value of fraction 1 over 2x^3 + 5.2y when x = 2 and y = 3?

Without the height of the popcorn machine, the exact length cannot be calculated. The length is three-quarters of the height. If the height were known, the length would be determined by multiplying the height by 3/4.

To determine the length of the popcorn machine, we need to know the height of the machine since the length is expressed as a fraction of the height. Without the height measurement, we cannot calculate a specific length. However, if we were provided with the height (let's call it H), then we could easily find the length by multiplying the height by 3/4:

Length = (3/4) × H

For example, if the height of the popcorn machine were 4 feet, then the length would be calculated as follows:

Length = (3/4) × 4 feet = 3 feet

Therefore, the length of the popcorn machine is three-quarters of whatever its height is.

The fraction of the pie given to his friend is [tex]\frac{1}{2}[/tex]

The leftover given to his friends will be determined adding the portion Christine and her brother ate which are [tex]\frac{1}{6}[/tex] and [tex]\frac{1}{3}[/tex] respectively, then subtracted from the whole portion.

= [tex]\frac{1}{6}[/tex] + [tex]\frac{1}{3}[/tex] (The lowest common denominator of 6 and 3 = 6)

= (1 x 1) + (2 x 1) /6

= (1) + (2) / 6

= 1 + 2 / 6

= [tex]\frac{3}{6}[/tex]

Thus, total portion of the pie eaten by Christine and her brother = [tex]\frac{3}{6}[/tex] . Also the fraction of the whole portion of the pie = [tex]\frac{6}{6}[/tex]  

Determining the portion given to the friend =

Subtracting [tex]\frac{6}{6}[/tex] – [tex]\frac{3}{6}[/tex]

= [tex]\frac{6}{6}[/tex] – [tex]\frac{3}{6}[/tex] (The lowest common denominator of 6 and 6 = 6)

= (1 x 6) – (1 x 3) / 6

= (6) – (3) / 6

= 6 – 3 / 6

= [tex]\frac{3}{6}[/tex]

= [tex]\frac{1}{2}[/tex] (further broken down to this)

Therefore the fraction given to the friend is [tex]\frac{1}{2}[/tex].

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Answer:

Step-by-step explanation:

If Stephen divided 46.8 by 0.5, the right quotient would be:

[tex]\frac{46.8}{0.5} = 93.6[/tex]

Therefore, the correct quotient would be 93.6, because if Stephen multiply 93.6 times 0.5, it would result in 46.8.

Remember that the quotient is basically the result of a division or fraction.