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The radius of this exoplanet's orbit is equal to 4.71 × 10¹¹ meters.

In order to calculate the radius of the exoplanet's orbit, we would apply  Kepler's Third Law of planetary motion.

Mathematically, Kepler's third law of planetary motion can be calculated by using this formula:

T² = 2π√(r³/GM)

Where:

Making radius (r) the subject of formula, we have:

Radius, r = ∛(GMT²/2π)

Note: Universal gravitational constant is equal to 6.67 × 10⁻¹¹ m³kg⁻¹s⁻².

Orbital period, T = 3.95 × 365 × 24 × 60 × 60 = 341,280 seconds

Substituting the given parameters into the formula, we have;

Radius, r = ∛(6.67 × 10⁻¹¹ × 3.97×10³⁰ × (341,280)²/2 × 3.142)

Radius, r = 4.71 × 10¹¹ meters.

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1. The decrease in dollars in Tammy's investment account, based on a 7.5 percent decrease, is $615.

2. The balance in Tammy's investment account at the end of last year was $7,585.

The percentage is the proportion of a value in relation to another.

Percentages show how much a variable is contained in another.

The percentage gives the fractional value of the decrease in the investment account.

Initial investment = $8,200

Decrease in investment = 7.5%

Decrease in dollars = $615 ($8,200 x 7.5%)

Balance = $7,585 ($8,200 - $615)

Thus, we can conclude that Tammy's investment account decreased by $615, representing a 7.5% decrease.

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Given the two functions:

We need to find (RoS)(4). THis is the functional composition. We take S(x) and put it into R(x) and then put "4" into that composed function. Shown below is the process:

When we plug in "4", into "x", we have:

16 ounces is equivalent to 453.6g when rounding to nearest tenth.

What is rounding off ?

Rounding off means a number is made into simpler form by keeping its value fixed but closer to the next number.

To round off the number to the nearest tenth we need to look at the hundredths place digit. If the digit is 1, 2, 3, 4 then we don't have to do anything, if the digit is 5, 6, 7, 8, 9 we must round up.

here the given data is :

1 ounce = 28.35 grams

Conversion of ounce to grams :

This is the conversion of a mass unit from ounce to grams. Given that 1 ounce is equal to 28.35 grams, let us calculate how grams would be in 16 ounces.

The easiest way about this is simply multiply 16 by 28.25g

1 ounce = 28.35 grams

16 ounce = x

x = 16 x 28.25

x= 453.6 g

From the calculations above, 16 ounces is equivalent to 453.6g.

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Answer:

P(X = 2) = 43.2%

Step-by-step explanation:

P(X = 2) = 3 * 0.6^2 * (1 - 0.6)^(3 - 2)

P(X = 2) = 54/125

P(X = 2) = 0.432

P(X = 2) = 43.2%

B. 2/10 = 20%

The total number of weeks shown in the simulation = 10

By observing the simulation, we would see that there is no 0 or 1 in group 2 and group 3. This means that Juan was late everyday of week 2 and week 3

The number of weeks that Juan was late everyday = 2

The estimated probability that Juan will be late evryday of next week = 2/10 = 20%

To be able to determine if the figure is a right triangle.

The given length must satifies the given conditions,

a.) The sum of the two sides must always be lesser than the other side. We get,

Given: a = 14 ; b = 16 ; c = 18

Let's check,

a + b > c ; 14 + 16 > 18 = 30 > 18 Satisfies the criteria

b + c > a ; 16 + 18 > 14 = 34 > 14 Satisfies the criteria

a + c > b ; 14 + 18 > 16 = 32 > 16 Satisfies the criteria

b.) The square of the longest side is equal to the sum of the squares of the other two sides (Pythagorean Theorem). We get,

Therefore, checking the relationships of the given the following lengths, the figure is not a right tiangle.

The linear equation that passes through the two points (0, 360) and (10, 560) is:

y = 20*x + 360

Remember that the slope-intercept form of a linear equation is:

y = a*x + b

Where b is the y-intercept and a is the slope or rate of change.

If we know that the line passes through the points (x₁, y₁) and (x₂, y₂) then the slope is:

[tex]a = \frac{y_2 -y_1}{x_2 - x_1}[/tex]

Here the line must pass through (0, 360) and (10, 560), so the slope is:

[tex]a = \frac{560 - 360}{10 - 0} = 20[/tex]

And because of the point (0, 360) we can see that the y-intercept is 360, then the linear equation is:

y = 20*x + 360

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1) f(x)-3

Therefore, f(x)-3=2x-4-3

2) f(x-3)

Thus, f(x-3)=2(x-3)-4

3) f(-3x)

Then, f(-3x)=2(-3x)-4

4) -3f(x)

Hence, -3f(x)=-3(2x-4)

Answer: 40000

+ 5000

+ 800

+ 3

Step-by-step explanation:

The expanded form splits the number, and it represents the number in units, tens, hundreds and thousands form.

The value of expression ( – 5q–1)–( – 2q–8) is -3q + 7.

As per the known fact, the similar signs are consequently takes as positive for calculation. So, the two negative signs will be takes as positive. So, rewriting the expression to solve and find its value.

Value of expression = (-5q - 1) + 2q + 8

Rearrange the expression

Value of expression = - 5q + 2q - 1 + 8

Performing addition of numerals written with q and subtraction of constant values

Value of expression = - 3q + 7

Thus, the value of expression mentioned in question is -3q + 7.

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Answer:

A line perpendicular to another has a slope that is the negative reciprocal of the slope of the other line.

Answer:

78.59$

Step-by-step explanation:

To find the area of a circle given its radius,

The value of the radius r = 8 inches, and the value of pi is 3.14. Hence;

The area of the circle is 200.96 inches squared

Answer:

Step-Congruent angles are frequently used in the world of architecture, construction, design, and art. Congruent angles have the same angle measure. For example, a regular pentagon has five sides and five angles, and each angle is 108 degrees. Regardless of the size or scale of a regular polygon, the angles will always be congruent.

Answer: 17x - 39

Step-by-step explanation:

1) Find all sides of the hallway.

P = 4x-9 + x-2 + x+2 + 3x - 11 + x-2 + 3x - 11 + x+4 + 2x-9 + x-1

2) Add it together

P= 17x - 39

The graph of the figure is attached below.

Given equation of line:-

y = (-3/2)x - 1

First we will find the x and y intercepts of the line to plot in the line.

Putting x = 0 to find the y-intercept, we get,

y = (-3/2)(0) - 1

y = -1

Hence, the coordinates of the point are (0,-1).

Putting y = 0 to find the x-intercept, we get,

0 = (-3/2)x - 1

1 = (-3/2)x

x = -2/3

Hence, the coordinates of the point are (-2/3,0).

We can find another point on the line.

Putting x = 2, we get,

y = (-3/2)(2) - 1

y = -3 - 1

y = -4

Hence, the coordinates of the point are (2,-4).

Plotting these in a graph, we can get a straight line.

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From the given expression, it is found that:

a) When x = 7 and y = 11, the numeric values are given as follows:

b) They will only have the same numeric value when x = y.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function by the desired value.

The same is true for multi-variable expressions, as each variable will have a numeric value that we will replace in the function.

In the context of this problem, the expressions are given as follows:

When x = 7 and y = 11, the numeric values are given as follows:

The notable product of the square of the sum is different of the sum of the squares, and the same holds true for the subtraction, hence both expressions will only have the same value when x = y, as factors (x - y)² and (x² - y²) will both be of 0, resulting in a multiplication of 0 in each expression and a value of 0.

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Answer:

You were right. The answer is (C)

Step-by-step explanation:

Remember, the line always goes up in the top right corner, also the first dot is 2,20, to 4,40, to 6,60, and last 8,80 which is the number of the same total amount and number of hours.

Answer:

  150 km

Step-by-step explanation:

You want to know the number of kilometers each train has traveled when they meet. The first goes 60 km/h and has a half-hour head start. The second goes 75 km/h.

At t hours after 10 am, the distance of the first train from Kanpur will be ...

  distance = speed × time

  distance = 60t

At t hours after 10 am, the distance of the second train from Kanpur will be ...

  distance = 75(t -1/2) . . . . . . the distance is 0 at 10:30 am, 1/2 after 10 am

These distances will be equal when ...

  60t = 75(t -1/2)

The time at which the trains meet will be the solution to the above equation.

  60t = 75t -37.5 . . . . eliminate parentheses

  0 = 15t -37.5 . . . . . . subtract 60t

  0 = t -2.5 . . . . . . . . . divide by 15

  2.5 = t . . . . . . . . . the trains meet 2.5 hours after the first one leaves

The distance traveled by each of the trains is the same at that time. It will be the distance traveled by the first train:

  60t = 60(2.5) = 150 . . . . km

The two trains will be together 150 km from Kanpur.

The greater triangle and the smaller ones (the two triangles inside the original one, that share the side y) are similar triangles, then we can formulate the following expressions:

• For the larger triangle and the triangle on the left

From this equation, we can solve for z, to get:

Then, z equals 3√5

• Similarly, with the larger triangle and the one on the right:

From this expression, we can solve for x, like this:

Then, x equals 6

• With the triangles on the right and on the left:

Solving for y, we get:

Then, y equals 2√5

Recall that to complete the table we have to evaluate the given function at every value of x:

Answer:

Table:

Graph:

Answer:

124

Step-by-step explanation:

Since the amount of time is being multiplied by 4, the number of parts will also be multiplied by 4.

[tex]31(4)=124[/tex]

First, lets perform each transformation and then take a look at its graph:

1.

The only etiquette that matches this plot is: Function decreases as x increases

2.

The only etiquette that matches this plot is: x-intercept at (1.5 , 0)

3.

The only etiquette that matches this plot is: Asymptote of x = 0

The correct option is True, there is enough information given to say that both line are parallel.

For the given question.

The two lines are given with angles measure from 1 to 8.

Where,

As, the sum of the angles is;

∠4 + ∠3 = 91° + 89°

∠4 + ∠3  = 180° (supplementary angles)

Thus, we can say that both lines are parallel to each other.

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The numbers that Linda should put on her number line are 5,10,15,20...1000 .

Integers are frequently represented as specifically labelled dots evenly spaced on a line. Despite the fact that the graphic only depicts the integers from -3 to 3, the product contains all real numbers, which continue indefinitely in each direction, as well as numbers that lie between the integers. It is frequently used to help teach simple numerals, particularly with negative numbers.

The numbers are skip counted. so each number differs from the preceding number by 5.

let us take the number counting starts from 0. so the second number will be 5+5=10

The third number 10+5 = 15 and so on and so forth.

Hence it forms an arithmetic sequence of numbers whose first term is 5 and common difference is 5.

A number line is really a picture of a stepped straight line as serves as a visual representation of real numbers in primary mathematics. Every point of a x axis is assumed to coincide to a true figure, and every decimal digits to a point.

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Answer:

h = 9 cm

Explanation:

The volume of the solid can be calculated as:

So, we can replace the value of the Volume by 1323 cm³ and B by 147 cm² as:

Then, dividing by 147 into both sides, we get:

Therefore, the height h of the solid is 9 cm.