The distance d, in miles, of the nth planet from the sun is given by the formula below.
d = 9,275,200[3(2n − 2) + 4]

To the nearest million miles, find the distance of Earth and the distance of Mars from the sun. Give each answer in scientific notation. (Round your answers to the nearest million miles.)
Earth
✕ 10
mi
Mars
✕ 10
mi

In this case we have a translation of 8 units to the left and 11 units upwards.

To find the translation, we just need to compare the two known vertices before and after the translation.

If we have a translation of a units in the x-axis and b units in the y-axis, we will get:

T(a, b)L ---> L'

We know that L = (7, -3) and L' = (-1, 8)

Then we can write:

(7 + a, -3 + b) = (-1, 8)

Then we have two equations:

7 + a = -1 ---> a = -1 - 7 = -8

-3 + b = 8 ---> b = 8 + 3 = 11

Then we have a translation of 8 units to the left and 11 units up-.

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Complete question:

"Right triangle LMN has vertices L(7, –3), M(7, –8), and

N(10, –8). The triangle is translated on the coordinate plane so the coordinates of L’ are (–1, 8).

Find the translation done"

Answer:

the image is sideways

Step-by-step explanation:

Answer:

well buddy see you thinking to hard its right there just relax and look closely

Step-by-step explanation:

Answer:

The probability that the selected number is an odd number or a multiple of 3 is 6/9, or 2/3. This is because there are 6 numbers that meet the criteria out of the 9 numbers in the set: 1, 3, 5, 7, 9, and 3.

Step-by-step explanation:

31 + 6x + x + 16 = 180

7x + 47 = 180

7x = 180 - 47

x = 133/7

x = 19

Answer:

a) The proportion of the jury described that is from a minority race is 0.15 or 15.38%, both to 2 d.p.

b) The probability that 2 or fewer out of 13 jurors are minorities, assuming that the proportion of the population that are minorities is 48%, is 0.0162

c) Option C is correct.

The lawyer of a defendant from this minority race should argue that

'The number of minorities on the jury is unusually low, given the composition of the population from which it came'.

Step-by-step explanation:

(a) What proportion of the jury described is from a minority race?

Of the 13 jurors, it is given in the question that only 2 of them are from a minority race.

Hence,

The proportion of the jury described that is from a minority race = (2/13) = 0.1538461538 = 0.154

(b) If 13 jurors are randomly selected from a population where 48% are minorities, what is the probability that 2 or fewer jurors will be minorities?

This problem is a binomial distribution problem

If X denotes the number of jurors that are from a minority race amongst the 13 jurors

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = number of jurors = 13

x = Number of successes required = 2 or fewer jurors = ≤ 2

p = probability of success = probability that a randomly picked member of the population as a juror is from a minority race = 48% = 0.48

q = probability of failure = probability that a randomly picked member of the population as a juror is NOT from a minority race = 1 - p = 1 - 0.48 = 0.52

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)

= 0.00020325604 + 0.00243907252 + 0.01350870934

= 0.01615103791 = 0.0162 to 4 d.p.

(c) What might the lawyer of a defendant from this minority race argue?

Normally, the distribution of 13 jurors should reflect the population distribution with each race represented according to their population proportion or at least a proportion close to that.

But for this case, the proportion of the population from a minority race (48%) is more than 3 times the proportion of the jurors that are from a minority race (15.38%). This can introduce a very unfair bias in the decision of the jurors, hence, the lawyer of a defendant from this minority race might argue that the number of minorities on the jury is unusually low, given the composition of the population from which it came (less than ⅓).

Hope this Helps!!!

Answer:

43

Step-by-step explanation:

Green:  9 - 2(-3) = 9 + 6 = 15

Red:  -2(-3) + 4 = 6 + 4 = 10

Dark blue:  7x + 5 = 19

7x = 19 - 5 = 14

x = 14/7 = 2

Light blue:  6x + 3 = 21

6x = 21 - 3 = 18

x = 18/6 = 3

Red(Lt blue) - Dk blue + Green = 10(3) - 2 + 15 = 43

Answer:

M

Step-by-step explanation:

the height of a binary tree is the number of edges in the longest path from the root to a leaf.The best-case height of a binary tree with seven nodes is 3.

A binary tree is a type of tree structure consisting of nodes that are connected by edges. The number of edges in the longest path from a binary tree's root to a leaf determines the tree's height.In the best-case scenario, the binary tree is perfectly balanced and each node has exactly two children. With seven nodes, the best-case height is three because each node has two children and three edges connect the root node to the leaves. This means that the longest path from the root to a leaf is three edges, resulting in a height of three.

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The standard form of the equation is (x - 1)² - (y - 1)² + (z + 2)²  = 3

The equation is given as:

x² -y² + z² - 2x + 2y + 4z + 1 = 0

Subtract 1 from both sides

x² -y² + z² - 2x + 2y + 4z = -1

Rewrite the equation as:

x² - 2x -y² + 2y + z² + 4z = -1

Next, we complete the square on each variable term.

Using a graphing calculator, we have:

(x - 1)² - (y - 1)² + (z + 2)²  = -1 + 1 + 4 - 1

Evaluate the sum and difference

(x - 1)² - (y - 1)² + (z + 2)²  = 3

x^2 - 2x + 2 - (y^2 - 2y + 2) + z^2 + 4z + 4 = 3

Hence, the standard form of the equation is (x - 1)² - (y - 1)² + (z + 2)²  = 3

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Answer:

Hello There!!

Step-by-step explanation:

The answer is that=>Yes It is a rational number.

hope this helps,have a great day!!

~Pinky~

Answer:

Yes.

Step-by-step explanation:

A rational number is any number that can be written as a fraction. These include whole numbers, fractions, decimals that end, and decimals that repeat. Positive and negative do not affect rationality.

Answer:

2nd option

Step-by-step explanation:

the length of the arc is calculated as

arc = circumference × fraction of circle

     = 2πr × \(\frac{120}{360}\) ( r is the radius )

    = 2π × 10 × \(\frac{1}{3}\)

    = 20π × \(\frac{1}{3}\)

   = \(\frac{20\pi }{3}\) in

Answer:

g = 8

Step-by-step explanation:

Hello!

We can solve for g by isolating the variable.

The value of g is 8.

Answer:

\( \sf \: g = 8\)

Step-by-step explanation:

Now we have to,

→ find the required value of g.

The equation is,

→ 2.8(g - 6) + 1.06 = 6.66

Then the value of g will be,

→ 2.8(g - 6) + 1.06 = 6.66

→ 2.8g - 16.8 = 6.66 - 1.06

→ 2.8g - 16.8 = 5.6

→ 2.8g = 5.6 + 16.8

→ g = (22.4)/(2.8)

→ [ g = 8 ]

Hence, the value of g is 8.

You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.

When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.

A cuboid has six faces, but each face has a pair that is identical in size and shape.

Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.

To find the surface area of a cuboid, you can add up the areas of all its faces.

However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:

(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.

By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.

Essentially, you are considering one face from each pair and then summing their areas.

Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.

When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.

Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.

Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.

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Answer:

the possible values of c = -23,  -10,  -5,  or -2

Step-by-step explanation:

The possible values of c that will allow the polynomial to be factored must be a factor of "-24"

1 x (-24) = -24    (for this case c = -23)

2 x (-12) = -24    (for this case c = -10)

3 x (-8) = -24     (for this case c = -5)

4 x (-6) = -24     (for this case c = -2)

Therefore, the possible values of c = -23,  -10,  -5,  or -2

The quadrilateral you're describing is a Kite. A kite is a quadrilateral with two pairs of consecutive congruent sides, and its diagonals meet at a right angle.

Answer:

sssssssssiiiiiiiiiiiiii

Answer:

6

Step-by-step explanation:

Answer:

x^2-5xy+4y^2

Step-by-step explanation:

In the equation we see only 1 example of like terms, 2xy-7xy=-5xy

So the simplified equation is

x^2-5xy+4y^2

This is your answer:

x^2+5xy+4y^2

Answer:

5/64

Step-by-step explanation:

numerators 1 time 5 is 5 and denominators 8 times 8 is 64;  5/64

Answer:

the orange one

Step-by-step explanation:

(10 + 10) : (5-3) =

20 : 2 =

10

If the first quartile is 39 years old, it means that approximately one-fourth of the employees at CCNHS – Main Campus are 39 years old or younger.

The first quartile (Q1) of the ages of the 256 employees of CCNHS – Main Campus being 39 years old implies that 25% of the employees have an age equal to or less than 39 years old.

In statistical terms, the first quartile represents the point below which 25% of the data falls. It divides the data set into four equal parts, with each part containing 25% of the data. Therefore, if the first quartile is 39 years old, it means that approximately one-fourth of the employees at CCNHS – Main Campus are 39 years old or younger.

This information provides insight into the age distribution of the employees at the institution. It indicates that a significant portion of the employees are relatively young, with a quarter of them falling below the age of 39. Understanding the age demographics of the workforce can be useful for various purposes, such as planning professional development programs or implementing age-specific policies.

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Answer:

54.20

Step-by-step explanation:

When you round you look at the number to the right of the number you're rounding. So you look at the 7. If it is larger than five (in this case it is) you round the number up.

Answer:215.768

Step-by-step explanation:

Answer: about 216 liters

Step-by-step explanation:

The final answer is (f o g)(x) = x^4 - 16x^2 + 72

(g o f)(x) = x^4 + 16x^2 + 56

(f o g)(2) = 24

To find the composite functions (f o g)(x) and (g o f)(x), we need to substitute one function into the other.

(f o g)(x):

To find (f o g)(x), we substitute g(x) into f(x):

(f o g)(x) = f(g(x))

Let's substitute g(x) = x^2 - 8 into f(x) = x^2 + 8:

(f o g)(x) = f(g(x)) = f(x^2 - 8)

Now we replace x in f(x^2 - 8) with x^2 - 8:

(f o g)(x) = (x^2 - 8)^2 + 8

Simplifying further:

(f o g)(x) = x^4 - 16x^2 + 64 + 8

(f o g)(x) = x^4 - 16x^2 + 72

Therefore, (f o g)(x) = x^4 - 16x^2 + 72.

(g o f)(x):

To find (g o f)(x), we substitute f(x) into g(x):

(g o f)(x) = g(f(x))

Let's substitute f(x) = x^2 + 8 into g(x) = x^2 - 8:

(g o f)(x) = g(f(x)) = g(x^2 + 8)

Now we replace x in g(x^2 + 8) with x^2 + 8:

(g o f)(x) = (x^2 + 8)^2 - 8

Simplifying further:

(g o f)(x) = x^4 + 16x^2 + 64 - 8

(g o f)(x) = x^4 + 16x^2 + 56

Therefore, (g o f)(x) = x^4 + 16x^2 + 56.

(f o g)(2):

To find (f o g)(2), we substitute x = 2 into the expression (f o g)(x) = x^4 - 16x^2 + 72:

(f o g)(2) = 2^4 - 16(2)^2 + 72

(f o g)(2) = 16 - 64 + 72

(f o g)(2) = 24

Therefore, (f o g)(2) = 24.

In summary:

(f o g)(x) = x^4 - 16x^2 + 72

(g o f)(x) = x^4 + 16x^2 + 56

(f o g)(2) = 24

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The three true statements are as follows:

In the list, there are several true statements and some of them include the facts that all triangles are polygons, they are closed figures and they have three straight sides.

A polygon is a shape with two or more sides. Triangles ahve three sides, so we can easily address them as polygons. Also, all triangles are closed figures and they also have three straight sides.

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Answer:

5.6 - 4.8 = 0.8

Step-by-step explanation:

5.6 - 4.8 = 0.8

The solution by substituting 15 for b in the Original equation. The answer is true.

The steps needed to solve the equation b + 6 = 21 are:

Subtract 6 from both sides of the equation: b + 6 - 6 = 21 - 6, which simplifies to b = 15.

Check the solution by substituting 15 for b in the original equation: 15 + 6 = 21, which is true.

Therefore, the correct steps to solve the equation are:

Subtract 6 from both sides of the equation. The answer is b = 15

the solution by substituting 15 for b in the original equation. The answer is true.

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Answer:

42

Step-by-step explanation:

Shanice =88

If greg won x pieces of gum, and 88 was 4 more than twice as many as Greg

2x+4=88

2x=84

x=42

Answer: x<4

Step-by-step explanation:

If we break this down as

-2+4x<14 and we add 2 to both sides

4x+<16 and divide by 4

and you get x<4