Earth's distance from the sun is 1. 496 x 108 km. Saturn's distance from the sun is 1. 4246 x 10 km. How many times further from the sun is Saturn? Explain how you arrived at your answer. ​

Firstly, we can simplify the numerator which is 35x raised to the power 5 times y raised to the power 3. To do this, we can multiply the coefficients and add the exponents of the variables with the same base. Thus, the numerator simplifies to 35x^5y^3.

Next, we need to simplify the denominator which is 7xy raised to the power 2. Similarly, we can multiply the coefficients and add the exponents of the variables with the same base. Thus, the denominator simplifies to 7x^1y^1 (since x and y each have a power of 1).

Now we can divide the numerator by the denominator. To do this, we divide the coefficients (35/7 = 5) and subtract the exponents of the variables with the same base (x^5/x^1 = x^4 and y^3/y^1 = y^2). Therefore, the simplified form of the given expression is 5x^4y^2.

In summary, to simplify the given expression, we used the power and quotient rules of exponents. We multiplied coefficients and added exponents of variables with the same base, and then divided coefficients and subtracted exponents of variables with the same base. The final simplified form is 5x^4y^2.

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Answer:

Principal = $21,592.31

Step-by-step explanation:

The formula for continuous compound interest is

[tex]A = Pe^r^t[/tex], where A is the amount (aka investment worth), r is the interest rate, and t is the time in years (the number e simply shows us that we're dealing with continuous compound interest)

Since we're already given that have A = $58,226.31, r = 0.062 (we must convert the percentage to a decimal by simply moving the decimal two places to the left, which is the same as dividing by 100), and t = 16 years, we can simply solve for P:

[tex]58226.31=Pe^(^0^.^0^6^2^*^1^6^)\\58226.31=Pe^0^.^9^9^2\\58226.31/(e^0^.^9^9^2)=P\\21592.31176=P\\21592.31=P[/tex]

Kate's mistake was in Step 2: "Divide the volume of Wesley's tank by 2." Since she wants a tank with half the volume of Wesley's tank, she should have divided the volume of Wesley's tank by 2, not the radius.

The correct approach would be to use the formula for the volume of a sphere:

V = (4/3)πr^3

Since Wesley's tank has a diameter of 30 cm, its radius is 15 cm. Substituting this value into the formula gives:

V = (4/3)π(15)^3

V ≈ 14,137 cm^3

To find the radius of the smaller tank with half the volume, Kate should have solved for the radius using the formula for the volume of a sphere:

(4/3)πr^3 = (1/2)(4/3)π(15)^3

Simplifying this equation gives:

r^3 = (1/2)(15)^3

r ≈ 10.8 cm

Therefore, the approximate diameter of the smaller tank should be 21.6 cm (twice the radius), not 10.8 cm.

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Answer:

To gain our understanding of the plot (13, 10) on graph paper. We need to look at the picture reflecting or "flipping" that point over the x-axis. In this case, it "flips the point down"  the original point was in first quadrant or Quadrant |, the reflected point is in the fourth quadrant of Queadrant ||||.  The x coordinate would stay the same, but the new y coordinate would be the "opposite" sign of the original.  So the reflected point is (13, -10)

Step-by-step explanation:

(x, y) → (x, - y)

Reflection over x-axis for (13,-20) → (13, 20)

Technically some of the explanations is above /\

Thus the answer is, To gain our understanding of the plot (13, 10) on graph paper. We need to look at the picture reflecting or "flipping" that point over the x-axis. In this case, it "flips the point down"  the original point was in first quadrant or Quadrant |, the reflected point is in the fourth quadrant of Queadrant ||||.  The x coordinate would stay the same, but the new y coordinate would be the "opposite" sign of the original.  So the reflected point is (13, -10)

The ∠ ABE and ∠HCD are alternate exterior angle.option(D) is correct.

An alternate exterior angle is an angle formed by a pair of lines and a transversal, such that the angle is located on the outside of the two lines, and on the opposite side of the transversal. More specifically, if line AB is intersected by transversal CD at point E, and angles 1 and 2 are formed as shown in the diagram below, then angle 1 and angle 2 are alternate exterior angles:

Alternate exterior angles are congruent if the two intersected lines are parallel. This means that the measure of angle 1 is equal to the measure of angle 2.

So, ∠ ABE and ∠HCD are alternate exterior angle.option(D) is correct.

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Tabitha could pay $4,408.29 less for her SUV if she takes the loan for five years in place of 7.

To calculate the total amount Tabitha might pay for the SUV with a 7-year loan, we are able to use the compound interest formula for calculating the total amount of a loan, that is:

[tex]total amount = principal x (1 + interest charge)^{time}[/tex]

Wherein:

With a 7-year loan, the full amount Tabitha could pay is:

[tex]total amount = $29,000 x (1 + 0.043)^{7} = $37,501.76[/tex]

To calculate the overall amount she could pay with a 5-year loan and a 5% decrease interest rate, we first need to calculate the new interest price. A 5% discount inside the interest price of 4.3% is:

New interest price = 4.3% - 5% = 3.3%

Then we can use the equal formula as before to calculate the total amount with the 5-year mortgage:

[tex]total amount = $29,000 x (1 + 0.033)^{5} = $33,093.47[/tex]

The difference in the overall amount among the two loans is:

$37,501.76 - $33,093.47 = $4,408.29

Therefore, Tabitha could pay $4,408.29 less for her SUV if she takes the loan for five years in place of 7.

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The calculated value of the length of segment KM is 11.83

From the question, we have the following parameters that can be used in our computation:

JM = 10

LM = 14

Using the similar triangle ratio, we have

JM/KM = KM/LM

substitute the known values in the above equation, so, we have the following representation

10/KM = KM/14

So, we have

KM^2 = 10 * 14

Evaluate

KM^2 = 140

This gives

KM = 11.8321595662

As a decimal rounded to the nearest hundredth, we have

KM = 11.83

HEnce, the value of KM is 11.83

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There are 20 different ways to assign five students to cover the morning and afternoon shifts at the food pantry.

There are different methods to solve this problem, but one possible way is to use a combination of counting techniques.

Since there are two shifts (morning and afternoon) and each shift must be covered by at least two students, there are two cases to consider:

Case 1: Two students cover the morning shift, and three students cover the afternoon shift.

Case 2: Three students cover the morning shift, and two students cover the afternoon shift.

For Case 1, we can choose two students out of five for the morning shift in C(5,2) = 10 ways, and the remaining three students will cover the afternoon shift. For each of the 10 ways of selecting the morning shift, we can choose three students out of the remaining three for the afternoon shift in C(3,3) = 1 way (since there are only three students left). Therefore, there are 10 x 1 = 10 ways to assign the students for Case 1.

For Case 2, we can choose three students out of five for the morning shift in C(5,3) = 10 ways, and the remaining two students will cover the afternoon shift. For each of the 10 ways of selecting the morning shift, we can choose two students out of the remaining two for the afternoon shift in C(2,2) = 1 way (since there are only two students left). Therefore, there are 10 x 1 = 10 ways to assign the students for Case 2.

The total number of ways to assign the students is the sum of the ways for Case 1 and Case 2, which is 10 + 10 = 20 ways.

Therefore, there are 20 different ways to assign the five students to cover the morning and afternoon shifts at the food pantry.

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The expressions that could represent the length and width are (x - 2) units and (x - 7) units respectively.

To find the expressions that represent the length and width of the rectangle, we need to factor the given expression.

x² - 9x + 14 = (x - 2)(x - 7)

The length and width of the rectangle are represented by two factors of the expression.


To find the length and width of the rectangle, we need to understand the formula for the area of a rectangle, which is length multiplied by width. The given expression x²-9x+14 represents the area of the rectangle. To find the expressions that represent the length and width, we need to factor the given expression.

We can do this by finding two numbers that multiply to 14 and add up to -9. These numbers are -2 and -7. Therefore, we can factor the given expression as (x - 2)(x - 7). From this, we can see that the length of the rectangle is represented by the factor (x - 2) units and the width is represented by the factor (x - 7) units.

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Answer:

see explanation

Step-by-step explanation:

the arc BX is equal to the measure of the central angle BCX

the measure of the inscribed angle BNX is half the measure of its intercepted arc BX

The correct sequence for the samples in order of least variation to greatest variation is:

Sample A: A sample of 10 people

Sample D: A sample of 20 people

Sample B: A sample of 50 people

Sample C: A sample of 100 people

The reason for this sequence is that larger sample sizes tend to provide more accurate estimates of the population parameters, while smaller sample sizes are more prone to random fluctuations and sampling error.

Therefore, sample A (with the smallest sample size of 10) is likely to have the greatest variation from the expected value, while sample C (with the largest sample size of 100) is likely to have the least variation from the expected value.

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Answer:

$626.76

Step-by-step explanation:

Since the loan is at a simple interest rate of 8% for 5 years, the total amount that the mysterious hand will pay is:

Total amount = Principal + Interest

where Principal is the initial amount of the loan, and Interest is the amount of interest charged on the loan.

The interest charged on the loan can be calculated using the simple interest formula:

Interest = Principal x Rate x Time

where Rate is the interest rate per year, and Time is the time period in years.

Plugging in the given values, we get:

Interest = 6600 x 0.08 x 5 = 2640

So the total amount that the mysterious hand will pay is:

Total amount = 6600 + 2640 = 9240

Therefore, the total amount that the mysterious hand will pay for the massage chair is $9,240.

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The speed of the boat is 21 km/h and the speed of the stream is 2 km/h.

The area of the King-sized mattress is 4,800 square inches and the area of the Queen-sized mattress is 3,200 square inches.

To find the dimensions of the Queen-sized mattress, let x be the width. Then, the length of the mattress is x + 16. The area of the Queen-sized mattress is x(x + 16) = x² + 16x.

Since the King-sized mattress has the same length as the Queen-sized mattress, its length is x + 16. Also, its width is 20 inches wider than the Queen-sized mattress, so its width is x + 16 + 20 = x + 36. Therefore, the area of the King-sized mattress is (x + 16)(x + 36) = x² + 52x + 576.

The area of the King-sized mattress is 1,600 square inches larger than the area of the Queen-sized mattress. So, we can set up the following equation:

x² + 52x + 576 - (x² + 16x) = 1600

Simplifying this equation, we get:

36x + 576 = 1600

36x = 1024

x = 28

Therefore, the width of the Queen-sized mattress is 28 inches and the length is 44 inches. So, its area is 3,200 square inches.

The width of the King-sized mattress is 28 + 36 = 64 inches and the length is 44 inches. So, its area is 4,800 square inches.

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The gross income for selling 348 bushels of apples at a price of $16.50 per bushel is $5,742.

The gross income is the total revenue earned from the sales of a product or service, before any expenses or deductions are taken out. To calculate gross income, we multiply the quantity of goods sold by the price per unit.

In this case, we are given that 348 bushels of apples were sold at a price of $16.50 per bushel. Multiplying these two values together gives us the total revenue earned from the sale of these apples, which is the gross income.

To calculate the gross income, we can use the formula:

Gross income = Quantity sold x Price per unit

Plugging in the given values, we get:

Gross income = 348 x $16.50

Simplifying the calculation, we get:

Gross income = $5,742

Therefore, the gross income for selling 348 bushels of apples at a price of $16.50 per bushel is $5,742.

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To prove that 5^7 + 5^6 is divisible by 6, we can factor out the common term 5^6 and apply the divisibility rule for 6. Here's the solution:

1. Factor out the common term 5^6:
5^7 + 5^6 = 5^6(5 + 1) = 5^6 * 6

2. Apply the divisibility rule for 6:
A number is divisible by 6 if it is divisible by both 2 and 3. Since 6 is already a multiple of 6 (6*1), the expression 5^6 * 6 is divisible by 6.

Thus, we have proved that 5^7 + 5^6 is divisible by 6.

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- If the equation is overdamped, b ∈ (-∞, -2√6) ∪ (2√6, ∞).
- If the equation is underdamped, b ∈ (-2√6, 2√6).
- If the equation is critically damped, b ∈ {-2√6, 2√6}.

To determine the behavior of the solution for the given differential equation s′′ + bs′ + 6s = 0, we need to analyze the roots of the characteristic equation:

r^2 + br + 6 = 0

For this quadratic equation, the discriminant Δ is given by:

Δ = b^2 - 4(1)(6) = b^2 - 24

The behavior of the solution depends on the value of Δ:

1. Overdamped: If Δ > 0, the solution will be overdamped.
2. Underdamped: If Δ < 0, the solution will be underdamped.
3. Critically damped: If Δ = 0, the solution will be critically damped.

Now, we find the intervals of b for each case:

1. Overdamped (Δ > 0):
b^2 - 24 > 0
This inequality holds for b ∈ (-∞, -2√6) ∪ (2√6, ∞).

2. Underdamped (Δ < 0):
b^2 - 24 < 0
This inequality holds for b ∈ (-2√6, 2√6).

3. Critically damped (Δ = 0):
b^2 - 24 = 0
This equation holds for b = -2√6 and b = 2√6.

In conclusion:
- If the equation is overdamped, b ∈ (-∞, -2√6) ∪ (2√6, ∞).
- If the equation is underdamped, b ∈ (-2√6, 2√6).
- If the equation is critically damped, b ∈ {-2√6, 2√6}.

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Answer:-12 with the weird checkmark symbol then a five inside the checkmark symbol times u squared v

Step-by-step explanation:

The value of y is 116°.

Three given Adjacent angles are 28°, 36° and y°.

When two angles are adjacent, they have a common side between them and share a common vertex where the two sides meet. The angles are said to be adjacent because they are next to each other.

We know that if a ray stands on a straight line, then the sum of adjacent angles is 180°.

So, 28° + y° + 36° = 180°

y° + 64° = 180°

Subtracting 64° from both sides.

y°- 64° = 180° - 64°

y° = 116°

Hence, the value of y is 116°.

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1. It's impossible to determine exactly when Lin's battery will die without more information on her phone's battery capacity and usage patterns. However, we can estimate that it will likely die sometime after noon if the rate of battery drain remains constant.

2. Yes, battery life is a function of time. The longer a battery is in use, the more its charge will deplete. However, it is not necessarily a linear function as the rate of battery drain can vary depending on factors such as usage patterns, app activity, and temperature. In this specific case, it appears that the rate of battery drain may be slowing down as the percentage decrease from 90% to noon is less than the decrease from fully charged to 90%.

In calculus and related areas, a linear function is a function whose graph is a straight line, that is, a polynomial function of degree zero or one. For distinguishing such a linear function from the other concept, the term affine function is often used. A linear function from the real numbers to the real numbers is a function whose graph (in Cartesian coordinates) is a non-vertical line in the plane. The characteristic property of linear functions is that when the input variable is changed, the change in the output is proportional to the change in the input.

Linear functions are related to linear equations.

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The initial volume of the solution in container Q is 1.6 liters.

Let's first discover how a lot solution was poured from container Q into container P:

0.4 x volume of solution in container Q = 0.4Q

the total volume of solution in container P after this transfer is:

800 ml + 0.4Q ml

Subsequent, 3/8 of this overall volume in container P is poured into container R:

(3/eight) x (800 ml + 0.4Q ml) = 300 ml + 0.15Q ml

We recognise that field R includes 540 ml of solution now, so we are able to set up an equation:

300 ml + 0.15Q ml = 540 ml

Solving for Q, we get:

0.15Q ml = 240 ml

Q = 1600 ml

Consequently, the initial volume of the solution in container Q is 1.6 liters.

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The probability of randomly selecting an orange hat is 1/12 or 0.0833.

In the sample, there are total of 4 pieces of clothing and 3 colors.

The possible outcomes is:

= 4 x 3

= 12

So, the outcomes when randomly selecting a piece of clothing and a color is 12.

From 12 possible outcomes, there is only one outcome where you end up with an orange hat.

So, the probability of randomly selecting an orange hat is:

= 1/12

= 0.0833.

Correct question "You're at a clothing store that dyes your clothes while you wait. You get to pick from 4 pieces of clothing (shirt, pants, socks, or hat) and 3 colors (purple, blue, or orange). If you randomly pick the piece of clothing and the color, what is the probability that you'll end up with an orange hat?"

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The radius of the circle of the equation is 19 units

From the question, we have the following parameters that can be used in our computation:

x² + y² = 19²

The equation of a circle is represented as

(x - a)² + (y - b)² = r²

Where

Center = (a, b)

Radius = r

using the above as a guide, we have the following:

Center = (a, b) = (0, 0)

Radius = r = 19

Hence, the radius of the circle of the equation is 19 units

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The factory can make 500 batches of candle wax with 25 grams of red coloring powder.

For the given question the easiest and the simplest approach will be by using the unit conversion method to solve the problem.

We need to convert the unit from grams to milligrams.

So, 25 grams of red coloring powder will be equal to:

25 grams * 1000mg/grams = 25000mg.

Now it is given that it takes 50 mg to make a single batch of candle wax. So, the number of batches that can be made using 25,000 mg of red coloring powder is equal to:

25000mg/50mg per batch = 500 batches.

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The solution to the inequality given is false.

To determine whether x = 5 is a solution of the inequality x + 3 > 12, we substitute x = 5 into the inequality and see if the resulting statement is true or false:

5 + 3 > 12

8 > 12

In this case, when we substitute x = 5 into the inequality, we get the statement 5 + 3 > 12, which simplifies to 8 > 12. This statement is false, since 8 is not greater than 12. Therefore, x = 5 is not a solution of the inequality x + 3 > 12.

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The full question is:

Tell whether the given value is a solution of the inequality X + 3 > 12; x = 5

The function best represent the value of hybrid car that is worth 40000 and it declines by 3% every year is  [tex]40,000(0.97)^{t}[/tex]

The value of the car = 40,000

The value of car declines at the rate of 3% every year

function is represented as F(t)

F(t) = [tex]P( 1 - \frac{R}{100} )^{t}[/tex]

P is principal amount value of the car which is 40,000

R is rate at which it declines every year which is 3%

t is no. of year

Putting all the values in the equation we get

F(t) = [tex]40000(1-\frac{3}{100} )^{t}[/tex]

F(t) = [tex]40000(\frac{97}{100}) ^{t}[/tex]

F(t) = [tex]40000(0.97)^{t}[/tex]

The function represent the value of the hybrid car is [tex]40000(0.97)^{t}[/tex] .

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The area of the triangle is approximately 31.3049 square inches.

The area of a triangle can be found using the formula: A = (1/2)bh, where b is the length of the base of the triangle, and h is the height (or perpendicular distance from the base to the opposite vertex).

However, in this case, we don't have the height. Instead, we can use

Heron's formula, which only requires the lengths of the three sides of the triangle:

A = √[s(s-a)(s-b)(s-c)],

where a, b, and c are the lengths of the sides of the triangle, and s is the semiperimeter (half the perimeter):  s = (a + b + c)/2.

Using the given values, we have:

s = (7 + 9 + 12)/2 = 14

A = √[14(14-7)(14-9)(14-12)]

A = √[14(7)(5)(2)]

A = √(980)

A ≈ 31.3049 square inches

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Answer:

[tex]2( {3}^{x} ) = 258280326[/tex]

[tex] {3}^{x} = 129140163[/tex]

[tex]x = \frac{ ln(129140163) }{ ln(3) } = 17[/tex]

n = 17 + 1 = 18

[tex]s = \frac{2( 1 - {3}^{18} )}{1 - 3} = 387420488[/tex]

The sum of this finite geometric series is 387,420,488.

The closest value to the total cost of Francine's calls is $191.07

To find the total cost of Francine's calls, we need to know the total number of minutes she spent on the phone. We can calculate this by adding up the lengths of all 11 calls:

Total minutes = 11 + 14 + 12 + 20 + 25 + 16 + 11 + 22 + 18 + 19 + 15 = 193

The total cost of Francine's calls can then be found by multiplying the total number of minutes by the cost per minute:

Total cost = 193 * 0.99

= 191.07

Therefore, the closest value to the total cost of Francine's calls is $191.07.

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