earth is approximately 9 x 10^7 miles from the sun. neptune is approximately 3x10^9 miles from the sun. neptune is approximately _____ times farther from the sun than earth

Answer:

7) 7/2 (its the only number between 3 and 4)

8) 7/10 ( its the only number between 3/5 and 4/5)

9) 5/8 (its the only number between 1/2 and 3/4)

Answer:

9/16

is already in the simplest form. It can be written as 0.5625 in decimal form (rounded to 6 decimal places).

Step-by-step explanation:

The interest Raymond will pay this month is $54.98

What does APR mean?

APR means annual percentage rate, which means that since we are computing monthly interest, the annual rate which is the whole 12 months needs to be divided by 12 to ascertain the equivalent monthly interest rate

monthly interest=21.99%/12

What is the monthly interest amount in dollars?

The monthly interest amount in dollars is determined as the monthly interest rate multiplied by the credit card balance at the end of the month

monthly interest=$3,000*21.99%/12

monthly interest=$54.98

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Answer:

9514 1404 393

Answer:

 $67,200

Step-by-step explanation:

The amount if interest is given by the formula ...

I = Prt

where P is the amount invested, r is the annual rate, and t is the number of years. Here, we want to find P when r = 0.05 and t = 1/2 such that I = 1680.

 P = I/(rt) = $1680/(0.05·0.5) = $1680/0.025

 P = $67,200

The amount invested was $67,200.

Step-by-step explanation:

Answer:

325

Step-by-step explanation:

Notice you are adding 7 everytime.

So the sequence would be:

a(n) = 10 + 7n

n=0 gives a(0)=10, which is the first term.

so the 46th term has n=45.

a(45)=10 + 7*45=325

Answer:

325

Step-by-step explanation:

since the series have the same common difference(d) is known as arithmetic progression so 46th is obtained by 46th=1term+45d but d is obtainned by taking difference between 1st and 2nd term or 2nd and 3rd term and 1st term=10

The cost of admission to the library for each student will be $0.3125. And the admission cost of the zoo will be $156.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Mrs. Hudson's class of 18 understudies is going to the zoo. Every understudy will pay for confirmation and purchase lunch. Mr. Weaver's class of 24 understudies is going to the library. Every understudy will pay for affirmation and pay for transport passage.

Let 'x' be the cost of admission to the library for each student. Then the equation is given as,

$7.50 + $8.25 × 18 + $5.75 × 18 = 24x + $10.50 × 24

Simplify the equation, then we have

$7.50 + $8.25 × 18 + $5.75 × 18 = 24x + $10.50 × 24

$7.50 + $148.5 + $103.5 = 24x + $252

$259.5 - $252 = 24x

x = $0.3125

And the admission cost of the zoo will be given as,

⇒ $7.50 + $8.25 × 18

⇒ $156

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The amount that would be in the account when Alana is 21  is $2890

We have to know the formula for simple interest.

This is expressed as;

S.I = PRT/100

Given that the parameters of the formula are enumerated as;

From the information given, substitute the values, we have;

SI = 1000 × 9 × 21/100

Multiply the values,

Then, divide by the denominator, we have;

SI = $1890

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Answer:

Please read the complete answer below!

Step-by-step explanation:

You have the following function:

\(f(x)=x^3-3x^2-9x+4\)   (1)

a) To find the interval on which f is increasing or decreasing, you first calculate the critical points of f(x).

You calculate the derivative f(x) respect to x:

\(\frac{df}{dx}=3x^2-6x-9\)    (2)

Next, you equal the derivative to zero, and then you find the roots of the polynomial by using the quadratic formula:

\(3x^2-6x-9=0\\\\x_{1,2}=\frac{-(-6)\pm\sqrt{(-6)^2-4(3)(-9)}}{2(3)}\\\\x_{1,2}=\frac{6\pm12}{6}\\\\x_1=-1\\\\x_2=3\)

Then, the critical points are x=-1 and x=3

Next, you calculate df/dx for a values of x to the left and to the right of the critical points x1 and x2. If df/dx < 0 the function is decreasing, if df/dx > 0 the function is increasing.

for x = -1.01

\(\frac{df(-1.01)}{dx}=3(-1.01)^2-6(-1.01)-9=0.12\)

Then, in the interval (-∞,-1), the function is increasing

for x = -0.99

\(\frac{df(-0.99)}{dx}=3(-0.99)^2-6(-0.99)-9=-0.11\)

In the interval (-1,3) the function is decreasing

for x = 3.01

\(\frac{df(3.01)}{dx}=3(3.01)^2-6(3.01)-9=0.12\)

In the interval (3,+∞) the function is increasing

b) To find the local minimum and maximum you use the second derivative of the function:

\(\frac{d^2f}{dx^2}=6x-6\)     (3)

you evaluate the second derivative for the critical points x1 and x2, if the second derivative is positive, you have a local minimum. If the second derivative is negative, you have a local maximum:

for x1 = -1

\(6(-1)-6=-12<0\)

x=-1 is a local maximum

for x2 = 3

\(6(3)-6=12>0\)

x=3 is a local minimum

c) upward concavity: (-1,3)

downward concavity: (-∞,-1)U(3,+∞)

The inflection points are calculated with the second derivative equal to zero:

\(6x-6=0\\\\x=1\)

For x = 1 you have an inflection point

Answer: 5

Step-by-step explanation:

First of all, keep in mind that absolute value of any real number (positive and negative) is always positive because it stands for the distance from zero, and distance will never be negative.

         i.e. |x|=x, |-x|=x

-------------------------------------------

 |-9|-|-4|

=9-4

=5

Hope this helps!! :)

Answer:

\(\huge \boxed{5}\)

Step-by-step explanation:

\(|-9|-|-4|\)

Apply rule : \(|-a|=a\)

\(9-4\)

Subtract.

\(=5\)

Answer:

To calculate the total amount payable under a hire purchase agreement, we need to add up the deposit and all the instalments.

The deposit is given as 80,000.

The number of instalments over the three-year period is:

3 years x 12 months/year = 36 months

So, the total cost of the car under the hire purchase agreement is:

80,000 + (2,500 x 36) = 170,000

To determine how much more the hire purchase price is than the cash price, we can subtract the cash price from the hire purchase price:

170,000 - 300,000 = -130,000

So, the hire purchase price is 130,000 less than the cash price. This means that the cash price is 130,000 higher than the hire purchase price.

The correct answer is 3/2. In this case, x = 3/2, and its square, (3/2)^2 = 9/4, is rational. x satisfies the given condition.option (c)

To explain further, we need to understand the properties of rational and irrational numbers.

A rational number can be expressed as a fraction of two integers, while an irrational number cannot be expressed as a fraction and has non-repeating, non-terminating decimal representations.

In the given options, (a) √5102.0 (£) and (b) √2 are both irrational numbers.

Their squares, (√5102.0)^2 and (√2)^2, would also be irrational, violating the given condition. On the other hand, (d) 4/5 is rational, and its square, (4/5)^2 = 16/25, is also rational.

Option (c) 3/2 is rational since it can be expressed as a fraction. Its square, (3/2)^2 = 9/4, is rational as well.

Therefore, (c) 3/2 is the only option where x is rational, but its square is irrational, satisfying the condition mentioned in the question.

In summary, the number x that satisfies the given condition, where x^2 is irrational but x is rational, is (c) 3/2.option (c)

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Answer:

44 862,07

Step-by-step explanation:

SUM=21000*(1+8,8/100)^9

SUM=21000*(108,8/100)^9

SUM=44862,07

Answer: We need we need 10 pints of the second fruit juice (85% pure fruit juice). Therefore, we need

(60-10 = 50) pints of the first fruit juice (55% pure fruit juice).

Step-by-step explanation:

Let x be number of pints of the first fruit drink which is ( 55% pure fruit juice), while y will be the number of pints of second fruit drink (85% pure fruit juice).

We know that there are 60 total pints. Therefore:

x + y = 60

We also know that 60% of the 60 pints will be pure fruit juice, and the pure fruit juice will either come from

x or y.

For x pints of first juice, there is 0.55x pure fruit juice while for y pints of first juice, there is 0.85y pure fruit juice. Therefore, we get:

0.55x + 0.85y = 60 × 0.6

0.55x + 0.85y = 36

We will get rid of the decimals by multiplying through by 100. This will be:

55x + 85y = 3600

Combining both equations

x + y = 60 .......... i

55x + 85y = 3600 ........ ii

Multiply equation i by 55

Multiply equation ii by 1

55x + 55y = 3300

- 55x + 85y = 3600

Then subtract

-30y = -300

y = 10

Therefore, we need we need 10 pints of the second fruit juice (85% pure fruit juice). Therefore, we need

(60-10 = 50) pints of the first fruit juice (55% pure fruit juice).

The required probability of the random event is 0.273.

Keep in mind that a president, vice president, and treasurer will be chosen at random from the 15 members. The number of options to choose from to fill these spots is thus:

\(_{15}P_3=\frac{15!}{(15-3)!} =2730\).

The required probability of the random event is 0.273.

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Answer:

-116/37

Step-by-step explanation:

Answer:

z = -3.1

Step-by-step explanation:

just divide both sides by -3.7, you get z = -3.135

A function is a relationship that maps each member of a set of input values into only one member of the set of output values

The correct response values are as follows:

(a) At 470 miles per hour, the cost is approximately $189.48 per passenger

At 590 miles per hour, the cost is approximately $191.9 per passenger

(b) The domain of the function C is 0 < x ≤ ∞

(c) Please find attached the required graph of the function C = C(x)

(d) The table with TblStsart = 0 and Tbl = 50 is included in the following solution

(e) The ground speed that minimizes the cost per passenger is 500 miles per hour

The reason the above values are correct is as follows:

The known parameters are:

The length of the Atlantic ocean the airplane crosses = 3,000 miles

The airspeed with which the airplane crosses the Atlantic ocean = 500 mi/hr

The given function that gives the cost per passenger is presented as follows;

\(C(x) = \mathbf{50 + \dfrac{x}{7} + \dfrac{34,000}{x}}\)

Where x is the ground speed of the airplane = airspeed ± windspeed

(a)  Required:

(i) The cost when the ground speed is 470 miles per hour

Solution:

\(The \ cost \ \mathbf{ C(470)} = 50 + \dfrac{470}{7} + \dfrac{34,000}{470} \approx \mathbf{ 189.48}\)

The cost C, when the ground speed is 470 miles per hour is approximately $189.48 per passenger

(ii)  The cost when the ground speed is 590 miles per hour

Solution:

\(The \ cost \ \mathbf{ C(590)} = 50 + \dfrac{590}{7} + \dfrac{34,000}{590} \approx \mathbf{ 191.9}\)

The cost C, when the ground speed is 590 miles per hour is approximately $191.9 per passenger

(b) Required:

To find the domain of C

Solution:

The domain of a function is given by the values of the function for which the function is defined, or possible, or for which there is an output

Given that the independent variable, x, is a denominator, we have that the function is not defined (Does not exist) at x = 0

The domain of the function C is 0 < x ≤ ∞

c) Required:

Graph the function using a graphing calculator

Solution:

Please find attached the required graph of the function created with MS Excel

(d) Required:

(i) To create a TABLE of values for the groundspeed with TblStsart = 0 and Tbl = 50

Solution:

Please find the required TABLE as follows

\(\begin{array}{|c|cc|}Airspeed&&Cost \ C\\0&&Does \ Not \ Exist\\50&&737.14\\100&&404.29\\150&&298.1\\200&&248.57\\250&&221.71\\300&&206.19\\350&&197.14\\400&&192.14\\450&&189.84\\500&&189.43\\550&&190.39\\600&&192.38\\650&&195.16\end{array}\right]\)

(e) Required:

To find the required ground speed that gives the minimum cost per passenger

Solution:

By differentiation, we get;

\(\dfrac{d\left( 50 + \dfrac{x}{7} + \dfrac{34,000}{x}\right)}{dx} = \dfrac{7 \cdot x(2 \cdot x+350)-7 \cdot \left(x^2+350 \cdot x +238000\right)}{(7 \cdot x)^2} = 0\)

Which gives;

7·x² - 1666000 = 0

7·x² = 1666000

x = √(1666000/7) ≈ 487.85

Therefore, to the nearest 50 miles per hour;

The ground speed that minimizes the cost per passenger is 500 miles per hour

Please find response summary at the top

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Answer:

c

Step-by-step explanation:

100% on edge

Answer:

:)

Step-by-step explanation:

ta da, hope this is what you're looking for

Answer:

0.75x+3

Step-by-step explanation:

Using polynomial division, it is found that the expression that represents the amount of candy sold each year per type at Cassandra's Candy Corner is:

\(2x^2 - 5x + 52\)

The amount of candy sold per type is given by the following division:

\(\frac{C(x)}{T(x)} = \frac{4x^3 + 10x^2 + 54x + 520}{2x + 10}\)

The denominator can be written as:

\(2x + 10 = 2(x + 5)\)

At the numerator, to see if we can simplify, we verify if x = -5 is a factor:

\(C(-5) = 4(-5)^3 + 10(-5)^2 + 54(-5) + 520 = 0\)

Since C(-5) = 0, it is a factor of the numerator, and thus, since the numerator is of the 3rd degree, it can be written as a 3 - 1 = 2nd degree polynomial multiplying x + 5:

\((ax^2 + bx + c)(x + 5) = 4x^3 + 10x^2 + 54x + 520\)

\(ax^3 + (5a + b)x^2 + (5b + c)x + 5c = 4x^3 + 10x^2 + 54x + 520\)

Equaling both sides:

\(a = 4\)

\(b = 10 - 5a = -10\)

\(5c = 520 \rightarrow c = 104\)

Thus:

\(C(x) = (4x^2 - 10x + 104)(x + 5)\)

And:

\(\frac{C(x)}{T(x)} = \frac{(4x^2 - 10x + 104)(x + 5)}{2(x + 5)} = 2x^2 - 5x + 52\)

Thus, the expression is:

\(2x^2 - 5x + 52\)

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$8.11 was the percent increase in the median monthly rent prices from 2000 to 2003.

What is a linear equation in mathematics?

A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.

                         Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.

2000 = $602

2003  = $651

               = 651 - 602/602  * 100

                = $8.11

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To find the value of r

We will follow the steps below

Usinf the equation of a slope:

slope(m) =

from the question given;

m= -3/4

x₁ = 3

y₁=4

x₂=-1

y₂=r

substituting the values into the slope formula

we can now simplify and then solve for r

cross-multiply

-3 x -4 = 4(r-4)

12 = 4(r-4)

Divide both-side of the equation by 4

3 = r - 4

add 4 to both-side of the equation

3+4 = r-4+4

7 = r

r=7

Therefore the value of r is 7

Answer:

5 1/2 x 1/3 = 11x/6

a. Monthly payment for the bank's car loan is $407.67

b. Monthly payment for the savings and loan association's car loan is $315.99

c. Total amount paid would be $2,035 less for the bank's car loan than for the savings and loan association's car loan.

The cost of borrowing money, usually expressed as a percentage of the amount borrowed, is what a lender charges a borrower to use their money. This cost is known as an interest rate.

(a) To find the monthly payment for the bank's car loan, we can use the formula for the present value of an annuity:

\(PV = PMT * \frac{1 - (1 + \frac{r}{n})^{(-n*t)}}{\frac{r}{n} }\)

putting the given values,

⇒ \(21000 = PMT * \frac{1 - (1 + \frac{0.065}{12})^{(-12*5)}}{\frac{0.065}{12} }\)

Solving for PMT, we get:

PMT = $407.67

Therefore, the monthly payment for the bank's car loan is $407.67

(b) To find the monthly payment for the savings and loan association's car loan, we can use the same above formula:

where PV is still $21,000, PMT is the monthly payment, r is still 0.065, n is still 12, but t is now 7 years x 12 months/year = 84 payments.

putting the given values,

\(21000 = PMT * \frac{1 - (1 + \frac{0.065}{12})^{(-12*7)}}{\frac{0.065}{12} }\)

Solving for PMT, we get:

PMT = $315.99

Therefore, the monthly payment for the savings and loan association's car loan is $315.99.

(c) Bank's car loan: $407.67 x 60 = $24,460.20

Savings and loan association's car loan: $315.99 x 84 = $26,495.16

Therefore, the bank's car loan would have the lowest total amount to pay off, by: $26,495.16 - $24,460.20 = $2,034.96

Therefore, the total amount paid would be $2,035 less for the bank's car loan than for the savings and loan association's car loan.

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Answer:

  x = 3

Step-by-step explanation:

The side ratios of an isosceles right triangle are ...

  1 : 1 : √2

  AB : BC : AC

  = 1 : 1 : √2

  = 6 : 6 : 6√2   ⇒   BC = 6

The side ratios of a 30°-60°-90° right triangle are ...

  BD : DC : BC

  = 1 : √3 : 2

  = 3 : 3√3 : 6

  BD = x = 3