Suppose that, in some distant part of the universe, there is a star with four orbiting planets . One planet makes a trip around the star in 6 earth years , the second planet takes 9 earth years, the third takes 15 earth years and the fourth takes 18 earth years . Suppose that at some time the planets are lined up. How many years will it take for them to all line up

Answer:

The answer to your question is: 48.6 ft

Step-by-step explanation:

See the picture below

Use the Thales's theorem to solve this exercise

                 x / 27 = 45 / 25

                 x = 45(27) / 25

                x = 1215 / 25

                x = 48.6 ft

Answer: 48.6

Step-by-step explanation:

((:

Answer:

  $2300

Step-by-step explanation:

The commission earned by the representative is ...

  commission = 0.02 × $15,000 = $300

so the total to be paid to the sales representative is ...

  salary + commission

  = $2000 +300 = $2300

Answer:

[tex]\frac{9x}{40}[/tex] is the answer.

Step-by-step explanation:

The question has some typo errors.

Rashid and Mikhail submitted a total of x pastries to a baking competition.

Suppose say :

Mikhail made x pastries .

Hence Rashid made [tex]\frac{2x}{3}[/tex] pastries.

And in total they made [tex]\frac{5x}{3}[/tex] pastries.

Now we have that out of x, [tex]\frac{5}{8}[/tex] of x were brushed with olive oil.

So, [tex]\frac{3}{8}[/tex] of x that is [tex]\frac{3x}{8}[/tex] are brushed by butter.

So, it becomes [tex](\frac{3}{8}) / ( \frac{5x}{3} )[/tex]

= [tex]\frac{3}{8} \times\frac{3x}{5}[/tex] = [tex]\frac{9x}{40}[/tex]

Hence, answer is option B.

Answer:

The rectangle is 16*18

Step-by-step explanation:

The area of a rectangle is length * width and the perimeter is 2 times length * width

A = l*w

P = 2(l+w)

Replacing A and P

288 = l*w

68 = 2(l+w) => 34 = l+w => 34 - w = l

replacing l in the area

288 = (34 - w) w

w^2 - 34w + 288 = 0

(w - 16)(w - 18)

w = 16

w = 18

replacing in 34 - w = l

you get that when w = 16, l = 18 and when w = 18, l = 16

Hello!

if he bought it with no interest applied, then the last payment will be $1400

1670 - 100 = 1570

if he has to pay it off in 18 months (1 and a half years), and only pays $10 per month, that means he will pay off $170 before the last payment is due.

1570 - 170 = 1400

so his last payment will have to be $1400 to pay it off completely

I hope this helps, and have a nice day!

$1,400 is the amount of his last payment.

1. First, determine the total amount Adam needs to pay after the down payment. Adam made a $100 down payment on the $1,670 system, so the remaining amount to be paid is:

[tex]\[ \text{Remaining amount} = \$1,670 - \$100 = \$1,570 \][/tex]

2. Next, calculate the total number of monthly payments Adam will make. Since he agreed to pay off the purchase in 1 and a half years, and there are 12 months in a year, the total number of payments is:

[tex]\[ \text{Total payments} = 1.5 \times 12 = 18 \text{ payments} \][/tex]

3. The minimum monthly payment is $10. To find out how much Adam will have paid after 17 payments (one less than the total number of payments), we multiply the monthly payment by the number of payments:

[tex]\[ \text{Amount paid after 17 payments} = 17 \times \$10 = \$170 \][/tex]

4. Now, subtract the amount paid after 17 payments from the remaining amount to find the last payment:

[tex]\[ \text{Last payment} = \$1,570 - \$170 = \$1,400 \][/tex]

Therefore, the amount of Adam's last payment will be $1,400.

Answer: Taylor, by 3.9 pp ($184.81)

Step-by-step explanation:

Marcus: Invested 80 x 74.19 = 5935.20

Taylor: Invested 65 x 85.21 = 5538.65

After 2 y

Marcus: Sold for 6404.57

Taylor: Sold for 6192.83

Net profit

Marcus: 6404.57 - 5935.20 = 469.37

Taylor: 6192.83 - 5538.65 = 654.18

ROI

Marcus: 469.37/5935.20 * 100 = 7.91%

Taylor: 654.18/5538.65 * 100 = 11.81%

Taylor had a higher ROI by 3.9 percentage points (11.81 - 7.91)

Answer:

G1=36,G2=12,G3=4,G4=4/3,G5=4/9

Step-by-step explanation:

Since the nth term is given by;

Gn= 36(1/3)^n-1, then, substitute the values of n as 1,2,3,4 and 5 to get the values of G1,G2,G3,G4 and G5 respectively.

G1=36(1/3)^1-1 = 36

G2= 36(1/3)^2-1= 12

G3= 36(1/3)^3-1 = 4

G4= 36(1/3)^4-1 = 4/3

G5= 36(1/3)^5-1=4/9

Answer:

36, 12, 4, 4/3, 4/9.

Step-by-step explanation:

We find each term by substituting the sequence number.

So the first term (where n = 1)

= 36(1/3)^(1-1)

=  36(1/3)^0

=  36 * 1

= 36.  

The second term is 36(1/3)^(2-1)  = 36 * 1/3

= 12.

We can  find subsequent terms by just multiplying the previous term by 1/3 so the third term = 12 * 1/3 = 4.

So the first 5 terms are   36, 12, 4, 4/3, 4/9.

Answer:

[tex]PT =-0.0005^2 +5x - 500[/tex]

Step-by-step explanation:

We have price (P) = [tex]-0.0002x + 9[/tex]

to calculate Total revenue (TR) we have to multiply Price by Production quantity.

[tex]TR=P * X[/tex]   , we denote production quantity with the letter X.

[tex] TR=(-0.0002x + 9)*x[/tex]  

We apply distributive law and then we have:

[tex] TR=-0.0002x^2 + 9x[/tex]  , this is the Total revenue (TR) of selling X amount of production at a P price.

Now we only have to find the Profit (PT) using the formula:

[tex]PT=TR - TC[/tex]  , TR is total revenue and TC is total cost

The expression of the daily profit (PT) for the manufacturer is:

[tex] PT=-0.0002x^2 + 9x - (0.0003x^2 + 4x + 500)[/tex]

[tex] PT= - 0.0002^2 + 9x -0.0003^2 -4x -500[/tex]

[tex]PT =-0.0005^2 +5x - 500[/tex]

The daily profit for the manufacturer, given by P, is equal to -0.0005x^2 + 5x - 500, where x represents the number of rackets manufactured and sold each day.

In this example, the manufacturer's daily profit, P, is given by the difference between the total revenue and the total cost. The total revenue is found by multiplying the price of each racket, p , by the number of rackets sold daily, x. i.e, px. The total cost is given by the equation 0.0003x^2 + 4x + 500. Thus, the daily profit is P = (px) - (0.0003x^2 + 4x + 500). Substituting the expression for p gives P = [(−0.0002x + 9)x] - (0.0003x^2 + 4x + 500), which simplifies to P = - 0.0002x^2 + 9x - 0.0003x^2 - 4x - 500. Further simplification leads to P = -0.0005x^2 + 5x - 500. Therefore, the daily profit for the manufacturer is given by P = -0.0005x^2 + 5x - 500.

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Answer:

PQ = 6 and QR = 7.5

Step-by-step explanation:

The lengths of the sides of two similar triangles are proportional. That is, if Δ ABC is similar to Δ PQR, then the following equation is established.

[tex]\frac{AC}{PR}=\frac{AB}{PQ}=\frac{BC}{QR}[/tex]

[tex]\frac{6}{9} = \frac{4}{PQ} = \frac{5}{QR}[/tex]

[tex]\frac{6}{9} = \frac{4}{PQ}[/tex]

PQ = 6

[tex]\frac{6}{9} = \frac{5}{QR}[/tex]

QR = 7.5

Answer:

c = 63

w = 85

Step-by-step explanation:

Since the 2 lines are parallels c is the same angle as 63 and w is the supplementary angle of 95

Answer:

[tex]2 = x[/tex]

Step-by-step explanation:

THIS IS CORRECT! These two angles are somewhat linear pairs, so you set both expressions equal to 180°:

[tex]180° = 52° + (2^{3x + 1})°[/tex]

- 52° - 52°

______________________

128° = [tex](2^{3x + 1})°[/tex]

7 = 3x + 1

-1 - 1

_______

[tex]\frac{6}{3} = \frac{3x}{3} \\ \\ 2 = x[/tex]

[tex]128° = [2^7]°[/tex]

I am joyous to assist you anytime.

Answer:

y = - 2x

Step-by-step explanation:

Given that x and y vary directly then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition x = - 5, y = 10, thus

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{10}{-5}[/tex] = - 2, hence

y = - 2x ← is the equation relating them

Final answer:

Juanita will arrive at her aunt's home around 3:00 pm after accounting for 5 hours and 20 minutes of driving time and a 40-minute break to her journey that began at 9:00 am.

Explanation:

The question is asking us to estimate the arrival time for Juanita who is traveling to her aunt's home 320 miles away. Juanita leaves at 9:00 am, drives at an average speed of 60 miles per hour, and plans to take a 40-minute break halfway through her trip.

To estimate the time it will take Juanita to reach her aunt's house, we need to calculate the driving time and add the time for the break.

The driving time is calculated by dividing the total distance by the average speed. The total driving time is 320 miles \'d'vided by' 60 miles per hour, which equals approximately 5.33 hours or 5 hours and 20 minutes of driving time.

Next, we add the 40-minute break to the driving time. Convert 40 minutes to hours by dividing by 60, which is approximately 0.67 hours or 40 minutes. Now, we sum the hours: 5 hours and 20 minutes driving + 40 minutes break = 6 hours total time spent.

Juanita left at 9:00 am, so we add the 6 hours to this time. Therefore, Juanita should arrive at her aunt's home around 3:00 pm.

Answer: B) 18.2 inches

Step-by-step explanation:

We know that the circumference of a circle is given by :-

[tex]\text{Circumference}=\pi d[/tex]

Given : Diameter of a circle = 5.8 inches

Then, the circumference of the circle will be :-

[tex]\text{Circumference}=(3.14)\times5.8=18.212\approx18.2\text{inches}[/tex]

Hence, the circumference of the circle = 18.2 inches

Answer:

Option B.

Step-by-step explanation:

It is given that diameter of the circle is 5.8 inches.

[tex]d=5.8[/tex]

Radius of the circle is

[tex]r=\dfrac{d}{2}=\dfrac{5.8}{2}=2.9[/tex]

We need to find the circumference of the circle.

Circumference of a circle is

[tex]C=2\pi r[/tex]

Substitute π= 3.14 and r=2.9 in the above formula, to find the circumference of the circle.

[tex]C=2(3.14)(2.9)[/tex]

[tex]C=18.212[/tex]

Round the answer to the nearest tenth.

[tex]C=18.2[/tex]

The circumference of the circle is 18.2 inches. Therefore, the correct option is B.

The common denominator is 42

Given,

5/6-2/7

Now,

Take LCM of 6 and 7 for obtaining the common denominator,

LCM of 6,7  

As 7 is a prime number and 6 is non prime number than there LCM is obtained by multiplying the two numbers .

Hence LCM  is  6* 7

LCM = 42

Now

Multiply the denominators 6 and 7

Hence the result will be,

35 - 12 /42

23/42 .

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Final answer:

To find the common denominator of 5/6 and 2/7, multiply each fraction by a factor that will give the least common denominator of 42, then subtract the resulting fractions with the same denominator.

Explanation:

To find the common denominator for the fractions 5/6 and 2/7, we need to determine a shared denominator that both original denominators can be multiplied into without changing the value of the fractions. Multiplication is the key technique to creating a common denominator. In this case, the least common denominator (LCD) is 42 because 6 and 7 have no common factors other than 1, and 6 times 7 equals 42. To transform these fractions, we multiply the numerator and denominator of each fraction by the number that will give us our LCD as the new denominator.

To calculate the difference using the LCD:

Multiply 5/6 by 7/7 to get 35/42.

Multiply 2/7 by 6/6 to get 12/42.

Now, subtract the two new fractions: 35/42 - 12/42 = 23/42.

It is essential to remember that we never add or subtract the denominators when combining fractions; we only combine the numerators after establishing a common denominator.

The expression (4 + 5i)(4 - 5i) simplifies to 41, as the multiplication of complex conjugates yields a real number.

The expression (4 + 5i)(4 - 5i) is a product of two complex conjugates. When multiplied, the product of complex conjugates results in a real number because the imaginary parts cancel out. The multiplication proceeds as follows:

Multiplying the real parts: 4 * 4 = 16.

Multiplying the outer terms: 4 * (-5i) = -20i (but this will cancel out with the next step).

Multiplying the inner terms: 5i*4 = 20i (which cancels out the -20i from the outer multiplication).

Multiplying the imaginary parts: 5i * -5i = -25[tex]i^2[/tex]. Remembering that i^2 = -1, we simplify this to -25 * -1 = 25.

Adding the results from steps 1 and 4, we get 16 + 25 = 41.

Therefore, the simplified expression is 41.

Answer:

The initial population P0 is 7500

Step-by-step explanation:

First of all, we are told that the population is proportional to time. This means that as time goes by, the population will increase. This type of relationship between two variables has the form of a linear equation expressed as:

y = mx + b,

where m is the slope of the curve and b is the intercept of it.

In this case we can state the following equation:

P = mt + P0

Where P is the population at a certain time "t", "m" is the slope of the curve, "t" is the time (this is the independent variable) and P0 is the intercept of the curve and represents the initial population.

Once we state the equation, let's see what we know:

If t = 0, then P = P0

If t = 3, then P = 12000 just as we are told

and if t = 5, then P = 2 P0 because after five years the population has doubled compared to the initial population (P0).

From the definition of the slope of the curve:

(Y2 - Y1)/(X2-X1) = m

and using the data described before we can formulate the slope value:

m = (2P0 - P0)/(5-0)

m = (2P0 - P0)/5

m = P0/5

Then, let's replace the value of m in the following equation:

P = mt + P0

12000 = (P0/5) × 3 + P0 → This is the equation presented when 3 years has gone by and we now have a population of 12000.

12000 = (3/5) P0 + P0

12000 = (8/5) P0

12000×5/8 = P0 = 7500

Then we can calculate the value of the slope m:

m = P0/5

m = 7500/5 = 1500

Now, knowing the value of m and the initial population P0 we are able to calculate the population at any value of "t".

Answer:

They all arrive at the station at the same time after 120 minutes.

Step-by-step explanation:

For solving these types of question we use Least Common Multiples (L.C.M.).

Since for getting a common time they will meet, we interested in a multiplier.

Now, We will take L.C.M. of all the numbers:

10 = 2 × 5

8 = 2 × 2 × 2

12 = 2 × 2 × 3

∴ L.C.M. = 2 × 2 × 2 × 3 × 5 = 120 {taking smallest common multiples)

Thus, they all lines will meet after 120 minutes.

Answer:

What we know is that 30% of the group have brown hair and are girls. It means that in the other 70% we have the boys with brown hair, the other boys and the other girls.

In the case all the girls have brown hair, the 70% remaining would be boys. So 70% of then would have brown hair. (0.7*0.7=0.49 -> 49% of the children would be brown hair) so 49% (boys) and 30% (girls) are more than 50%..

Now, let's suppouse that 90% of the group are girls. It means 10% are boys and 70% of that 10% (=7%) are the boys in the group that have brown hair. Now 7% + 30% of the children have brown hair, wich isn't more than the half.

We have explained with two extreme cases that the information is not enough for making a precise answer

Answer:

(a) The temperature at a specific location as a function of time.

This is a continuous function as the temperature cannot increase in an instant like time.

(b) The temperature at a specific time as a function of the distance due west from New York City.

This is a continuous function as the temperature in one location is affected by its neighboring places.

(c) The altitude above sea level as a function of the distance due west from New York City.

The altitude above sea level can be discontinuous at a cliff, or continuous at very deep hole.

(d) The cost of a taxi ride as a function of the distance traveled.

This is a discontinuous function as the cost still raises if you make a stop.

(e) The current in the circuit for the lights in a room as a function of time.

This is a discontinuous function as the function takes the value of 0 when the switch is off and 1 when the switch is on.

The electron traveling speed makes this discontinuous.

Final answer:

a) Continuous

b) Continuous

c) Continuous

d) Discontinuous

e) Continuous

Explanation:

In examining whether a function is continuous or discontinuous, we consider if there are any interruptions in the value of the function as the input changes. Here's an analysis for each given scenario:

A continuous probability function has been defined such that probability equals area under the curve of the function over an interval. For real-world phenomena like temperature and altitude, these functions tend to be continuous as they reflect gradual changes over time or distance.

Answer:

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If this is calculus AP the answer will be right

=73

you add both angles 56 and 51 then you compare it with the high of the rectangle 7.9 ft to get the answer.

Answer:

180h + 15h²

Step-by-step explanation:

Since both have same function i.e. function of f, so we simply put 6 + h and 6 in place of x in f(x)

Here,

f(x) = 15x² + 6

Then, f(6+h) - f(6)

= [15(6 + h )² + 6] - [15(6 )² + 6]

⇒ [15 (36 + 12h + h²) + 6] - [15 × 36 + 6]

⇒ [ 15 × 36 + 15 × 12h + 15h² + 6 - 15 × 36 - 6 ]

⇒ 15 × 12h + 15h²

⇒ 180h + 15h²

10(x/2 + 9) = 13

5x + 90 = 13

5x = 13 - 90

Can you do the rest?

Answer: a) 70%

b) 6%

c) 24%

d) and: 6%

   or: 66%

e) 46.2%

Step-by-step explanation:

Living on campus = 30%

Living off Campus = 70%

Living on campus with car = 20% of 30% = 0.2 x 0.3 = 0.06 = 6%

Living on campus w/o car = 80% of 30% = 0.8 x 0.3 = 0.24 = 24%

Living off campus with car = 60% of 70% = 0.6 x 0.7 = 0.42 = 42%

Living off campus w/o car = 40% of 70% = 0.4 x 0.7 = 0.28 = 28%

a) 70%

b) 6%

c) 24%

d) Student lives on campus and has an automobile: 6%

   Student lives on campus or has an automobile = 66%

living on campus 30%

students with car = 6% (on campus)  42% (off campus)

30 - 6 + 42 = 66

e) P (living on campus/not have a car) = P(living on campus w/o a car)/P(not have a car)

P(living on campus w/o a car) = 24

P(not have a car) = 24+28 = 52

P (living on campus/not have a car) = 24/52 = 0.462 = 46.2%

Answer:

y = 0.5x

Step-by-step explanation:

Given that x and y vary directly then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition x = 1, y = 0.5, then

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{0.5}{1}[/tex] = 0.5, hence

y = 0.5x ← equation of variation

Yes, the average speed for the entire trip from A to C is equal to 80 km/h.

Given

You travel from point A to point B in a car moving at a constant speed of 70 km/h.

You travel the same distance from point B to another point C, moving at a constant speed of 90 km/h.

The average speed is defined as the change in displacement and change in a time interval.

The formula is used to calculate average speed;

[tex]\rm Average \ speed= \dfrac{V_1+V_2}{2}[/tex]

Where [tex]\rm V_1[/tex] is 70 and [tex]\rm V_2[/tex] is 90.

Substitute all the values in the formula

[tex]\rm Average \ speed= \dfrac{V_1+V_2}{2}\\\\\rm Average \ speed= \dfrac{70+90}{2}\\\\\rm Average \ speed= \dfrac{160}{2}\\\\\rm Average \ speed= 80[/tex]

Hence, the average speed for the entire trip from A to C is equal to 80 km/h.

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Answer:

The answer to your question is:   F = (-6, -4)

Step-by-step explanation:

Segment = EF

mpM = (-2, 2)

first point = E = (2, 8)

second point = F = (x, y)

Formula

      Xmp = (x1 + x2) / 2                         Ymp = (y1 + y2) / 2

      x2 = 2xmp - x1                                y2 = 2ymp - y1

Process

     x2 = 2(-2) - 2                                   y2 = 2(2) - 8

     x2 = -4 - 2                                       y2 = 4 - 8

     x2 = -6                                            y2 = -4

                     F = (-6, -4)

The coordinates of the other endpoint of the line segment EF, given that the midpoint M is (-2,2) and the endpoint E is (2,8), are (-6,-4). This is determined by using the midpoint formula and solving for the remaining variables.

To find the coordinates of the other endpoint F, we apply the midpoint formula which is M ( (x₁ + x₂) / 2, (y₁ + y₂) / 2 ). Here, we have the midpoint M(-2,2) and one endpoint E(2,8).

It's like saying: (-2,2) = ( (2 + x₂) / 2, (8 + y₂) / 2 ).

To solve for x₂ (the x-coordinate of point F) and y₂ (the y-coordinate of point F), we will set up two separate equations based on the x and y coordinates.

For the x-coordinate, (-2) = (2 + x₂) / 2. Solve for x₂ gives x₂ = -2*2 - 2 = -6.

For the y-coordinate, 2 = (8 + y₂) / 2. Solve for y₂ gives y₂ = 2*2 - 8 = -4.

So, point F, the other endpoint of the line segment EF, has the coordinates (-6,-4).

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Answer:

A

Step-by-step explanation:

Option: A is the correct answer.

A.    There is a charge of $0.15 for each minute of use.

We know that the slope of the line of best fit represents the ratio of change in the dependent variable to the change in the independent variable.

Here the dependent variable is: Phone bill

and the independent variable is the number of minutes used.

Let the line of best fit passes through (100,60) and (300,90).

This means that the slope of the line of best fit is:

[tex]Slope=\dfrac{90-60}{300-100}\\\\Slope=\dfrac{30}{200}\\\\Slope=0.15[/tex]

Hence, the answer is: Option: A

Answer:

[tex]\frac{2}{5}*\frac{3}{5} +\frac{2}{5}*\frac{2}{5}+\frac{3}{5} *\frac{3}{5}  = \frac{19}{25}[/tex]

Step-by-step explanation:

We must remember that in order to get one even number we need to multiply one even number times one odd number or two even numbers. So, the first term tells the probability of having an even number from A and an even number from B, the next would be even from A and odd from B and the last one tells the likelihood of having odd from A and even from B

Answer:

  ₹30/cap

Step-by-step explanation:

To gain 15%, the dealer must have total revenue of ...

  ₹1500 × 1.15 = ₹1725

His revenue so far is ...

  15 × ₹35 +15 × ₹40 = ₹1125

There are 50 -15 -15 = 20 caps remaining, and the dealer wants additional revenue of ₹1725 -1125 = ₹600. He must sell them at a price of ...

  ₹600/(20 caps) = ₹30/cap