A dealer bought 50 caps for Rs 1500. He sold 15 for Rs. 35 each and 15 for Rs. 40 each. At what price per cap should he sell the remainder to gain 15% on his outlay?

Answer:

  5(x -3)

Step-by-step explanation:

The GCF of 5 and 15 is 5, since 5 is a factor of 15. Factoring that out gives ...

  5x -15 = 5(x -3)

10(x/2 + 9) = 13

5x + 90 = 13

5x = 13 - 90

Can you do the rest?

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:

Step-by-step explanation:

Let w represent the width of the rectangle. The perimeter is twice the sum of length and width so is ...

  P = 2(L + w) . . . . . . equation for perimeter

  66 = 2((5w-3) +w) . . . substitute the given values

  33 = 6w -3 . . . . . . . divide by 2 and collect terms

  36 = 6w . . . . . . . . . add 3

  6 = w . . . . . . . . . . . .divide by 6

  L = 33-6 = 27

The length is 27 inches; the width is 6 inches.

The plywood needed for 15 strips is 20.5 inches.

[tex]\rm 1\dfrac{1}{4}\ inches = \dfrac{(4 \times 1) +1 }{4} =\dfrac{5}{4}\ inches[/tex]

As to cut 15 strips of plywood a total of 14 cuts will be needed.

therefore, the waste of plywood in these 14 strips will be

= Lost in each cut x Number of cuts

[tex]=\dfrac{1}{8}\times 14\\\\=\dfrac{14}{8}\\\\ = \dfrac{7}{4} inches[/tex]

Total plywood needed for all single strip

                        = width of the strip x number of strips

                        [tex]=\dfrac{5}{4} \times 15\\\\ =\dfrac{75}{4}\\\\[/tex]

Plywood needed

= Total plywood needed for all strip +  Total waste of plywood

[tex]=\dfrac{7}{4}+\dfrac{75}{4}\\\\=\dfrac{82}{4}\\\\=20.5\ \rm inches[/tex]

Hence, the plywood needed for 15 strips is 20.5 inches.

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Answer:

0.2983

Step-by-step explanation:

Let X be the reading on thermometer.  Given that X is N(0,1)

We are to find the probability that a randomly selected thermometer reads between negative 0.12 and 1.02

Reqd probability = [tex]P(0.12<x<1.12)[/tex].

Since this x is already normal std variable x=z

i.e. reqd prob = [tex]P(0.12<z<1.02) =0.3461 -0.0478\\=0.2983[/tex]

Hence answer is 0.2983

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:

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

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:

$528.12

Step-by-step explanation:

499-10

489×1.08= 528.12

Answer:

The final cost is $115.74.

Step-by-step explanation:

Total amount of 30 days with tax = [tex]499+(0.08\times499)[/tex] = 538.92 dollars

This value is for 30 days, and its prorated for 7 days, so value for 7 days is =

[tex]\frac{538.92}{30}\times7[/tex] = 125.74 dollars

And $10 is off, so final cost is [tex]125.74-10=115.74[/tex] dollars

(Suppose the discount coupon is applied at the end of billing)

The final cost is $115.74.

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: The answer is d.

Step-by-step explanation: Ok, so, we know that we have 3 radio stations, each one has a 30% chance of broadcasting a song that leo likes.

Lets see the cases:

Station A has a probability of 0.30 to broadcast a song, but let's suppose that it doesn't, then we go to station B, who has te same probability, 0.30, but for this to happen, we first must have the 0.70 prob of A to broadcasting another song, so here we have a probability of (0.30)*(0.70).

Now with a similar way of thinking, if Station B also fails, we will have a probability of 0.70*0.70*0.30 for Station C succes.

Also, there is the case were station A broadcast the nice song, which we already know that is with probability of 30%.

So, the total probability will be the sum of the 3 cases: 0.30 + 0.30*0.70 + 0.30*0.70*0.70 = 0.657.

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.

Mary has $37, Erin has $111, and John has $119 and together they have $267 .

1. Mary has a third of the money that Erin has. Let's represent the amount of money Mary has as "m" and the amount Erin has as "e."

Based on the information given, we can write the equation:

m = (1/3)e

2. Erin has $8 less than John. Let's represent the amount Erin has as "e" and the amount John has as "j."

Based on the information given, we can write the equation:

e = j - 8

3. Together they have $267. This means the total amount of money they have is the sum of what Mary, Erin, and John have:

m + e + j = 267

Now, let's substitute the values we know into the equations to solve for the unknowns.

From equation 1, we have m = (1/3)e. Substituting this into equation 3, we get:

(1/3)e + e + j = 267

To simplify the equation, let's multiply all terms by 3 to eliminate the fraction:

e + 3e + 3j = 801

4e + 3j = 801

From equation 2, we have e = j - 8. Substituting this into the above equation, we get:

4(j - 8) + 3j = 801

Simplify and solve for j:

4j - 32 + 3j = 801

7j - 32 = 801

7j = 801 + 32

7j = 833

j = 833 / 7

j = 119

Now that we know the value of j (which represents the amount John has), we can substitute it back into equation 2 to find the value of e (the amount Erin has):

e = j - 8

e = 119 - 8

e = 111

Finally, we can substitute the values of e and j into equation 1 to find the value of m (the amount Mary has):

m = (1/3)e

m = (1/3)111

m = 37

So, Mary has $37, Erin has $111, and John has $119.

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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:

Probability of winning the game: 1/10000

Step-by-step explanation:

The nominator in the only outcome possible for you to win the bet. So that would be your only selected fourdigit number.

The denominator is the total possibles outcomes. If the first posible number is 0000 and the last number is 9999. There are a total of 10000 possible outcomes that the selected number is drawn.

The general rule is [tex]\frac{p}{q}[/tex]

Where p are the draws where i win.

And q is the total population of possible numbers.

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:

c. 4 - 12x.

Step-by-step explanation:

-6(-2/3 + 2x)

Using the distributive law:

= -6*-2/3 - 6*2x

=  12/3 - 12x

= 4 - 12x.

Answer:

4-12x

Step-by-step explanation:

multiply each term by -6

-6 × (2/3)

reduce the numbers with the greatest common divisor 3

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:

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]n=3,587\ units[/tex]

Step-by-step explanation:

we know that

The term Break even is when the Revenue is equal to the Cost (the profit is equal to zero)

so

we have

[tex]C=15n+269,000[/tex]

[tex]R=95n[/tex]

Equate the equations

[tex]95n=15n+269,000[/tex]

Solve for n

[tex]95n-15n=269,000[/tex]

[tex]75n=269,000[/tex]

[tex]n=3,587\ units[/tex]

Answer:

It’s C, 3363

Step-by-step explanation:

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)

The greatest number of identical arrangements that can be made using only the carnations and asters with no flowers left over is 6

.

The greatest number of identical arrangements that can be made using only the lilies and daffodils with no flowers left over is

12

ANSWER:

-6

-12

STEP-BY-STEP EXPLANATION:

The greatest number of identical arrangements that can be made using only the carnations and asters with no flowers left over is 6

The greatest number of identical arrangements that can be made using only the lilies and daffodils with no flowers left over is 12

Answer:

The common ratio r = 2.

Step-by-step explanation:

Now s2 = a1r and s4 = a1r^3  where a1 = first term and r = common ratio so

s4 / s2 = a1r^3  / a1r = r^2 = 32/8

r^2 = 4

r = 2.

Hey!

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

Answer:

r = 2

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

Solution:

So we know that s2 = 8 and s4 = 32.

We need to find s1!

32 / 8 = 4

8 / 4 = 2 (ratio is 2)

8 / 2 = 4

32 / 2 = 16

s1 = 4

s3 = 16

Each number is multiplied by 2.

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

Hope This Helped! Good Luck!

Answer:

The answer to your question is: 4

Step-by-step explanation:

         first day          second day         third day

              2                        6                         10

                                                              represent them considering number two

              2                   2 + 4                   2 + 8

                                                            Here, we can notice that the increase

                                                           from day 1 to day 2 was 4 and the

                                                           increase from day 2 to three was also 4

                                                           then the slope will be 4.

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:

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

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.

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:I would rather be playing Minecraft

Step-by-step explanation:

I like Minecraft

Answer:

Step-by-step explanation:

First of all we need to find the proportion of the sample. To do that, we sum all the books and then divide by the sample we need, which is 50

[tex]\frac{50}{235+290+166} =\frac{50}{691}[/tex], because we need 50 books among 691 total.

Now, with this ratio, which is the same for all sample we would make here, we find the stratified sample of books, specifically, for sports books which are 290.

[tex]s=290 \times \frac{50}{691}\\ s \approx 21[/tex]

Thefore, she should take 21 sports books.

Remember that stratified sampling refers to a type of sampling method where the population is divided into separate groups, which in this case represented the type of books. Then, we use a "probability" sample, or a proportion of the sample to apply it.