two fair dice are rolled. the score is the difference between the two dice. some of the possible scores are shown in the table.
c) which score has a probability of occurring 1/18

Answer:

1.67 hours

Step-by-step explanation:

Let the original speed of Jonathan = [tex]x[/tex] units/hr

Let the original time taken by Jonathan = [tex]y[/tex] hours

Let the distance = [tex]D[/tex] units

Formula for distance is given as:

[tex]Distance = Speed \times Time[/tex]

Given that half the distance is covered by original speed.

[tex]\Rightarrow \dfrac{D}{2} = \dfrac{x}{2}\times \dfrac{y}{2}\\\Rightarrow D = \dfrac{xy}{2} ..... (1)[/tex]

Half the distance is covered by increasing the rate by 25%.

i.e. increased speed:

[tex]\dfrac{5}{4}x\ units/hr[/tex]

Hence, Time taken:

[tex]\dfrac{y}{2}-\dfrac{1}{2}[/tex]

Distance traveled is half of the total distance:

[tex]\Rightarrow \dfrac{D}{2} = \dfrac{5x}{4}\times (\dfrac{y}{2}-\dfrac{1}{2})\\\Rightarrow D = \dfrac{5x}{2}\times (\dfrac{y}{2}-\dfrac{1}{2}) .... (2)[/tex]

Dividing (1) by (2):

[tex]\dfrac{xy\times 4}{2\times 5x(y-1)} = 1\\\Rightarrow 2y=5y-5\\\Rightarrow 3y=5\\\Rightarrow y =1.67\ hours[/tex]

Answer:

f(x)=18

Step-by-step explanation:

When it gives you f(3), it is basically telling you that you need to plug in 3 for x. Doing so would give you f(3)=6(3) and you can multiply 6 and 3 together to get 18.

Answer:

15

Step-by-step explanation:

120=8x-10

130=8x

15=x

Answer:

x=15

sorry that should be right now tho

Answer:

2

Step-by-step explanation:

1/5*10

Answer:

AC+CB=AB

Step-by-step explanation:

Let's see.... If you are a visual learner this could help.

[tex]A----------C---------------B[/tex]

So you can see that C is right in between them so the distance between AC and the distance between CB would equal the whole line AB. So if you add AC and CB you would get AB.

Full question attached

Answer attached

Answer and Step-by-step explanation:

We are asked to find the percentage of each asset or liability in total assets and liabilities. To find  percentage of each asset or liability in the balance sheet, we divide the asset or liability's value(from each year in the balance sheet)  by total assets and liabilities for that year and multiply by 100:

Answer:

60

Step-by-step explanation:

Let the original number be x.

According to the question we can write as (2/3)x+20x

On rearranging x−(2/3)x=20

Now taking the L.C.M od 1 and 3 is 3

(3x−2x)/3=20

x/3=20

Again by transposing x=60

So the original number is 60

Answer:

60

Step-by-step explanation:

Let the number be x

2/3 x = x -20

20 =x -2/3x

1/3 x =20

60 = x.

Answer:

See Below.

Step-by-step explanation:

1) Given:

[tex]3x+2y+7=5x+3y+10[/tex]

2) Subtraction Property of Equality (subtract 2y from both sides):

[tex]3x+7=5x+y+10[/tex]

3) Subtraction Property of Equality (subtract 5x from both sides):

[tex]-2x+7=y+10[/tex]

4) Subtraction Property of Equality (subtract 10 from both sides):

[tex]-2x-3=y[/tex]

5) Symmetric Property:

[tex]y=-2x-3[/tex]

6) Slope-intercept form:

[tex]y=mx+b\text{, where $m$ is slope and $b$ is y-intercept.}[/tex]

7) Substitution:

[tex]m=-2[/tex]

4 intersection points

Answer:

Confusion

Step-by-step explanation:

Answer:

£300.

Step-by-step explanation:

He has £900 left after paying rent.

The fraction he spends on bills = 3(4+3+2)

= 3/9

= 1/3.

So he spends 900 * 1/3 = £300 on bills.

Answer:

A. (-3, 2)

Step-by-step explanation:

First step is to revert the equation into y = mx  + b form.

-4x + 2y = 16 turns into y = 2x+8

Now just plug in the points given to see which one matches.

(-3,2) the x is -3 so if you plug that into the equation it should get you 2 which is the y.

2 = 2(-3) + 8

2 = 2

So we know that (-3, 2) is the solution.

If you plug in the other points they wont come out equal. For example, (4,-1)

-1 = 2(4) + 8

-1 = 16

So (4,-1) cant be a solution. The same thing applies for (2, -3).

Answer: $75

Step-by-step explanation:

Answer:

w greater than 2

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

The value of the expression of 2106÷162 can be calculated as follows

= 2106÷162

= 13

Hence the value of the expression 2106 ÷ 162 is 13

Answer:

a) 257/50 or 5.14

b) 657/100 or 6.57

c) 43/10 or 4.3

Step-by-step explanation:

Answer:

1the answer is 1! hope this helps.

The answer is x^2+ y^2-27

Answer:

(3-7)x or -4x depends on what your teacher is looking for

Answer:

1. A=1, B=4, C=9

2.A=5 B=6, C=-2

Replace y with 200 ( amount of water in the tank) and solve for x:

200 = 450 -20x

Subtract 450 from both sides:

-250 = -20x

Divide both sides by-20:

X = 12.5

The answer is A. 12.5 minutes

Answer: 948

Step-by-step explanation:

From the question, we are informed that 4-pound pumpkin will yield about 1.5 cups of mashed pumpkin (pumpkin puree).

Therefore, the number of cups of pumpkin puree that Steve Geddes' 2,528-pound pumpkin will yield will be:

= (2528/4) × 1.5

= 632 × 1.5

= 948 cups of pumpkin puree

Answer:

3200

Step-by-step explanation:

growth = current population + rate * time

            = 2000 * .04 * 15

            = 1200

original population + growth = total

2000 + 1200 = 3200

Answer:

a. The correct option is C. No, because you will probably have to pay for service and insurance with either plan.

b. The correct option is A.Yes, the total cost of the car at the end of the lease is $47,400.

c. The correct option is D. Not all of the money is needed up front and you have years to decide if you want to buy the car.

Step-by-step explanation:

Note: This question is not complete. The complete question is therefore given as follows:

You are deciding whether to buy a car for $21,000 or to accept a lease agreement. The lease entails a $800 fee plus monthly payments of $250 for 48 months. Under the lease agreement, you are responsible for service on the car and insurance. At the end of the lease, you may purchase the car for $9000. Complete parts a through c below.

a. Should the cost of service and insurance determine which option you choose?

A. Yes, because you probably don't have to pay for services when you buy the car.

B. No, because it is cheaper to lease the car than to buy it.

C. No, because you will probably have to pay for service and insurance with either plan.

D. Yes, because you get a discount on your insurance when you lease the car.

b. Does the total cost of purchasing the car at the end of the lease agreement exceed the cost of purchasing the car at the outset?

A.Yes, the total cost of the car at the end of the lease is $___ (fill in the blank)

B. No, the total cost of the car at the end of the lease is $___(fill in the blank)

c. What are some possible advantages of leasing the car?

A. You can sell the car whenever you want and you can make money on the car when you sell it.

B. The insurance costs less and you get a service discount.

C. You can give the car back whenever you want and you can get a new car whenever you want.

D. Not all of the money is needed up front and you have years to decide if you want to buy the car.

The explanation of the answer is now provided as follows:

a. Should the cost of service and insurance determine which option you choose?

No matter the option, wither buy or lease, that is chosen, the car will still have to be serviced and the insurance cost will have to be paid for. Therefore, the cost of service and insurance should not determine which option to choose.

Therefore, the correct option is C. No, because you will probably have to pay for service and insurance with either plan.

b. Does the total cost of purchasing the car at the end of the lease agreement exceed the cost of purchasing the car at the outset?

From part a above, it is stated that the cost of service and insurance should not determine which option to choose.  Therefore, the cost of service and insurance should not be included in calculating the total cost of purchasing the car at the end of the lease agreement.

This implies the only relevant costs to use in calculating the total cost of purchasing the car at the end of the lease agreement are the $800 monthly fee and the $9,000 cost of purchase at the end of the lease.

Therefore, the total cost of purchasing the car at the end of the lease agreement can be calculated as follows:

Total lease cost = (Monthly fee * Number of months) + Cost of Purchase = ($800 * 48) + $9,000 = $38,400 + $9,000 = $47,400

Therefore, the correct option is A.Yes, the total cost of the car at the end of the lease is $47,400.

c. What are some possible advantages of leasing the car?

Under a lease agreement, there is no need to pay all the money required to buy an item at once. The leasing of an item also enables one to examine the item in details to decide whether to buy it or not at the end of the lease agreement.

Based on the explanation above, the correct option is D. Not all of the money is needed up front and you have years to decide if you want to buy the car.

Answer:

The value of 11+x at x=12 will be 23.

Step-by-step explanation:

Given the expression

As we have to evaluate the expression at x=12

so substitute the value x=12 in the expression

[tex]11 + x[/tex]

[tex]=11+12[/tex]

[tex]=23[/tex]

Therefore, the value of 11+x at x=12 will be 23.

Answer:

f = 10·√3/3 ≈ 5.774

d = 5·√3/3 ≈ 2.887

Step-by-step explanation:

The given parameters are;

The angles opposite the 90°, right angle, = 60° and 30°

The length of the leg opposite the 60° angle = 5

Therefore, by Pythagorean Theorem, we have;

f² = d² + 5²

However, by trigonometry, we have;

sin(θ) = Opposite/Hypotenuse

For the angle of the triangle, θ = 30°, we have;

sin(30°) = d/f = 0.5

∴ d = f × 0.5 = 0.5·f

Substituting the value of d in the equation given by Pythagorean Theorem, we have;

f² = (0.5·f)² + 5² = 0.25·f² + 5²

f² = 0.25·f² + 5²

f² - 0.25·f² = 5²

0.75·f² = 5²

f² = 5²/0.75 = 100/3

f = 10/√3 = 10·√3/3

f = 10·√3/3

d = f × 0.5 = 10·√3/3 × 0.5 = 5·√3/3

d = 5·√3/3.

not tryna be rude but theres no map

Step-by-step explanation:

a) The three figures are 480 km, 240 km, and 300 km.

b) Kenzi has driven 60 km further than Jafar.

We have,

a)

The three figures bearing B from A are:

1 cm = 200 km

This means,

AB = 2.4 cm

So,

2.4 x 200 = 480 km

And,

BC has two parts:

1.2 cm and 1.5 cm

1.2 cm x 200 km = 240 km

1.5 x 200 km = 300 km

The three figures are 480 km, 240 km, and 300 km.

Now,

Jafar distance.

= AB

= 480 km

Kenzi distance.

= BC

= 240 km + 300 km

= 540 km

The difference between the distance driven.

= 540 km - 480 km

= 60 km

This means,

Kenzi has driven 60 km further than Jafar.

Thus,

The three figures are 480 km, 240 km, and 300 km.

Kenzi has driven 60 km further than Jafar.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ4

Answer:

B. (5x - 4)(3x + 2)

Step-by-step explanation:

Factor the following:

[tex] \longrightarrow [/tex] 15x² - 2x - 8

The coefficient of x² is 15 and the constant term is -8. The product of 15 and -8 is -120. The factors of -120 which sum to -2 are 10 and -12.

So,

[tex] \longrightarrow [/tex] 15x² + (10 - 12)x - 8

[tex] \longrightarrow [/tex] 15x² + 10x - 12x - 8

[tex] \longrightarrow [/tex] 5x(3x + 2) - 4(3x + 2)

[tex] \longrightarrow [/tex] (5x - 4)(3x + 2)

Answer:

3 students

Step-by-step explanation:

Twice as many students go to the park than to the theater :

Let number who go the theater = t

Number who goes to park = 2t

5 more students go to the theater than to the museum

Number who goes to museum = t - 5

If number of students who goes to park = 16

How many students goes to the museum :

2t = 16

t = 16/2

t = 8

Number who goes to museum = t - 5

t - 5 = 8 - 5 = 3

Hence, number of students who goes to the museum = 3