A lost tourist arrives at a point with 2 roads A and B. Road A leads to the city and takes either 4 or 8 hours, depending on traffic, with equal probability. Road B brings him to the city after 7 hours on average. Since there are no signs on the road, the tourist chooses a road with equal probability; what is the expected time until the tourist arrives to the city

Answer

8. b

9.C

10.a

11.a

12. c

13. b

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The solution for each system of equations is given as follows:

1) x = -4, y = -8.

2) x = 5, y = -1.

3) x = -7, y = 2.

4) No solution.

5) x = 2, y = -6.

6) x = -3, y = 4.

The system of equations are solved using the elimination method, writing  one variable as a function of another, replacing in the other equation, and then obtaining each variable.

For item 1, we eliminate x, as follows:

x = 12 + 2y.

Hence the solution for y is obtained as follows:

5(12 + 2y) + 3y = -44

60 + 10y + 3y = -44

13y = -104

y = -104/13

y = -8.

Then the solution for x is given as follows:

x = 12 + 2y = 12 + 2(-8) = -4.

For item 2, we have that:

y = 19 - 4x.

Hence:

7x - 2(19 - 4x) = 37

7x - 38 + 8x = 37

15x = 75

x = 5.

Hence the solution for y is of:

y = 19 - 4(5) = -1.

For item 3, we can simplify the second equation by two, hence:

-x + y = 9.

y = 9 + x.

Hence:

3x + 8(9 + x) = -5

3x + 72 + 8x = -5

11x = -77

x = -7.

Hence the solution for y is of:

y = 9 - 7 = 2.

For item 4, we have that:

x = 7 + 3y.

Hence:

2(7 + 3y) - 6y = 12

14 + 6y - 6y = 12

0y = -2. (no solution, division by zero).

For item 5, we have that:

y = -2 - 2x.

Hence:

5x + 3(-2 - 2x) = -8

5x - 6 - 6x = -8

-x = -2

x = 2.

Hence the solution for y is of:

y = -2 - 2(2)

y = -6.

For item 6, we simplify the second equation by two, hence:

2x + y = -2

y = -2 - 2x.

Replacing on the first equation, we have that:

2x + 5(-2 - 2x) = 14.

2x - 10 - 10x = 14

-8x = 24

8x = -24

x = -3.

Hence the solution for y is obtained as follows:

y = -2 - 2(-3)

y = -2 + 6

y = 4.

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Answer:

z = 450 - 135

z + 135 = 450

Step-by-step explanation:

Han's house is 450 meters from school. Lin's house is 135 meters closer than Han's house from school. So,

450 - 135 = 315 <-- equation to look for

Lin's house is 315 meters from school.

The kilogram of fruits sold each day are 135 kg, 110 kg and 70 kg

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

Day 2 = Day 1 - 25

Day 3 = 2/7 * (Day 1 + Day 2)

Total weights = 315

Next, we use the following representations

x = Day 1, y = Day 2 and z = Day 3

So, we have the following equations

y = x - 25

z = 2/7(x + y)

x + y + z = 315

Substitute y = x - 25 in z = 2/7(x + y) and x + y + z = 315

z = 2/7(x + x - 25) = 2/7(2x - 25)

x + y + z = 315 ⇒ x + x - 25 + z = 315

So, we have

z = 2/7(2x - 25)

2x + z = 340

Substitute z = 2/7(2x - 25) in 2x + z = 340

2x + 2/7(2x - 25) = 340

So, we have

7x + 2x - 25 = 1190

Evaluate the like terms

9x = 1215

Divide by 9

x = 135

So, we have

y = x - 25 = 135 - 25 = 110

z = 2/7(x + y) = 2/7 *(135 + 110) = 70

Hence, the amounts are 135 kg, 110 kg and 70 kg

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On solving the expression for (y), we get two possible values, one real and one complex as -

y = √{ (a²x²/c² + a² + 2a²x/c) - (x² + c² + 2xc)}    -- Real

y = i√{(a{x/c + 1})² + (x² + c² + 2xc)}    -- Complex

Given is the expression as follows -

√{(x + c)² + y²} = x (a/c) + a

√{(x + c)² + y²} = xa/c + a

√{(x + c)² + y²} = a{x/c + 1}

√{x² + c² + 2xc + y²} = a{x/c + 1}

{x² + c² + 2xc + y²} = ± (a{x/c + 1})²

Now, we can write -

{x² + c² + 2xc + y²} = (a{x/c + 1})²              ...... (1)

and

{x² + c² + 2xc + y²} = - (a{x/c + 1})²                 ......... (2)

Solving (1) as -

{x² + c² + 2xc + y²} = (a{x/c + 1})²    

{x² + c² + 2xc + y²} = a²(x/c + 1)²

{x² + c² + 2xc + y²} = a²(x²/c² + 1 + 2x/c)

{x² + c² + 2xc + y²} = (a²x²/c² + a² + 2a²x/c)

y² = (a²x²/c² + a² + 2a²x/c) - (x² + c² + 2xc)

y = √{ (a²x²/c² + a² + 2a²x/c) - (x² + c² + 2xc)}

Solving (2) as -

{x² + c² + 2xc + y²} = - (a{x/c + 1})²                

y² =  - (a{x/c + 1})² - (x² + c² + 2xc)

y² = - {(a{x/c + 1})² + (x² + c² + 2xc)}

y = √- {(a{x/c + 1})² + (x² + c² + 2xc)}

y = i√{(a{x/c + 1})² + (x² + c² + 2xc)}

Therefore, on solving the expression for (y), we get two possible values, one real and one complex as -

y = √{ (a²x²/c² + a² + 2a²x/c) - (x² + c² + 2xc)}    -- Real

y = i√{(a{x/c + 1})² + (x² + c² + 2xc)}    -- Complex

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The equation is y = 1000 - 10x, where y is the number of blankets sold and x is the price in dollars.

This equation represents the relationship between the number of blankets sold (y) and the price of each blanket (x). The equation starts with the total number of blankets Christina has to sell (1000) and then subtracts 10 for every $1 increase in the price of the blanket. This means that as the price of the blanket increases, the number of blankets sold will decrease by 10 for every $1 increase. For example, if Christina charges $50 for a blanket, the number of blankets sold would be 500 (1000 - (10x50)).

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a) A function w(t) to represent the amount of water in the pool using the two functions is w(t) = -3t + 5.

b) The pool will leak out the water when w(t)=0.

c) It will take 1.67 hours to leak out all the water from the pool.

d) Yes, functions f(t) and d(t) will intersect on the graphs when the pool stops leaking all the water out.

e) The domain of the functions  f(t), d(t) and w(t) are 0 ≤ t ≤ 1.67.

What are functions?

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

Subtract the amount flowing into the pool by the amount being drained out the pool to get the amount of water in the pool .

The given functions are -

Flowing: f(t) = t² + 8t + 9.

Draining: d(t) = t² + 11t + 4.

The amount of water in the pool is -

w(t) = f(t) - d(t)

w(t) = t² + 8t + 9 - t² - 11t - 4

w(t) = -3t + 5.

Therefore, the function obtained is w(t) = -3t + 5.

When the condition is w(t) = 0 then, the pool will have leaked all the water.

Plugging in the values -

-3t + 5 = 0.

3t = 5

t = 1.67.

Therefore, the pool will leak all the water in 1.67 hours.

Functions f(t) and d(t) intersect on the graph when all the water of the pool has been leaked. The graph is shown below.

The domain of a function is the set that contains all input values of the function. The input is the time in the given situation, so -

Time cannot be negative, hence t ≥ 0.

When all the water has been drained, everything stops, hence t ≤ 1.67.

Therefore, the domain of the function is 0 ≤ t ≤ 1.67.

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A. Commutative property of addition

B. Distributive property

C. Commutative property of addition

D. Associative property of multiplication

                                    a + b =b + a

        Here, a and b is whole numbers, integers or decimals, or even fractions.

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The complete question is:

Name the property that is shown by each equation.

A. 6a + 4 = 4 + 6a

B. 30 + 60 = 15(2 + 4)

C. 3(8x + 4) = 3(4 + 8x)

D. 4(6a) = (4 · 6)a

Answer:

r=4.2

d=9

Step-by-step explanation:

The radius is 4.2cm

The diameter is d=9

Solution

d=2r=2·4.5=9

Hope this helped!!!!!

The Distance that Ellie ran each evening is 16.5 miles for a entirety week.

We can use the following equation to find how many miles, x, Ellie ran each afternoon:

x + 2.5(3) = 24

Here, x represents the number of miles Ellie ran each afternoon, 2.5 represents the number of miles she ran each morning, and 3 represents the number of days she trained. The total number of miles she ran, 24, is on the right side of the equation.

To solve for x, we can start by simplifying the left side of the equation:

x + 7.5 = 24

Then, we can subtract 7.5 from both sides:

x = 16.5

So, Ellie ran 16.5 miles each afternoon.

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Answer:

Refer to the step-by-step

Step-by-step explanation:

To minimize the cost of producing the box, we would want the box to be a cube.

Where the volume, [tex]V=s^{3}[/tex], where s is the length of one side of the box.

We were given the value, [tex]V=4096 cm^{3}[/tex], plug this into the equation above so we can find the dimensions of the box...

[tex]4096=s^{3} = > s=\sqrt[3]{4096} = > s=16[/tex]

Thus the dimensions to minimize the cost of the production of the box would be 16cm by 16cm by 16cm.

The value of AB= 24 BD is congruent to BC. BD=BC

BD = 5x – 26, BC = 2x + 1, and AC = 43

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I think it's answer this .

Answer:

b

Step-by-step explanation:

Answer:

The answer is 48

Step-by-step explanation:

Answer:

48 students

4*12=48

Answer:

6.  175/125=x/100

Cross products  equal 125x=17500

Solve for x and you get 140%

7.  20% of 720 is 144.  You need to find 120% so add the full 720 (100%) to the 144 and you get 864 (120%)

Step-by-step explanation:

Answer:

6. 140%    7. 864

Step-by-step explanation:

Step for #1:

1.) 175 ÷ 125 = 1.4

2.) 1.0=100   0.4=40

3.) 1.4 = 140%

Answer; 140%

Step for #2:

1.) 120% × 720 = ?

2.) 120 x 720 = 86,400

3.) 86,400 ÷ 100 = 864

Answer; 864

Answer:

y = 1

Step-by-step explanation:

Since the line is a horizontal line through 1, y = 1.

Answer:

$27

Step-by-step explanation:

If we know that %25 is equal to 1/4, or 0.25, then we can use an equation that look like this:
108 × 0.25 = 27

Therefore, the amount of the discount was $27

Solving for percentages can be tricky, and you may need help on trying to solve a problem including one. If you need to find a percentage of a number, the easiest way to do that is to convert the percentage into a fraction or decimal and multiply the total by that number.

For ex.

What is 15% of 60?

To do this, convert the percentage into a decimal.

15% converted into a decimal is 0.15.

Now multiply 60 by 0.15.

60 ÷ 0.15 = 9

So, the answer to this example would be 9.

The measure of the length MP is equal to 6.

Two triangles are similar triangles if they have the same corresponding angle measures and proportional side lengths.

Given is a triangle ΔOMN.

Now, ΔOMN and ΔOPQ are similar. This means that the side lengths are proportional to each other. We can write -

OP/OM = PQ/MN

12/OM = PQ/MN

12/(OP + PM) = PQ/MN

It is given that -

PQ = MP + 2

12/(OP + PM) = (MP + 2)/MN

12MN = (MP + 2)(OP + PM)

12 x 12 = (MP + 2)(MP + 12)

(MP)² + 12MP + 2MP + 24 = 144

(MP)² + 14(MP) - 120 = 0

Let MP = x, then we can write -

x² + 14x - 120 = 0

(x + 20)(x - 6) = 0

(x + 20) = 0   and    (x - 6) = 0

x = - 20   and   x = 6

x = 6      {Lengths cannot be negative}

Therefore, the measure of the length MP is equal to 6.

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Step-by-step explanation:

The blue figure is translated 2 units down and 6 units across from the red figure.

Step-by-step explanation:

To answer this, we need to find the scale factor which is to find how much one individual car is worth.

So we need to divide 3.84 and 4.

3.84 ÷ 4 = 0.96

So each car is $0.96.

To find 20 toy cars, we need to multiply 0.96 and 20.

The answer is:

$19.20

The vertex and axis of symmetry of the graph is shown in image.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The function is,

⇒ f (x) = 1/4 (x + 6)² - 5

Now,

Since, The function is,

⇒ f (x) = 1/4 (x + 6)² - 5

Hence, The points corresponds to x = - 2 and - 4 are;

For x = - 2;

⇒ f (x) = 1/4 (x + 6)² - 5

⇒ f (x) = 1/4 (-2 + 6)² - 5

⇒ f (x) = 1/4 (4)² - 5

⇒ f (x) = 4 - 5

⇒ f (x) = - 1

For x = - 4;

⇒ f (x) = 1/4 (x + 6)² - 5

⇒ f (x) = 1/4 (-4 + 6)² - 5

⇒ f (x) = 1/4 (2)² - 5

⇒ f (x) = 1 - 5

⇒ f (x) = - 4

Thus, The points are;

⇒ (- 2, - 1) , (- 4, - 4)

And, The vertex of the function is,

⇒ ( - 6, - 5 )

And, The axis of symmetry of the graph is,

⇒ x = - 6

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The equation to model the given situation is 120 - 4.5t= 75 and the solution to the equation is 10 minutes.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation.

The balloon will reach an altitude of 75 meters above the ground.

Now, 120-75 =45 meters

Let t be the time to descends 45 meters

So, 120 - 4.5t= 75

= -4.5 t = 75-120

= -4.5t = -45

= t = -45/(-4.5)

= t = 10 minutes

Hence, the equation to model the given situation is 120 - 4.5t= 75 and the solution to the equation is 10 minutes.

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Answer:

[tex]A\simeq3250.83[/tex]

Step-by-step explanation:

The amount formula in compound interest is:

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

where:

P = principal amount

r = annual interest

n = number of compounding periods

t = number of years

We already know that:

P = $2000

[tex]r = 7\% = \frac{7\%}{100\%}=0.07[/tex]

t = 7 (number of years from 6th to 13th bday)

n = 4 (quarterly in a year)

Then,

[tex]A=2000(1+\frac{0.07}{4} )^{(4)(7)}\\\\A=2000(1+\frac{0.07}{4} )^{28}\\\\A=3250.825792\\\\A\simeq3250.83[/tex]

Answer:

see explanation

Step-by-step explanation:

there is a common ratio between consecutive terms, that is

12 ÷ 6 = 24 ÷ 12 = 48 ÷ 24 = 96 ÷ 48 = 2

this indicates the sequence is geometric

the nth term of a geometric sequence is

f(n) = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

here a₁ = 6 and r = 2 , then

f(n) = 6 [tex](2)^{n-1}[/tex]

Answer:

1 meter to the Left

Step-by-step explanation:

Displacement is the distance between the start and ending points

By having it at first 2 meters to the left, then to move it back 1 meter to the right, you are subtracting from the initial movemnet to the left.

(2-1) = 1 meter to the Left

The x-coordinate of the solution of the system of equations is x = 20/3

Here we have a system of equations below:

3x - y = 6

3x + y = 34

And we want to find the x-cordinate of the solution, so we need to solve this for x.

We can use the elimination method, you can see that if we add both equations we will get:

(3x - y) + (3x + y) = 6 + 34

6x = 40

x = 40/6

We can simplify that fraction to get:

x = 20/3

That is the x-coordinate of the solution.

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Answer:

Step-by-step explanation:

Answer:

Last option: f(x) = [tex]\sqrt[5]{\frac{x}{7} }[/tex]

Hope this helps!

Answer:

bottom left: -6 + (-1/3)

Step-by-step explanation:

hope this helps :)