In London, the charge of a tour bus consists of a fixed rental price plus a per kilometre rate, that depends on the distance of the trip.
The per kilometre rate is $12/km. You decide to go on a 5 km trip, and it costs you $70.
a) What is the fixed rental cost? Show your work.
b) Determine the equation relating the cost, C, in dollars, and the distance, d, in km.
d) What is the cost of an 18 km trip?
e) What is the distance travelled if the total cost is $250?

PLEASEEEEEEEE

The computation shows that the values are 64000 acres and 563 metric tons.

1. A 100 square mile area of national forest is how many acres?

1 mile square = 640 acres

100 square miles = 100 × 640 = 64000 acres.

2. Fifty eight thousand kilograms of solid waste is equivalent to how many metric tons?

1 metric ton = 103kg

58000 kg = 58000/103 = 563 metric tons

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Answer:

y = x + 2

Step-by-step explanation:

You can find the slant asymptote using polynomial long division because the numerator is one degree higher than the denominator.

(x^2+x+4)/(x-1)

I'm not sure how to show long division but you should get:

x+2 with remainder 6

Then your slant asymptote is y = x + 2

You can graph it on Desmos to verify

The quotient of 3 by 1/ 6 and that of 3/4 by 1/ 8 is 1/2 and 4 respectively

From the given equation, we have to find

= 3/4 ÷ 1/8

First , we take the denominator of the second fraction to be the numerator, we have

=

[tex] \frac{3}{4} \times \frac{8}{1} [/tex]

Multiply through

=

[tex] \frac{24}{4} [/tex]

=

[tex]6[/tex]

To find the quotient of 3 by 1/6

=

[tex]3 \times \frac{1}{6} [/tex]

=

[tex] \frac{3}{6} [/tex]

=

[tex] \frac{1}{2} [/tex]

Thus, the quotient of 3 by 1/ 6 and that of 3/4 by 1/ 8 is 1/2 and 4 respectively

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Answer:

D.  10

Step-by-step explanation:

To find the distance between two points, use the distance formula:

Distance between two points

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]\textsf{where }(x_1,y_1) \textsf{ and }(x_2,y_2)\:\textsf{are the two points}[/tex]

Define the two points:

[tex]\textsf{Let }(x_1,y_1)=(4,-3)[/tex]

[tex]\textsf{Let }(x_2,y_2)=(-4,3)[/tex]

Substitute the two defined points into the distance formula and solve for d:

[tex]\implies d=\sqrt{(-4-4)^2+(3-(-3))^2}[/tex]

[tex]\implies d=\sqrt{(-4-4)^2+(3+3)^2}[/tex]

[tex]\implies d=\sqrt{(-8)^2+6^2}[/tex]

[tex]\implies d=\sqrt{64+36}[/tex]

[tex]\implies d=\sqrt{100}[/tex]

[tex]\implies d=\sqrt{10^2}[/tex]

[tex]\implies d=10[/tex]

Therefore, the distance between the two given points is 10 units.

Formula given by

[tex]\boxed{\sf Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}[/tex]

[tex]\\ \tt{:}\longrightarrow D=\sqrt{(-4-4)^2+(3+3)^2}[/tex]

[tex]\\ \tt{:}\longrightarrow D=\sqrt{8^2+6^2}[/tex]

[tex]\\ \tt{:}\longrightarrow D=\sqrt{10^2}[/tex]

[tex]\\ \tt{:}\longrightarrow D=10units[/tex]

Option D

The probability will be:

Case 1  matches with 5/48.

Case 2 matches with 1/12.

Case 3 matches with 1/4.

Case 4 matches with 1/8.

Case 5 matches with 5/16.

We have a total sample space of six-sided die and an eight  sided die.

(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8)

(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8)

(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(3,7),(3,8)  

(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(4,7),(4,8)

(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(5,7),(5,8)

(6,1),(6,2),(6,3),(6,4),(6,5),(6,6),(6,7),(6,8)  

Case 1: The Probability that both numbers are odd numbers and their product is greater than 10. are:  (3,5),(3,7),(5,3),(5,5),(5,7)

And the total number of outcomes are: 48.

The required probability is 5/48.

Case 2: The probability that the second number is twice the first number are:

(1,2),(2,4),(3,6),(4,8)

And the total number of outcomes are 48.

So, the required probability is 1/12.

Case 3: The probability of a number whose sum is a multiple of 4 are:

(1,3),(1,7),(2,2),(2,6),(3,1),(3,5),(4,4),(4,8),(5,3),(5,7),(6,2),(6,6).

And the total number of outcomes are: 48.

The required probability is 12/48 = 1/4

Case 4: The probability that the sum of two numbers is greater than 11.

(4,8),(5,8),(6,7),(6,8),(5,7),(6,6)

And a total number of outcomes are 48.

So, the required probability is 6/48 = 1/8.

Case 5: The probability that the second number rolled is less than the first number are:

(2,1),(3,1),(3,2),(4,1),(4,2),(4,3),(5,1),(5,2),(5,3),(5,4),(6,1),(6,2),(6,3),(6,4),(6,5)

And the total number of outcomes are: 48.

The required probability is 15/48 = 5/16.

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The width of the cooling tower is 36 meters.

A cooling tower is a vent that is built for the purpose of releasing waste heat back to the atmosphere.

Now we can model the system using;  x²/324 - (y² - 90)²/1600. Thus, the width can be obtained from;

2 × ✓324

= 2 × 18

= 36 meters

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Missing parts;

Cooling towers are used to remove or expel heat from a process. A cooling tower's walls are modeled by x squared over 324 minus quantity y minus 90 end quantity squared over 1600 equals 1 comma where the measurements are in meters. What is the width of the cooling tower at the base of the structure? Round your answer to the nearest whole number.

36 meters

48 meters

80 meters

89 meters

Answer: 1/5

Step-by-step explanation: You just subtract 4/5 from 1, or 5/5. And BOOM! you get 1/5.

When an arithmetic expression contains two or more different operators, such as * and , the order in which the operations is done is determined by: Operator precedence

Precedence is known to be a kind of rule that tells the order in which a specific operations need to be carry out in an arithmetic expression.

The precedence of an operator specifies how tightly it binds two arithmetic expressions together.

In the arithmetic expression 4 + 5 * 3 , the answer is 19 and not 27 because the multiplication (*) operator has a higher precedence than the addition (+) operator.

Operator associativity is nothing but how operators of the same precedence are evaluated in an arithmetic expression. It can be either from left to right or right to left.

Therefore, when an arithmetic expression contains two or more different operators, such as * and , the order in which the operations is done is determined by: Operator precedence

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Applying the sine ratio and law of sines, the correct measurements are:

B. m∠B = 15°

E. h ≈ 31.28 ft.

Sine ratio that can be used to determine the side length of a right triangle is, sin ∅ = opposite side/hypotenuse.

Find c using the law of sines:

C = 33°

A = 180 - 48 = 132 [linear pair]

B = 180 - 33 - 132 = 15° [triangle sum theorem]

b = 20 ft

c = ?

Using the law of sines, b/sin B = c/sin C, we have:

20/sin 15 = c/sin 33

(c)(sin 15) = (20)(sin 33)

c = (20 × sin 33)/sin 15

c ≈ 42.09

Use the sine ratio to find h:

∅ = 48°

Hypotenuse = c = 42.09

Opposite = h = ?

sin 48 = h/42.09

h = (sin 48)(42.09)

h ≈ 31.28

The correct measurements are:

B. m∠B = 15°

E. h ≈ 31.28 ft

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Answer:

B. and E.

Step-by-step explanation:

Answer:

C. [tex]\frac{1}{4}[/tex]× [tex]\frac{7}{2}[/tex]

Step-by-step explanation:

When you convert a fraction division into multiplication, you convert the divisor into its reciprocal. The reciprocal of [tex]\frac{2}{7}[/tex] is [tex]\frac{7}{2}[/tex]. So you get your answer  [tex]\frac{1}{4}[/tex]× [tex]\frac{7}{2}[/tex].

Answer:

answer is 6^2 × 6^2 = squate root 72

distance equals 8.485

Answer:

6[tex]\sqrt{2}[/tex] ≈ 8.49 units

Step-by-step explanation:

calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (2, - 3 ) and (x₂, y₂ ) = ( 8, - 9 )

d = [tex]\sqrt{(8-2)^2+(-9-(-3))^2}[/tex]

   = [tex]\sqrt{6^2+(-9+3)^2}[/tex]

   = [tex]\sqrt{36+(-6)^2}[/tex]

   = [tex]\sqrt{36+36}[/tex]

    = [tex]\sqrt{72}[/tex]

    = [tex]\sqrt{36(2)}[/tex]

     = [tex]\sqrt{36}[/tex] × [tex]\sqrt{2}[/tex]

     = 6[tex]\sqrt{2}[/tex] units ← exact length

     ≈ 8.49 units ( to 2 dec. places )

Answer:

Its A or B

Step-by-step explanation:

[tex]3x + 2 = 47 \\ 3x = 47 - 2 \\ 3x = 45 \\ x = \frac{45}{3} = 15[/tex]

Answer:

1425

Step-by-step explanation:

Each notebook costs 40, if she buys 30 you can find the total price of notebooks by multiplying the two numbers:

[tex]40*20=1200[/tex]

Each pen costs 15, the same process can be used, multiply price by quantity:

[tex]15*15=225[/tex]

Now just sum the two numbers to find the final price:

1425

Answer:

Step-by-step explanation:

30*40+15*15=

1200+625=

Rs1625

hope this helps

Answer:

39

Step-by-step explanation:

The coordinates of U after the reflection are: (-5, -3)

By looking at the graph, we can see that the coordinates of point U are:

U = (-1, -3)

And we want to reflect it across the line x = -3.

Notice that because this is a vertical line, the y-component does not change by the reflection. Only changes the x-component, such that the distance between the original coordinates and the final coordinates to the line don't change.

The original x-component is x = -1, the distance to the line is:

d = |-3 - (-1)| = 2 units.

Then the new x-component will also be at 2 units of the line, but in the other direction:

new x-component: x = -3 - 2 = -5

The coordinates of U after the reflection are:

(-5, -3)

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The height of the rectangular cereal box is 40 cm.

Volume of a rectangular prism = lwh

where

Therefore,

10000 = 25 × 10 × h

10000 = 250h

h = 10000 / 250

h = 40 cm

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Please see the explanation of this question to see procedure for the dilation of the triangle ABC and the image attached below to know the result.

In this question we must apply a kind of rigid transformation known as dilation. A dilation of a point around a point of reference is defined by the following operation:

P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]     (1)

Where:

Let assume that the point P is the origin of a rectangular system of coordinates. Then, the coordinates of the three vertices of the triangle ABC respect to the origin are: A(x, y) = (- 1, 2), B(x, y) = (- 1, - 1), C(x, y) = (2, 0).

Then, the vertices of the resulting triangle A'B'C' are, respectively:

A'(x, y) = (0, 0) + 3 · [(- 1, 2) - (0, 0)]

A'(x, y) = (- 3, 6)

B'(x, y) = (0, 0) + 3 · [(- 1, - 1) - (0, 0)]

B'(x, y) = (- 3, - 3)

C'(x, y) = (0, 0) + 3 · [(2, 0) - (0, 0)]

C'(x, y) = (6, 0)

Finally, we draw the resulting triangle with the help of a graphing tool.

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Answer: 3/2

Step-by-step explanation:

[tex]\frac{7-1}{5-1}=\frac{6}{4}=\frac{3}{2}[/tex]

The area of the rectangle is 108 square centimeters.

Given Information

The following information has been given in the question,

Length of the diagonal of the rectangle, l = 15 cm

Length of one of the sides of the rectangle, a = 9 cm

Let the other side of the rectangle be b.

Finding the Other Side of the Rectangle

According to Pythagoras Theorem,

(hypotenuse)² = (base)² + (perpendicular)²

Applying this theorem in the right-angle triangle formed by the diagonal and 9cm side of the rectangle, we get,

l² = a² + b²  [∵ The diagonal makes the hypotenuse]

(15)² = (9)² + b²

b² = (15)² - (9)²

b² = 225 - 81

b² = 144

b = √144

b = 12 cm

Calculating the Area of the Rectangle

Area of the rectangle, A = a × b

A = 9 × 12

A = 108 cm²

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Answer:

605

Step-by-step explanation:

We are starting at 110 and not zero, so I need to find have the distance between 110 and 110 and add that to 110.

110 + 1/2(1100 - 110)  Subtract what is in the parentheses

110 + 1/2(990) Find 1/2 of 990

110 + 495

604

Answer:

Step-by-step explanation:

32 = 2 : 5

32/7 = 4

2 x 4 : 4 x 5

8 : 20

The graph that represents y= cos(2x - π) +5 is illustrated below.

It should be noted that a graph simply means a series of connections among variables given.

In this case the graph that represents y= cos(2x - π) +5 is illustrated below.

The graph is attached.

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The z value for the probability in the standard normal table is 1.29.

In this question,

Z-Score, also known as the standard score, indicates how many standard deviations an entity is, from the mean. A standard normal table (also called the unit normal table or z-score table) is a mathematical table for the values of ϕ, indicating the values of the cumulative distribution function of the normal distribution.

The value of probability is 0.80

A standard normal random variable is between -z and +z, So

P(-z < 0 < z) = 0.80

⇒ 2P(0 < z) = 0.80

⇒ P(0 < z) = [tex]\frac{0.80}{2}[/tex]

⇒ P(0 < z) = 0.40

From the standard normal table, z value for the probability 0.40 is

⇒ z = 1.29

Thus P(0 < 1.29) = 0.40

Hence we can conclude that the z value for the probability in the standard normal table is 1.29.

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in standard form, 7 (10°) + 4 (10-3) + 5 (10³) is equal to 5. 04 × 10 ^3

Standard form is simply a value with an exponential powerl

Given the values;

It is important to note that any number to the power of O is equivalent to 1

So, we have

10^ 0 = 1

4( 10^-3) = 37

5(10^3) = 5000

Now, let's substitute the values

(10°) + 4 (10-3) + 5 (10³)

It is equivalent to

⇒1 + 4 × 10^-3 + 5 × 10^3

⇒1 + 37 + 5000

Add the values

= 5038

Let's convert it to standard form, we have

= 5. 04 × 10 ^3

Thus, in standard form, 7 (10°) + 4 (10-3) + 5 (10³) is equal to 5. 04 × 10 ^3

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Answer:

Step-by-step explanation:

The area for a triangle is

[tex]A=\frac{1}{2}bh[/tex]

Our base is given as x, the height is given as 1 more than 6 times the base which looks like this: 6x + 1. We know that the area is 13, so filling in everything:

[tex]13=\frac{1}{2} (6x+1)(x)[/tex]

We can get rid of the denominator of 2 by multiplying it on both sides to get:

[tex]26=(6x+1)(x)[/tex] and simplifying a bit:

[tex]26=6x^2+x[/tex]

Now we can move over the 26 and put the expression into standard quadratic form by setting it equal to 0:

[tex]6x^2+x-26=0[/tex] which is choice C

Answer:60g

Step-by-step explanation:

Hope this the answer

In one hour the plane will cover a distance of 1238 km.

solving this we will get the valve of Y is x is given.

calculation:-

today distance = 9904 km.

total time is taken = 8 hours.

∴total distance covered in one hour = 9904/8

                                                        = 1238 km.

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