All categories

2 years ago

The price of a train ticket consists of an initial fee plus a constant fee per stop.

Mathematics

2 answers:

murzikaleks [220]2 years ago

8 0

Answer:

Initial Fee is $2.

Step-by-step explanation:

Given:

Stops Price (dollars)

3 6.50

7 12.50

11 18.50

Also Given:

The price of a train ticket consists of an initial fee plus a constant fee per stop.

So let the Cost of initial fee be 'x'.

Also Let the Cost of Constant fee be 'y'.

Now Equation can framed as;

$Price (P) = x + (y\times \textrm{Number of Stops})$

Now According to table;

Number of stops = 3

Price = 6.50

So equation can be framed as;

$x+3y =6.50 \ \ \ \ equation \ 1$

Also According to table;

Number of stops = 7

Price = 12.50

So equation can be framed as;

$x+7y =12.50 \ \ \ \ equation \ 2$

Now Subtracting equation 1 from equation 2 we get;

$(x+7y)-(x+3y) =12.50-6.50\\\\x+7y-x-3y=6\\\\4y =6\\\\y= \frac{6}{4}=\$1.5$

Substituting the value of y in equation 1 we get;

$x+3\times1.5=6.50\\\\x+4.5=6.50\\\\x =6.50-4.5 = \$2$

Hence Initial Fee is $2.

krek1111 [17]2 years ago

7 0

Answer:

$2.00

Step-by-step explanation:

You might be interested in

Based only on the information given in the diagram, it is guaranteed that ABC XYZ

serious [3.7K]

This statement is true

5 0

2 years ago

Read 2 more answers

A million years ago, an alien species built a vertical tower on a horizontal plane. When they returned they discovered that the

velikii [3]

Answer:

$\theta=cos^{-1}(\frac{2}{3})$

Step-by-step explanation:

We are given that measurements of three points on the ground gave coordinates of (0,0,0),(1,2,0) and (0,2,1)

We have to find the angle by which the tower now deviate from the vertical

We find cross product of <1,2,0> and <0,2,1>

$\times =\begin{vmatrix}i&j&k\\1&2&0\\0&2&1\end{vmatrix}$

$\times =2\hat{i}-\hat{j}+2\hat{k}$

Now, we are finding the angle between $\times$ and vertical vector <0,0,1>

Angle between two vectors formula

$cos\theta=\frac{a.b}{\mid a\mid\cdot\mid b\mid }$

Now, using this formula

$cos\theta=\frac{2}{1\cdot 3}=\frac{2}{3}$

$\theta=cos^{-1}(\frac{2}{3})$

Hence, the tower deviate from the vertical by the angle $\theta=cos^{-1}(\frac{2}{3})$

6 0

2 years ago

If cos Θ = square root 2 over 2 and 3 pi over 2 < Θ < 2π, what are the values of sin Θ and tan Θ?

KIM [24]

Answer:

The answer is

$sin(\theta)=-\frac{\sqrt{2}}{2}$

$tan(\theta)=-1$

Step-by-step explanation:

we know that

$tan(\theta)=\frac{sin(\theta)}{cos(\theta)}$

$sin^{2}(\theta)+cos^{2}(\theta)=1$

In this problem we have

$cos(\theta)=\frac{\sqrt{2}}{2}$

$\frac{3\pi}{2}$

The angle $\theta$ belong to the third or fourth quadrant

The value of $sin(\theta)$ is negative

Step 1

Find the value of $sin(\theta)$

Remember

$sin^{2}(\theta)+cos^{2}(\theta)=1$

we have

$cos(\theta)=\frac{\sqrt{2}}{2}$

substitute

$sin^{2}(\theta)+(\frac{\sqrt{2}}{2})^{2}=1$

$sin^{2}(\theta)=1-\frac{1}{2}$

$sin^{2}(\theta)=\frac{1}{2}$

$sin(\theta)=-\frac{\sqrt{2}}{2}$ ------> remember that the value is negative

Step 2

Find the value of $tan(\theta)$

$tan(\theta)=\frac{sin(\theta)}{cos(\theta)}$

we have

$sin(\theta)=-\frac{\sqrt{2}}{2}$

$cos(\theta)=\frac{\sqrt{2}}{2}$

substitute

$tan(\theta)=\frac{-\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}}$

$tan(\theta)=-1$

8 0

2 years ago

Read 2 more answers

We suspect that automobile insurance premiums (in dollars) may be steadily decreasing with the driver's driving experience (in y

ANTONII [103]

Answer:

D) a chi square test for independence.

Step-by-step explanation:

Given that we suspect that automobile insurance premiums (in dollars) may be steadily decreasing with the driver's driving experience (in years), so we choose a random sample of drivers who have similar automobile insurance coverage and collect data about their ages and insurance premiums.

We are to check whether two variables insurance premiums and driving experience are associated.

Two categorical variables are compared for different ages and insurance premiums.

Hence a proper test would be

D) a chi square test for independence.

8 0

1 year ago

Danielle had planned her gift basket to be priced at $50 with a 40% gross margin. She forgot packaging costs which will be $3 pe

Scorpion4ik [409]

B 34% would be the gross margin

7 0

2 years ago

Read 2 more answers