the flat head rail tunnel in Montana is about 7 3/4 miles long. A train travels at a speed of 3/4 miles per minute. How long Will it take the train to go through the tunnel?

Answer:

  None of the above

Step-by-step explanation:

See the attachment for x-intercepts and vertex coordinates. These coordinates do not match any of the answer choices.

___

The closest choice is the last one. It has the direction of opening and the intercepts correct, but the vertex coordinates wrong.

We can write the graph of f(x) = (x - 1)(x + 4) as, "On a coordinate plane, a parabola opens up. It goes through (-4, 0), has a vertex at (-1.5, -6.25), and goes through (1, 0)."

What is a parabola?

A parabola is a plane curve created by a moving point whose distance from a stationary point equals its distance from a fixed-line.

How do we solve the given question?

In the question, we are given an equation of f(x) = (x - 1)(x + 4), and are asked to identify its graph.

The given equation is of a parabola in the intercept form f(x) = a(x - p)(x - q), which opens up if a > 0 and opens down if a < 0, and which has a vertex at the point   , and passes through the point (p, 0) and (q, 0).

Comparing the equation f(x) = (x - 1)(x + 4) to f(x) = a(x - p)(x - q), we get

a = 1, p = 1, q = -4.

Since, a > 0 (a = 1), we can say that it opens up.

Now, we calculate (p + q)/2 = (1 - 4)/2 = -1.5

f((p + q)/2) = f(1.5) = (-1.5 - 1)(-1.5 + 4) = (-2.5)(2.5) = -6.25.

Thus, the vertex is at point (-1.5, -6.25).

Also, the equation passes through the points (-4, 0) and (1, 0).

∴ We can write the graph of f(x) = (x - 1)(x + 4) as, "On a coordinate plane, a parabola opens up. It goes through (-4, 0), has a vertex at (-1.5, -6.25), and goes through (1, 0)."

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We have already discussed techniques for visually representing data (see histograms and frequency polygons). In this section, we present another important graph called a box plot. Box plots are useful for identifying outliers and for comparing distributions. We will explain box plots with the help of data from an in-class experiment. As part of the "Stroop Interference Case Study," students in introductory statistics were presented with a page containing 30 colored rectangles. Their task was to name the colors as quickly as possible. Their times (in seconds) were recorded. We'll compare the scores for the 16 men and 31 women who participated in the experiment by making separate box plots for each gender. Such a display is said to involve parallel box plots.

There are several steps in constructing a box plot. The first relies on the 25th, 50th, and 75th percentiles in the distribution of scores. Figure 1 shows how these three statistics are used. For each gender, we draw a box extending from the 25th percentile to the 75th percentile. The 50th percentile is drawn inside the box. Therefore,

the bottom of each box is the 25th percentile,

the top is the 75th percentile,

and the line in the middle is the 50th percentile.

The data for the women in our sample are shown in Table 1.

Answer:variability

Step-by-step explanation:

The requried number y must be less than 25 in order for the statement "5 less than a number y is under 20" to be true.

The phrase "5 less than a number y is under 20" can be represented as an inequality:

y - 5 < 20

This inequality states that if we subtract 5 from a number y, the result will be less than 20.

To solve this inequality for y, we can isolate y by adding 5 to both sides of the inequality:

y - 5 + 5 < 20 + 5

y < 25

Therefore, the number y must be less than 25 in order for the statement "5 less than a number y is under 20" to be true.

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Answer:

• 120 pens and 200 pencils.

Explanation:

You can set a system of two equations.

1. Variables

• x: number of pens
• y: number of pencils

2. Cost

• each pen costs $1, then x pens costs: x
• each pencil costs $0.5, then y pencil costs: 0.5y

• Then, the total cost is: x + 0.5y

• The cost of the whole purchase was $ 220, then the first equation is:

          x + 0.5y = 220 ↔ equation (1)

3. There were 80 more pencils than pens

Then:

  pencils  =      80   +   pens

       ↓                               ↓

       y        =      80   +      x        ↔ equation (2)

4. Solve the system

i) Substitute the equation (2) into the equation (1):

• x + 0.5(80 + x) = 220

ii) Solve

• x + 40 + 0.5x = 220

• 1.5x = 180

• x = 180/1.5

• x = 120 pens

iii) Substitute x = 120 into the equation (2)

• y = 80 + 120

• y = 200 pencils

Solution: 120 pens and 200 pencils ← answer

Answer:

NEGATIVE 3X + 5 OVER 11

Step-by-step explanation:

TO SUBTRACT FRACTIONS, FIND THE LCD, THEN COMBINE !

ANSWER =

Answer:

- 3x + 5/11  reduce - 3x/11 - 5/11

Step-by-step explanation: