Which statement is supported by the graphs?

This is a normal distribution problem, for the combined math and verbal scores for students taking a national standardized examination for college admission, the

Mean = μ = 560

Standard deviation = σ = 260

A college requires a student to be in the top 35 % of students taking this test, what is the minimum score that such a student can obtain and still qualify for admission at the college?

Let the minimum score that such a student can obtain and still qualify for admission at the college be x' and its z-score be z'.

P(x > x') = P(z > z') = 35% = 0.35

P(z > z') = 1 - P(z ≤ z') = 0.35

P(z ≤ z') = 1 - 0.35 = 0.65

Using the normal distribution table,

z' = 0.385

we then convert this z-score back to a combined math and verbal scores.

The z-score for any value is the value minus the mean then divided by the standard deviation.

z' = (x' - μ)/σ

0.385 = (x' - 560)/260

x' = (0.385×260) + 560 = 660.1

Hope this Helps!!!

8 0

4 years ago

A sidewalk has an area that can be represented bt the expression (8x+24) feet. List 3 possible lenghts and widths of the sidewal

Eddi Din [679]

Answer:

Length = 8 feet and Width = (x+3) feet

Length = 4 feet and Width = (2x+6) feet

Length = 2 feet and Width = (4x+12) feet

Step-by-step explanation:

We are given that,

Area of the rectangular sidewalk = (8x+24) feet²

Since, area of a rectangle = Length × Width

It is required to find three possible lengths and widths.

As, we can factor the given area in the following ways,

1. Area = (8x+24) = 8 × (x+3)

2. Area = (8x+24) = 4 × (2x+6)

3. Area = (8x+24) = 2 × (4x+12)

Thus, the three possible lengths and widths are given by,

1. Length = 8 feet and Width = (x+3) feet.

2. Length = 4 feet and Width = (2x+6) feet.

3. Length = 2 feet and Width = (4x+12) feet.

3 0

3 years ago

A raft and a motorboat simultaneously leave from the same point and move down the river. After 2 hours the motorboat turns aroun

lesya692 [45]

Answer:

2 hours

Step-by-step explanation:

Let x mph be the speed of motorboat in still water and y mph be the speed of current.

A raft and a motorboat simultaneously leave from the same point and move down the river, then speeds down the river are:

motorboat = x + y mph

raft = y mph

In two hours they will cover:

motorboat = 2(x+y) miles

raft = 2y miles

After 2 hours the motorboat turns around and starts moving towards the raft (against the current), so its speed is now x - y mph.

Let t be the time they move towards each other. In t hours, they cover

motorboat = t(x - y) miles

raft = ty miles

The distance from the starting point to the turning point is the same as the sum of the distances the raft covers and the motorboat covers after turning around, so

$2(x+y)=2y+t(x-y)+ty \\ \\2x+2y=2y+tx-ty+ty\\ \\2x=tx\\ \\t=2\ hours$

6 0

3 years ago