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WARRIOR [948]
2 years ago
12

The number of days each licensed driver in Marion County uses a commuter rail line annually is normally distributed with mean 66

and standard deviation 21. How many days must a driver use a commuter rail line annually to be in the top 5% of rail users? Round to the nearest integer.
Mathematics
1 answer:
alexira [117]2 years ago
3 0

Answer:

31.5 days

Step-by-step explanation:

We.solve using z score formula

z-score is is z = (x-μ)/σ,

where x is the raw score

μ is the population mean

σ is the population standard deviation.

The 5th percentile z score = -1.645

Mean = 66

Standard deviation = 21

Hence:

-1.645 = x - 66/21

-1.645 × 21 = x - 66

-34.545 = x - 66

-34.545 + 66 = x

x = 31.455 days

Approximately to the nearest round integer

= 31.5 days

Therefore, driver use a commuter rail line 31.5 days annually to be in the top 5% of rail users

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37 For a class picnic, two teachers went to the same store to purchase drinks. One teacher purchased 18 juice boxes and 32 bottl
Pavel [41]

Answer:

Step-by-step explanation:

Let j represent the cost of a juice box.

Let w represent the cost of a bottle of water.

One teacher purchased 18 juice boxes and 32 bottles of water, and spent $19.92.. This means that

18j + 32w = 19.92 - - - - - - - - - - - - 1

The other teacher purchased 14 juice boxes and 26 bottles of water, and spent $15.76. This means that

14j + 26w = 15.76- - - - - - - - - - - - 2

Multiplying equation 1 by 14 and equation 2 by 18, it becomes

252j + 448w = 278.88

252j + 468w = 283.68

Subtracting, it becomes

- 20j = - 4.8

j = - 4.8/- 20 = 0.24

Substituting j = 0.24 into equation 1, it becomes

18 × 0.24 + 32w = 19.92

4.32 + 32w = 19.92

32w = 19.92 - 4.32 = 15.6

w = 15.6/32 = 0.4875

Kara's prices are incorrect.

the cost of a juice box is $0.24

the cost of a bottle of water is $0.4875

7 0
2 years ago
Q. If heights of 3rd graders follow a normal distribution with a mean of 52 inches and a standard deviation of 2.5 inches, what
zaharov [31]

Answer:

-2

Step-by-step explanation:

3 0
2 years ago
Use an inequality symbol (<, >, =, ≥) to compare −17 ____ −1
iragen [17]
-17 is less than -1 so you will use the less than sign (<)

Answer: 17 __<__-1

< is less than
> is greater than
= is equal to
<span>≥ is greater than or equal to</span>
3 0
2 years ago
Read 2 more answers
Point b has coordinates (3,-4) and lies on the circle whose equation is x^2 + y^2= 25. If angle is drawn in a standard position
lakkis [162]
<span>Point B has coordinates (3,-4) and lies on the circle. Draw the perpendiculars from point B to the x-axis and y-axis. Denote the points of intersection with x-axis A and with y-axis C. Consider the right triangle ABO (O is the origin), by tha conditions data: AB=4 and AO=3, then by Pythagorean theorem:
</span>
<span>BO^2=AO^2+AB^2 \\ BO^2=3^2+4^2  \\ BO^2=9+16  \\ BO^2=25  \\ BO=5.
</span>
{Note, that BO is a radius of circle and it wasn't necessarily to use Pythagorean theorem to find BO}
<span>The sine of the angle BOA is</span>
\sin \angle BOA= \dfrac{AB}{BO} = \dfrac{4}{5} =0.8

Since point B is placed in the IV quadrant, the sine of the angle that is <span> drawn in a standard position with its terminal ray will be </span>
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3 0
2 years ago
The table below shows the amount of lemon juice and sugar needed to make three different-sized batches of lemonade using the sam
mash [69]

Answer:

<u>j = 2.5s</u>

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

                Lemon juice (mL)      Sugar (gr)

Batch A        500                             200

Batch B         750                             300

Batch C       1,500                             600

2. Write an equation to describe the relationship between j, the amount of lemon juice in mL, and s, the amount of sugar in g.

Ratio = Amount of lemon juice/Amount of sugar

Ratio = 500/200 = 750/300 = 1,500/600

Ratio = 2.5

Now, we can write the equation, this way:

<u>j = 2.5s</u>

8 0
2 years ago
Read 2 more answers
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