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AlekseyPX
3 years ago
12

Given that 10% of the nails made using a certain manufacturing process have a length less than 2.48 inches, while 5% have a leng

th greater than 2.54 inches, what are the mean and standard deviation of the lengths of the nails? Assume that the lengths have a normal distribution.
Mathematics
1 answer:
zvonat [6]3 years ago
7 0

Answer:

The mean, μ is 2.5063 and

The standard deviation, σ = 2.0499 × 10⁻²

Step-by-step explanation:

Here we have

z = \frac{x- \mu}{\sigma}

z \sigma ={x- \mu}{} and

10% have length < 2.48 in while

5% have length > 2.54 in

and

From the z score table

Critical z at 10% to the left = -1.282

Critical z at 5% to the right = 1.645

Therefore, the equations become

-1.282σ = 2.48 - μ → μ -1.282σ = 2.48

1.645σ = 2.54 - μ → μ + 1.645σ = 2.54

Solving the above equations gives

The mean, μ = 2.5063 and

The standard deviation, σ = 2.0499 × 10⁻².

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Which statement describes the end behavior of the exponential function f(x) = 2x – 3?
charle [14.2K]
The <u>correct answer</u> is:

As x→-∞, y→-3.
As x→∞, y→∞.

Explanation:

As our values of x get further into the negative numbers, the value of 2ˣ will approach 0.  This is because raising a number to a negative exponent "flips" the number below the denominator and raises it to a power; we end up with smaller and smaller fractions, eventually so small that they nearly equal 0.  

This will make the value of the function 0-3=-3.

As x gets larger and larger (towards ∞), the value of y, 2ˣ, continues to grow as well.  Since it continues to grow exponentially, we say the value approaches ∞.
3 0
3 years ago
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If Amanda ran 3/8 of a mile on Wednesday, how much more did she run on Monday and Tuesday than on Wednesday
Lorico [155]
I think 6/8 hope this help.
8 0
3 years ago
Given: <br><br>EM, EQ-secants<br><br>Prove: MP·EW=WQ·EP
Dennis_Churaev [7]

Answer:

Step-by-step explanation:

A secant is a straight line from a point outside a given circle that passes through two points on its circumference.

From the given diagram, EM and EQ are secants.

Thus,

<PEW ≅ <WEP    (common angles)

<EMP ≅ <EQW (secant-chord theorem)

<WMP ≅ <PQM (inscribed angles of arc WP)

Therefore,

\frac{EW}{WM} = \frac{EP}{PQ}   (corresponding sides of a triangle)

This implies that,

EW*PQ = EP*WM

Therefore,

MP*EW = WQ*EP  (properties of a similar triangle)

7 0
3 years ago
Lindsay buys 15 3/4 gallons of gasoline for $3.50 per gallon how much the whole tank cost
nydimaria [60]

Answer:

The whole tank cost $55.13

Step-by-step explanation:

All you have to do is multiply the fraction and cost, to ge thte total cost

15 3/4 also equals 15.75  (it will be easier to multiply two fractions)

now each gall of the 15.75 costs 3.50 so we multiply the number of gallons by the cost

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but now we must round since there isnt .125 cents

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nadezda [96]

Answer:

y = x - 10

Step-by-step explanation:

Find the slope:

-4 - (-8) ÷ 6 - 2

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Substitute into the slope-intercept equation:

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m = 1

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Write equation:

y = 1x -10 or y = x -10

3 0
3 years ago
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