Is -74.58 an integer

Suppose a batch of steel rods produced at a steel plant have a mean length of 178178 millimeters, and a standard deviation of 12

tatuchka [14]

To solve this problem we use the z statistic. The formula for z score is:

z = (x – u) / s

where,

x = sample value mean = 178 – 0.56 = 177.44 mm

u = total sample mean = 178 mm

s = standard deviation = 12 mm

z = (177.44 – 178) / 12

z = -0.05

from the tables P (z = -0.05) = 0.484

So the probability P is: [multiply by 2 since we account the two sides)

P = (0.5 – 0.484) * 2 = 0.0320

7 0

3 years ago

The base of a triangle is shrinking at a rate of 11 cm/s and the height of the triangle is increasing at a rate of 11 cm/s. Find

Mumz [18]

Answer:

the rate of changes of the area of the triangle

$\frac{dA}{dt} = -11 cm^2 /sec$

Step-by-step explanation:

Explanation :-

The area of triangle( A) = $\frac{1}{2} base X height$ ..........(1)

Let 'b' be the base and 'l' be the length of the triangle

The base of a triangle is shrinking( means decreasing) at a rate of 11 cm/s

that is $\frac{db}{dt} = -11cm/sec$

The height of a triangle is increasing at a rate of 11 cm/s

that is $\frac{dh}{dt} = 11cm/sec$

Given h= 10cm and b = 8cm

The rate of change of triangle

applying uv formula $\frac{d(uv)}{dx} = u( \frac{dv}{dx}) + v(\frac{du}{dx} )$

Differentiating equation (1) with respective to 't'

$\frac{dA}{dt} =\frac{1}{2} ( b(\frac{dh}{dt} )+h ( \frac{db}{dt}))$

substitute all values in above equation, we get

h= 10cm , b = 8cm , $\frac{db}{dt} = -11cm/sec$ and $\frac{dh}{dt} = 11cm/sec$

$\frac{dA}{dt} = 10 (-11) + 8(11 )$

After simplification , we get

$\frac{dA}{dt} =\frac{1}{2} (-110 +88) = -11 cm^2 /sec$

7 0

4 years ago

Read 2 more answers

Simplify the expression. 3 (15- 3)² - 4 ]

Jet001 [13]

Answer:

428.

Step-by-step explanation:

Work is in picture

5 0

3 years ago

Help please!<33:) i dont really understand it

belka [17]

Answer:

4. 8/15

Step-by-step explanation:

I will do #4. For dividing fractions, you multiply them together and remember to flip the second one.

Example: Instead of 2/5 divided by 3/4, it would be (2/5)(4/3), which = 8/15. Multiply the 2 and the 4 to get 8, then multiply the 5 and the 3 to get 15.

7 0

3 years ago

In ΔRST, r = 53 inches, ∠S=6° and ∠T=58°. Find the length of s, to the nearest inch.

yaroslaw [1]

Answer:

s = 6 inches

Step-by-step explanation:

Given:

r = 53 inches,

∠S = 6°

∠T = 58°.

Required:

Length of s

Solution:

Use Sine Rule

Thus:

$\frac{s}{Sin(S)} = \frac{r}{Sin(R)}$

<R = 180 - (58 + 6)

<R = 116°

r = 53 inches,

∠S = 6°

s = ?

Plug in the values

$\frac{s}{Sin(6)} = \frac{53}{Sin(116)}$

Multiply both sides by Sin(6)

$\frac{s}{Sin(6)} \times Sin(6) = \frac{53}{Sin(116)} \times Sin(6)$

$s = \frac{53 \times Sin(6)}{Sin(116)}$

$s = 6 inches$ (nearest inch)

7 0

3 years ago