What transformations preserve measure of side lengths and angles.

A company purchases shipments of machine components and uses this acceptance sampling plan: Randomly select and test 20 componen

musickatia [10]

Answer: Probability that this whole shipment will be accepted is 0.629

Step-by-step explanation:

The company randomly select and test 20 components and accept the whole batch if there are fewer than 3 defectives.

Applying normal distribution,

z = (x-u)/s

Where

n = number of components that were tested.

s = standard deviation

u = mean = np

p = probability that the component has defect

q = probability that the component does not have defect

x = r = the number of components

From the information given,

p = 8/100 = 0.08

q = 1-q = 1-0.08 = 0.92

n = 20

u = 20×0.08 = 1.6

s = √20 × 0.08 × 0.92 = √1.472

s = 1.21

Probability that this whole shipment will be accepted will be probability that fewer than 3 components have defects. This means that it must be lesser than or equal to 2 components.

P(x lesser than 3) =P(x lesser than or equal to 2). Therefore,

x = 2

z = (2-1.6)/1.21 = 0.33

Looking at the normal distribution table, the corresponding z score is 0.629

8 0

3 years ago

Which step in the solution contains the first error ?? Please helpp

kumpel [21]

Answer:

step 4 I believe

Step-by-step explanation:

6 0

3 years ago

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What is the simplest form for 10/42

QveST [7]

2 goes into both numbers, so divide both by 2;

10 ÷ 2 = 5

42 ÷ 2 = 21

so 10/42 in simplest form is: 5/21

7 0

3 years ago

in parallelogram ABCD, AC is diagonal, the measure <ABC is 40°, and the measure of <ACD IS 57°. what is the measure of &lt

Nutka1998 [239]

Answer: $\angle CAD = 83^\circ$ Option D

Step-by-step explanation:

In this question we use properties of parallelogram and angle sum property of a triangle.

In parallelogram ABCD

$\angle ABC=40^\circ$

As, we know that opposite angles of parallelogram are equal

Therefore,

$\angle ABC =\angle ADC =40^\circ$

Now, in triangle ADC

We know that sum of all the angles of a triangle is $=180^\circ$

$\angle ACD +\angle ADC +\angle DAC =180^\circ$

$57^\circ +40^\circ +\angle DAC =180^\circ$

$97^\circ + \angle DAC = 180^\circ$

Subtracting 97 from both sides we get

$\angle DAC = 180^\circ - 97^\circ$

$\angle DAC = 83^\circ$

Measure of $\angle CAD = 83^\circ$

3 0

3 years ago

A candle in the shape of a circular cone has a base of radius r and a height of h that is the same length as the radius. which e

ladessa [460]

Answer:

$\frac{r(1-\sqrt{2})}{-3}$

Step-by-step explanation:

Volume of cone = $\frac{1}{3} \pi r^{2} h$

Since we are given that a circular cone has a base of radius r and a height of h that is the same length as the radius

= $\frac{1}{3} \pi r^{2} \times r$

= $\frac{1}{3} \pi r^{3}$

Surface area of cone including 1 base = $\pi r^{2} +\pi\times r \times \sqrt{r^2+h^2}$

Since r = h

So, area = $\pi r^{2} +\pi\times r \times \sqrt{r^2+r^2}$

= $\pi r^{2} +\pi\times r \times \sqrt{2r^2}$

= $\pi r^{2} +\pi\times r^2 \times \sqrt{2}$

Ratio of volume of cone to its surface area including base :

$\frac{\frac{1}{3} \pi r^{3}}{\pi r^{2} +\pi\times r^2 \times \sqrt{2}}$

$\frac{\frac{1}{3}r}{1+\sqrt{2}}$

$\frac{r}{3(1+\sqrt{2})}$

Rationalizing

$\frac{r}{3(1+\sqrt{2})} \times \frac{1-\sqrt{2}}{1-\sqrt{2}}$

$\frac{r(1-\sqrt{2})}{-3}$

Hence the ratio the ratio of the volume of the candle to its surface area(including the base) is $\frac{r(1-\sqrt{2})}{-3}$

8 0

3 years ago

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