What is each percent of change?

A quality-control engineer samples 100 items manufactured by a certain process, and finds that 15 of them are defective. True or

goldenfox [79]

Answer: b) The probability that an item produced by this process is defective is likely to be close to 0.15, but not exactly equal to 0.15.

Step-by-step explanation:

Given that:

Number of samples = 100

Number of defective samples = 15

Proportion =number defective samples / total samples

P = 15 / 100 = 0.15

Hence, the probability that an item produces is defective is 0.15.

However, due to sampling Variations, the probability will be corrected for these variations. Hence, probability that an item produced by this process is defective is likely to be close to 0.15, but not exactly equal to 0.15.

5 0

2 years ago

7. A man makes a simple discount note for $6,200, at an ordinary bank discount rate of 8.84%, for 40 days. What is the effective

Elina [12.6K]

Answer:

The effective interest rate, rounded to the nearest tenth, is 0.1%.

Step-by-step explanation:

The banker's rule is the simple interest formula.

The simple interest formula is given by:

$E = P*I*t$

In which E are the earnings, P is the principal(the initial amount of money), I is the interest rate(yearly) and t is the time, in years.

The effective interest rate is given by the following formula:

$E_{IR} = \frac{E}{P}$ .

In this problem, we have that:

A man makes a simple discount note for $6,200, at an ordinary bank discount rate of 8.84%, for 40 days. We consider that the year has 360 days. This means that $P = 6200, I = 0.0884, t = \frac{40}{360} = \frac{1}{9}$ .

So

$E = 6200*0.0884*\frac{1}{9} = 60.9$

The effective interest rate is

$E_{IR} = \frac{E}{P} = \frac{60.9}{6200} = 0.0098 = 0.001$

The effective interest rate, rounded to the nearest tenth, is 0.1%.

8 0

3 years ago

Which is the graph of the system of equations? x + 2y = 2 4x - y = 4

Sladkaya [172]

Solve for x for x: x+2y=2
x+2y +-2y=2+-2y (add -2y on both sides.)
x=-2y+2
Substitute : -2y+2 for x in
4x-y=4:
4(-2y+2)-y=4
-9y+8=4 Simplify both sides of the equation.
-9y+8+-8=4+-8 Add -8 to both sides.
-9y=-4
-9/-9=-4-9 Divide both sides by -9
y=4/9
Substitute 4/9 for y in
x=-2y+2
x=-2(4/9)+2
x=10/9
y=4/9,x=10/9

4 0

3 years ago

Calculus Problem

Roman55 [17]

The two parabolas intersect for

$8-x^2 = x^2 \implies 2x^2 = 8 \implies x^2 = 4 \implies x=\pm2$

and so the base of each solid is the set

$B = \left\{(x,y) \,:\, -2\le x\le2 \text{ and } x^2 \le y \le 8-x^2\right\}$

The side length of each cross section that coincides with B is equal to the vertical distance between the two parabolas, $|x^2-(8-x^2)| = 2|x^2-4|$ . But since -2 ≤ x ≤ 2, this reduces to $2(x^2-4)$ .

a. Square cross sections will contribute a volume of

$\left(2(x^2-4)\right)^2 \, \Delta x = 4(x^2-4)^2 \, \Delta x$

where ∆x is the thickness of the section. Then the volume would be

$\displaystyle \int_{-2}^2 4(x^2-4)^2 \, dx = 8 \int_0^2 (x^2-4)^2 \, dx \\\\ = 8 \int_0^2 (x^4-8x^2+16) \, dx \\\\ = 8 \left(\frac{2^5}5 - \frac{8\times2^3}3 + 16\times2\right) = \boxed{\frac{2048}{15}}$

where we take advantage of symmetry in the first line.

b. For a semicircle, the side length we found earlier corresponds to diameter. Each semicircular cross section will contribute a volume of

$\dfrac\pi8 \left(2(x^2-4)\right)^2 \, \Delta x = \dfrac\pi2 (x^2-4)^2 \, \Delta x$

We end up with the same integral as before except for the leading constant:

$\displaystyle \int_{-2}^2 \frac\pi2 (x^2-4)^2 \, dx = \pi \int_0^2 (x^2-4)^2 \, dx$

Using the result of part (a), the volume is

$\displaystyle \frac\pi8 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{256\pi}{15}}}$

c. An equilateral triangle with side length s has area √3/4 s², hence the volume of a given section is

$\dfrac{\sqrt3}4 \left(2(x^2-4)\right)^2 \, \Delta x = \sqrt3 (x^2-4)^2 \, \Delta x$

and using the result of part (a) again, the volume is

$\displaystyle \int_{-2}^2 \sqrt 3(x^2-4)^2 \, dx = \frac{\sqrt3}4 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{512}{5\sqrt3}}$

7 0

2 years ago

Help....................

Romashka-Z-Leto [24]

Answer:

The interquartile range is 50.

Step-by-step explanation:

To find our answer we have to first quartile 1 and quartile 3 are equal too. When we look at the plot quartile 1 is equal to 20, quartile 3 is equal to 70 because it is in between 60 and 80. Now to find the interquartile range we will subtract 70 from 20 and we get 50. Therefore, 50 is our answer.

7 0

2 years ago

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