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3 years ago

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All items produced in a factory are checked for defects. Of the 300 items checked, 3% were found to be defective. How many of th

e items are defective?

1 answer:

Pani-rosa [81]3 years ago

5 0

Answer:

3%×300,=900

900÷100=9

Step-by-step explanation:

answer is 9

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Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter: 116 meters

Naily [24]

Answer:

Length = 29 m

Width = 29 m

Step-by-step explanation:

Let x and y be the length and width of the rectangle, respectively.

The area and perimeter are given by:

$A=xy\\p=116=2x+2y\\y=58-x$

Rewriting the area as a function of x:

$A(x) = x(58-x)\\A(x) = 58x-x^2$

The value of x for which the derivate of the area function is zero, is the length that maximizes the area:

$A(x) = 58x-x^2\\\frac{dA}{dx}=0=58-2x\\ x=29\ m$

The value of y is:

$y = 58-29\\y=29\ m$

Length = 29 m

Width = 29 m

4 0

3 years ago

Please Help NO LINKS

schepotkina [342]

$V = 864\pi$

Step-by-step explanation:

Since one of the boundaries is y = 0, we need to find the roots of the function $f(x)=-2x^2+6x+36$ . Using the quadratic equation, we get

$x = \dfrac{-6 \pm \sqrt{36 - (4)(-2)(36)}}{-4}= -3,\:6$

But since the region is also bounded by $x = 0$ , that means that our limits of integration are from $x=0$ (instead of -3) to $x=6$ .

Now let's find the volume using the cylindrical shells method. The volume of rotation of the region is given by

$\displaystyle V = \int f(x)2\pi xdx$

$\:\:\:\:\:\:\:= \displaystyle \int_0^6 (-2x^2+6x+36)(2 \pi x)dx$

$\:\:\:\:\:\:\:= \displaystyle 2\pi \int_0^6 (-2x^3+6x^2+36x)dx$

$\:\:\:\:\:\:\:= \displaystyle 2\pi \left(-\frac{1}{2}x^4+2x^3+18x^2 \right)_0^6$

$\:\:\:\:\:\:\:= 864\pi$

3 0

3 years ago

Use the extended form find the perimeter of the square shape of 10cm and 18cm

dexar [7]

The perimeter of the square would be 56 cm

3 0

3 years ago

Nick made a histogram showing the number of sport caps each of his friends own.

Alex17521 [72]

Its A 7 considering you minus 13 which is 2 or 3 cups and 6 which is 6 or 7 cups, so 13-6=7

4 0

3 years ago

Read 2 more answers

If the estimate of expected population proportion having a desired characteristic based on intuition is 60 percent and the accep

Anika [276]

Answer:

B

Step-by-step explanation:

Our values are:

N = 100,000 (We assume it)

Proportion is p = 0.6

Margin of error (E) = 0.05

confidence-level (cl) = 0.95

Z-value = 1.96

We need to approach through Proportion,

$n=\frac{ (z_2 * p *q) + ME_2}{ME_2 + z_2 * p * q / N}$

Substituting,

$n = \frac{(1.962*0.6*0.4)+0.052}{0.052 + \frac{1.962 * 0.6 * 0.4}{100000}}$

$n= \frac{(3.841 * 0.24)+0.0025}{0.0025+\frac{3.841*0.24}{100000}}$

$n =\frac{ 0.9243}{0.002509}$

$n= 368$

3 0

3 years ago