You can buy an 8-pack of paper towels for $7.92 or a 12-pack for $11.64. Which is the better buy?

A company purchases a small metal bracket in containers of 5,000 each. Ten containers have arrived at the unloading facility, an

MariettaO [177]

Answer:

Do the data from this shipment indicate statistical control: No

Step-by-step explanation:

Calculating the mean of the sample, we have;

Mean (x-bar) = sum of individual sample/number of sample

= (0+0+0+0.004+0.008+0.020+0.004+0+0+0.008)/10

= 0.044/10

= 0.0044

Calculating the lower control limit (LCL) using the formula;

LCL= (x-bar) - 3*√(x-bar(1-x-bar))/n

= 0.0044 - 3*√(0.0044(1-0.0044))

= 0.0044- (3*0.0042)

= 0.0044 - 0.01256

= -0.00816 ∠ 0

Calculating the upper control limit (UCL) using the formula;

UCL = (x-bar) + 3*√(x-bar(1-x-bar))/n

= 0.0044 + 3*√(0.0044(1-0.0044))

= 0.0044+ (3*0.0042)

= 0.0044 + 0.01256

=0.01696∠ 0

Do the data from this shipment indicate statistical control: No

Since the value 0.02 from the 6th shipment is greater than the upper control limit (0.01696), we can conclude that the data from this shipment do not indicate statistical control.

8 0

3 years ago

PROVE THAT:<br><br>cos 20° - sin 20° = \sqrt{2}sin25°<br><br>

Lemur [1.5K]

Answer:

See below.

Step-by-step explanation:

$\cos(20)-\sin(20)=\sqrt{2}\sin(25)$

First, use the co-function identity:

$\sin(90-x)=\cos(x)$

We can turn the second term into cosine:

$\sin(20)=\sin(90-70)=\cos(70)$

Substitute:

$\cos(20)-\cos(70)=\sqrt{2}\sin(25)$

Now, use the sum to product formulas. We will use the following:

$\cos(x)-\cos(y)=-2\sin(\frac{x+y}{2})\sin(\frac{x-y}{2})$

Substitute:

$\cos(20)-\cos(70)=-2\sin(\frac{20+70}{2})\sin(\frac{20-70}{2})\\\cos(20)-\cos(70) =-2\sin(45)\sin(-25)\\\cos(20)-\cos(70)=-2(\frac{\sqrt{2}}{2})\sin(-25)\\ \cos(20)-\cos(70)=-\sqrt{2}\sin(-25)$

Use the even-odd identity:

$\sin(-x)=-\sin(x)$

Therefore:

$\cos(20)-\cos(70)=-\sqrt{2}\sin(-25)\\\cos(20)-\cos(70)=-\sqrt{2}\cdot-\sin(25)\\\cos(20)-\cos(70)=\sqrt{2}\sin(25)$

Replace the second term with the original term:

$\cos(20)-\sin(20)=\sqrt{2}\sin(25)$

Proof complete.

4 0

4 years ago

Which figure shows the correct dimensions of a 1/3 scale drawing of the given figure?

Valentin [98]

Answer:

Step-by-step explanation:

Ok I cannot see the figure but let me explain to you how to do this. If you see the and know the measurments, just divide all the measurements by 3 and draw the figure again. If I have a rectangle with side lengths 12 and 9, and I want to draw a 1/3 scale drawing, I would divide 12/3 = 4 and 9/3 = 3. So your new sidelengths are 4 and 3. I hoped this helped a little!!

6 0

3 years ago

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Describe how the point-slope formula is useful when writing the equation of a trend line

Hitman42 [59]

Answer:

Trend lines are lines used to approximate the general shape of a scatter plot. A positive trend line tells us the scatter plot has a positive correlation. A negative trend line tells us the scatter plot has a negative correlation.

5 0

3 years ago

C gives the cost, in dollars, of a cafeteria meal plan as a function of the number of meals

SVETLANKA909090 [29]

Answer:

9

Step-by-step explanation:

First, write the equation.

C(n) = 4 + 3n

We know that C(n) = 31, so we can substitute it.

31 = 4 + 3n

Subtract 4 from both sides to isolate the term with the variable.

27 = 3n

Divide both sides by 3 to get the variable by itself.

9 = n

4 0

3 years ago

Read 2 more answers