![573589](/avatars/14662.jpg)
573589
23.11.2019 •
Mathematics
The top and bottom margins of a poster are 8 cm and the side margins are each 6 cm. if the area of printed material on the poster is fixed at 390 square centimeters, find the dimensions of the poster with the smallest area.
the top and bottom margins of a poster are 8 cm an
width = (include units)
height = (include units)
Solved
Show answers
More tips
- F Food and Cooking What to Give as a Wedding Gift?...
- F Food and Cooking Everything You Need to Know About Pasta...
- C Computers and Internet How to Choose a Monitor?...
- S Style and Beauty How to Get Rid of Peeling Nails: Natural Remedies...
- S Science and Technology Understanding Magnetic Storms: A Guide to This Natural Phenomenon...
- F Family and Home What is Most Important in Men s Lives?...
- G Goods and services Which TV is better - LCD or Plasma?...
- C Computers and Internet Are there special gaming mice?...
- G Goods and services LED-подсветка в LCD-телевизорах: 5 причин, почему она лучше других технологий...
- C Computers and Internet Keep Your Mouse Pad Clean: The Right Way to Clean It?...
Answers on questions: Mathematics
- M Mathematics If r = 25 cm and s = 7 cm, what is the length of t? a. 14 cm b. 24 cm c. 5589 cm d. 2v139 cm...
- M Mathematics Find the area of the figure. round to the nearest tenth if necessary. use 3.14 for . a. 67.7 units2 b. 69.1 units2 c. 132.48 units2 d. 66.2 units2...
- M Mathematics Ihave 12.32m of ribbon. i need 16 pieces 0.8 m long each. how many pieces can i cut....
- M Mathematics Afence is 10 ft wide by 10 ft long. if posts are placed 2 feet apart how many posts are needed?...
- M Mathematics Asmall bar of gold measures 40mm by 25mm by 2mm. one cubic millimeter of gold weights about 0.0005 ounces. find the volume in cubic millimeter and the weight in ounces of this...
- M Mathematics (geometry) how can technology be used to complete constructions? (i think it involves parallel and perpendicular not sure tho)...
- M Mathematics What is an equation in point slope form the line parallel to y=3x+2 that contain p(-7, -6)? a. y- 6=3(x + 7) b. x+6= -3(y +7) c. y+ 6= -3(x +7) d. y+ 6= 3(x + 7)...
- M Mathematics Boxes edges measuring 3 feet what is the volum...
- M Mathematics What is 2x +3x. a 5x b 2x c 3x d 1x...
- M Mathematics 21(2−x) 12x=44 i don t know what do what does x equal...
Ответ:
Dimensions of the poster
Width 29.10 cm
Height 38.80 cm
A(min) = 1129.08 cm²
Step-by-step explanation:
Printed area = 390 cm² = Ap
Lets call x and y dimensions of printed area
x width
y height
Then Ap = x*y and
y = Ap/x ⇒ y = 390/x
Then total area of the poster is:
A(t) = ( x + 12 ) * ( y + 16 ) and y = 390/x
A as a function of x
A(x) = ( x + 12 ) * ( 390/x + 16 ) ⇒ A(x) = 390 + 16x + 4680/x + 192
A(x) = 582 + 16x + 4680/x (1)
Taking derivatives
A´(x) = 16 - (4680/x²) ⇒ A´(x) = 0
[ 16x² -4680] /x² = 0 16x²- 4680 = 0 ⇒ x² = 4680/16
x = 17.10 cm and y = 390/x y = 390/17.10 y = 22.80 cm
A(t) = ( 17.10 + 12 ) * ( 22.80 + 16 )
A(t) = 29.10 * 38.80
A(t) = 1129.08 cm²
If we substitute in equation (1) the value of x ( 17.10) we see A(x) > 0
Then there is a minimun at the point x = 17.10
Ответ:
The p-value of the test is 0.1469 > 0.05, which means that there is no reason to believe that the proportion of adults favoring capital punishment today has increased, using a 0.05 level of significance.
Step-by-step explanation:
Suppose that, in the past, 40% of all adults favored capital punishment. Test if the proportion has increased:
At the null hypothesis, we test if the proportion is still of 40%, that is:
At the alternative hypothesis, we test if the proportion has increased, that is, is greater than 40%, so:
The test statistic is:
In which X is the sample mean,
is the value tested at the null hypothesis,
is the standard deviation and n is the size of the sample.
0.4 is tested at the null hypothesis:
This means that![\mu = 0.4, \sigma = \sqrt{0.4*0.6}](/tpl/images/1400/5392/708f2.png)
Random sample of 15 adults, 8 favor capital punishment.
This means that![n = 15, X = \frac{8}{15} = 0.5333](/tpl/images/1400/5392/6b074.png)
Value of the test statistic:
P-value of the test and decision:
The p-value of the test is the probability of finding a sample proportion of 0.5333 or more, which is 1 subtracted by the p-value of z = 1.05.
Looking at the z-table, z = 1.05 has a p-value of 0.8531.
1 - 0.8531 = 0.1469.
The p-value of the test is 0.1469 > 0.05, which means that there is no reason to believe that the proportion of adults favoring capital punishment today has increased, using a 0.05 level of significance.