What is the x-coordinate of the solution to the system?

How many weeks of data must be randomly sampled to estimate the mean weekly sales of a new line of athletic footwear? We want 98

Irina18 [472]

Answer:

$n=(\frac{2.33(1400)}{400})^2 =66.50 \approx 67$

So the answer for this case would be n=67 rounded up

Step-by-step explanation:

Information given

$\bar X$ represent the sample mean for the sample

$\mu$ population mean

$\sigma=1400$ represent the sample standard deviation

n represent the sample size

Solution to the problem

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

And on this case we have that ME =400 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

The critical value for 98% of confidence interval now can be founded using the normal distribution. And the critical value would be $z_{\alpha/2}=2.33$ , replacing into formula (b) we got:

$n=(\frac{2.33(1400)}{400})^2 =66.50 \approx 67$

So the answer for this case would be n=67 rounded up

8 0

3 years ago

Which graph represents the piecewise-defined function? y={−45x−3 if x<03x−10 if x≥2

Nikitich [7]

Step-by-step explanation:

$y=\left \Bigg\{ {\big{-45x-3 \qquad x < 0} \atop \big{3x - 10 \qquad x \geq2 }} \right.$

$\begin {array}{c|c}{ x&y}}\\ -\infty&-\infty\\-2&-93\\-1&-48\\ 0 &-3^*\\1&nothing\\2&-4\\3&-1\\4&2\\ \infty&\infty\\\end{array}$

* open dot

You did not provide the graphs to choose from so use the table above to determine which graph fits those coordinates.

Make sure that:

(0, -3) has an open dot
nothing is plotted between x = 0 and x = 2
(2, -4) has a closed dot

3 0

3 years ago

The area of a rectangular wall of a barn is 252 square feet. Its length is 10 feet longer than twice its width. Find the length

valentinak56 [21]

Answer: Length = 28 feet and width = 9 feet

Step-by-step explanation:

Let x = width of the wall.

Then, Length of the wall = 10+2x

Since , Area of rectangle = length x width

Then, as per given,

$252= (10+2x)x\\\\\Rightarrow\ 252=10x+2x^2\\\\\Rightarrow\ 2x^2+10x-252=0\\\\\Rightarrow\ x^2+5x-126=0\\\\\Rightarrow\ x^2+14x-9x-126=0\\\\\Rightarrow\ (x+14)-9(x+14)=0\\\\\Rightarrow\ (x+14)(x-9)=0\\\\\Rightarrow\ x=-14 \ or \ x= 9$

Since width cannot be negative , so x = 9

So width = 9 feet and length = 10+2(9)=10+18 = 28 feet

Hence, length is 28 feet and width is 9 feet of the wall of the barn.

7 0

3 years ago

If a positive integer is equal to the following product: 25b3c425b3c4, where b and c are distinct prime numbers greater than 2,

Vlad [161]

Answer: 64 distinct even factors

Step-by-step explanation:

let the 2 distinct numbers be b and c and the integer is expected to be 25b3c425b3c4

since b, c > 2 and prime numbers,

potential options include 3, 5, and 7

hence the likelihoods are (b = 3, c = 5), (b = 5, c = 3), (b = 3, c = 7), (b = 7, c = 3), (b = 5, c = 7), (b = 7, c = 5)

Possibility 1 (b = 3, c = 5)

integer is now 253354253354

the distinct even factors = 2, 202, 262, 1934, 19802, 26462, 195334, 253354, 2000002, 2594062, 19148534, 25588754, 262000262, 1934001934, 2508457954, 253354253354

number of distinct even factors = 16

Possibility 2 (b = 5, c = 3)

integer is now 255334255334

the distinct even factors = 2, 86, 202, 5938, 8686, 19802, 253354, 599738, 851486, 2000002, 25788734, 58792138, 25588754, 86000086, 2528061934, 1934001934, 5938005938, 253354253354

number of distinct even factors = 18

Possibility 3 (b = 3, c = 7)

integer is now 253374253374

the distinct even factors = 2, 6, 22, 66, 202, 242, 606, 698, 726, 2094, 2222, 6666, 7678, 19802, 23034, 24442, 59406, 70498, 73326, 84458, 211494, 217822, 253374, 653466, 775478, 2000002, 2326434, 2396042, 6000006, 6910898, 7188126, 8530258, 20732694, 22000022, 25590774, 66000066, 76019878, 228059634, 242000242, 698000698, 726000726, 836218658, 2094002094, 2508655974, 7678007678, 23034023034, 84458084458,253354253354

number of distinct even factors = 48

Possibility 4 (b = 7, c = 3)

integer is now 257334257334

the distinct even factors = 2, 6, 14, 22, 42, 66, 154, 202, 462, 606, 1114, 1414, 2222, 3342, 4242, 6666, 7798, 12254, 15554, 19802, 23394, 36762, 46662, 59406, 85778, 112514, 138614, 217822, 257334, 337542, 415842, 653466, 787598, 1237654, 1524754, 2000002, 2362794, 3712962, 4574262, 6000006, 8663578, 11029714, 14000014, 22000022, 25990734, 33089142, 42000042, 66000066, 77207998, 121326854, 154000154, 231623994, 363980562, 462000462, 849287978, 1114001114, 2547863934, 3342003342, 7798007798, 12254012254, 23394023394, 36762036762, 85778085778, 257334257334

number of distinct even factors = 64

Possibility 5 (b = 5, c = 7)

integer is now 255374255374

the distinct even factors = 2, 14, 34, 58, 74, 202, 238, 406, 518, 986, 1258, 1414, 2146, 3434, 5858, 6902, 7474, 8806, 15022, 19802, 24038, 36482, 41006, 52318, 99586, 127058, 138614, 216746, 255374, 336634, 574258, 697102, 732674, 889406, 1517222, 2000002, 2356438, 3684682, 4019806, 5128718, 9762386, 12455458, 14000014, 21247546, 25792774, 34000034, 58000058, 68336702, 74000074, 87188206, 148732822, 238000238, 361208282, 406000406, 518000518, 986000986, 1258001258, 2146002146, 2528457974, 6902006902, 8806008806, 15022015022, 36482036482, 255374255374

number of distinct even factors = 64

Possibility 6 (b = 7, c = 5)

integer is now 257354257354

the distinct even factors = 2, 202, 19802, 257354, 2000002, 25992754, 2548061954, 257354257354

number of distinct even factors = 8

From the six possibilities, the highest number of likely distinct even factors is 64

7 0

3 years ago

HELP PLS ASP WITH THE CORRECT ANSWER I WILL GUVE YOU 17 POINTS PLS ASP!!!! Drag and drop the angles pairs to correctly match the

Tems11 [23]

COB and COD complementary
AOB and BOC adjacent angle that is neither comp. or supp.
AOC and COD supplementary
AOE and COD vertical

6 0

3 years ago