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3 years ago

13

A nail manufacturer throws out nails with lengths that are not within 0.05 inch of the mean of the batch. The lengths (in inches

) of the nails in a batch are 0.42 0.53 0.55 0.48 and 0.51 which nails should be thrown out

1 answer:

Natasha_Volkova [10]3 years ago

7 0

Answer:

0.42 & 0.55

Step-by-step explanation:

Mean length = 0.42 + 0.53+ 0.55 + 0.48 + 0.51/5

= 0.498

0.42 - 0.498 = - 0.078‬

0.53 - 0.498 = 0.032‬

0.55 - 0.498 = 0.052‬

0.48 - 0.498 = - 0.018‬

0.51 - 0.498 = 0.012‬

The nails to be thrown out are:

0.42 & 0.55 because their deviations from the mean are not within 0.05 inch

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What is the multiplicative inverse of 5 in z11, z12, and z13? you can do a trial-and-error search using a calculator or a pc?

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A multiplicative inverse of an integer a is an integer x such that the product ax is congruent to 1 with respect to the modulus m.

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Check:

$5\cdot 0=\overline{0};$
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2. $Z_{12}=\{\overline{0},\overline{1},\overline{2},\overline{3},\overline{4},\overline{5},\overline{6},\overline{7},\overline{8},\overline{9},\overline{10},\overline{11}\}.$

Check:

$5\cdot 0=\overline{0};$
$5\cdot 1=\overline{5};$
$5\cdot 2=\overline{10};$
$5\cdot 3=15=\overline{3};$
$5\cdot 4=20=\overline{8};$
$5\cdot 5=25=\overline{1};$
$5\cdot 6=30=\overline{6};$
$5\cdot 7=35=\overline{11};$
$5\cdot 8=40=\overline{4};$
$5\cdot 9=45=\overline{9};$
$5\cdot 10=50=\overline{2};$
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The multiplicative inverse of 5 in $Z_{12}$ is 5.

3. $Z_{13}=\{\overline{0},\overline{1},\overline{2},\overline{3},\overline{4},\overline{5},\overline{6},\overline{7},\overline{8},\overline{9},\overline{10},\overline{11},\overline{12}\}.$

Check:

$5\cdot 0=\overline{0};$
$5\cdot 1=\overline{5};$
$5\cdot 2=\overline{10};$
$5\cdot 3=15=\overline{2};$
$5\cdot 4=20=\overline{7};$
$5\cdot 5=25=\overline{12};$
$5\cdot 6=30=\overline{4};$
$5\cdot 7=35=\overline{9};$
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$5\cdot 9=45=\overline{6};$
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$5\cdot 11=55=\overline{3};$
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