| u | = √(2² + (-1²)) = √5
| v | = √ ( 1² + (-8)² = √65
cos (u,v) = ( u * v ) / (| u | * | v |) =
(2 * 1 + ( -1 ) * ( - 8 )) / √5 √ 65 = (2 + 8) / √5 √65 = 10 / (√5 √ 65 )
The length of a larger diagonal:
d 1² = | u |² + 2 |u| |v| + | v |² = 5 + (2 √5 √65 * 10 / √5 √65 )+65
d 1² = 70 + 20 = 90
d 1 = √ 90 = 3√10
d 2² = 70 - 20 = 50
d 2 = √50 = 5√2
Answer:
The lengths of the diagonals are: 3√10 and 5√2 .
Answer:
Step-by-step explanation:
Given a total of 12 diesel engines
out of which 2 are defective
Company have to choose 5 good engines to ship.
Therefore no of ways in good engines are selected is 
no of ways in which any 5 engines are selected from a total of 12 engines is
Therefore the required probability =
=
=0.318
0 + (-3 1/4)
1 + (-4 1/4)
2 + (-5 1/4)
The landscape artist who designed New York City’s Central Park believed that providing scenic settings accessible to all would not only benefit the public’s physical and mental health <u>and also foster a sense of democracy. </u> (Option D: but also foster a sense of democracy).
<h3>What is sentence correction?</h3>
Sentence correction or sentence improvement is a type of grammatical practice where a sentence is given with a word or a phrase that requires grammatical changes or improvement.
Now,
- When 'not only' is used, 'but also' must come after it. When utilizing a correlative conjunction like "not only," "but also," the goal should be parallelism, meaning that the words that come after both sides of the conjunction should be from the same part of speech.
- Here, using 'and' after 'not only...' distorts the structure of the sentence.
Hence, Option D is the right response, i.e., The landscape artist who designed New York City’s Central Park believed that providing scenic settings accessible to all would not only benefit the public’s physical and mental health <u>and also foster a sense of democracy. </u> (Option D: but also foster a sense of democracy).
To learn more about sentence correction, refer to the link: brainly.com/question/14632568
#SPJ4
<span>(a) $7.04
(b) 704/1599
(c) 0.44
(d) 14
(e) $98.56
(a) How much profit does Lucy earn when she sells a necklace?
Since the problem states that her profit is the sale price minus the cost of materials and labor, we have the following equation.
P = $15.99 - $3.38 - $5.57
P = $12.61 - $5.57
P = $7.04
So her profit is $7.04 per necklace.
(b) Write a fraction of the profit per sale price of the necklace. Record your answer as a fraction using whole numbers.
The raw fraction is 7.04/15.99, to get rid of the decimal point, multiply top and bottom by 100, getting 704/1599.
The prime factors of 704 are 2,2,2,2,2,2,11 and the prime factors of 1599 are 3,13,41. Since neither 704, nor 1599 share any common factors, the fraction can't be reduced and the final answer is 704/1599.
(c) What decimal of every dollar of the sale price of the necklace is profit using the fraction from Part (b)?
Pardon the lack of formatting
704/1599 = 0.4403
Rounded to the nearest hundredth gives 0.44
(d) Lucy collected $223.86 selling necklaces at a craft fair. How many necklaces did Lucy sell? Show your work.
This question is asking for total cost. So divide the $223.86 by the sale price of $15.99.
$223.86 / $15.99 = 14
14 necklaces were sold.
(e) How much profit did she earn from the number of necklaces she sold? Show your work.
Since we know from (a) that she has $7.04 profit per necklace, just multiply the amount of profit by the number sold. So
$7.04 * 14 = $98.56</span>
