Answer:
Width (length of shorter side) = 3.5 cm.
Step-by-step explanation:
L = 8.5 cm
perimeter, P = 24 cm
2(L+W) = 24
substitute L = 8.5
2(8.5+W) = 24
8.5 + W = 24/2 = 12
W = 12 - 8.5 = 3.5 cm
Answer:The base of the ladder from the tree is 28ft
Step-by-step explanation:
Using pythagorean theorem
Let 100ft= hypothesis is the right angle triangle
Let 96ft be the height of the ladder
Let x be the base of the right angle triangle between the base of the ladder and the tree
h^2=a^2+b^2
100^2=96^2 +b^2
10,000=9216 +b^2
b^2=10,000-9216
b=sqrt(784)
b=28ft
Answer:
We conclude that the machine is under filling the bags.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 436.0 gram
Sample mean, 
= 429.0 grams
Sample size, n = 40
Alpha, α = 0.05
Population standard deviation, σ = 23.0 grams
First, we design the null and the alternate hypothesis
We use one-tailed(left) z test to perform this hypothesis.
Formula:
Putting all the values, we have
Now, 
Since,
We reject the null hypothesis and accept the alternate hypothesis. Thus, we conclude that the machine is under filling the bags.
For the first one, you have to convert the fractions to an improper fraction. To do that you need to multiply the bottom denominator number (3) by the whole number (1) then you need to add the numinator, so 3x1+2= 5. You have to keep the denominator so 1 2/3 is equal to 5/3. Then do the same to 2 1/5, and you get 11/5. Now you have to find a common denominator, that's basically the smallest number that both numbers can go Into, the lowest common denominator for 3 and 5 is 15. So 3x5= 15, so we have to multiply the top number by 5 which is 25. So 5/3 is equal to 25/15, then 5x3= 15, so you need to multiply 11 by 3 which is 33. So 11/5 is equal to 33/15. Then you add them. Add the numinators (25+33=58. Then you keep the denominator 15. So when u add it it's 58/15 then you need to simplify that and you get 3 13/15.
The second one you turn them into improper fractions like I told you how to before (multiply the bottom number by the whole number then add he top number, then add he same denominator.) do that for both. Then you line them right next to each other and multiply across. (I just realized that they were the same number so they are equal to 5/3 and 11/5)
Then you do 5x11 and you get 55 then do 3x5 and you get 15. 55/15 is your answer, but you need to simplify it, you need to divide 55 by 15, (not all the way just the first number) so you do 15x3 and that's 45, then you subtract that from 55, and you get 10, so then you take your denominator (15) and you answer is 3 10/15. But when you simplify it it's 3 and 2/3
Hope I helped sorry it's so long and sorry for any typos it's so long I didn't go back and check
Answer: 1.6
<u>Order the numbers</u>
5,6,6,8,10
<u>Add</u>
5+6+6+8+10=35
<u>Divide</u>
35÷5=7
Mean: 7
Sum divided by the count.
Final Answer: 1.6
