Sample size= n= 84
sample mean= x = 107 s
population standard deviation =σ= 11.7
As, population standard deviation is given so we use the estimate:
x(+/-) z(α/2)(σ/√n)
At 99% Confidence interval means significance level is α=1-0.99= 0.01
So,
α/2=0.005
Now, z at α/2=0.005
z= 2.576
Now, by putting values
107(+/-)((2.576)(11.7/√84))
( 107-((2.576)(11.7/√84)), 107+((2.576)(11.7/√84)) )
(103.7, 110.288)
Hi there! I can help you!
a. Okay. So we have to make a table for the amount of butterflies to total insects. Let's simplify the ratio. 36:100 simplifies to 9:25. We can use that ratio to make this table. Just multiply 25 by the amount it takes to get to 50 or 100, and multiply by the same amount at the top to find the amount of butterflies. If you do it correctly, your table should be as shown below in the image.
b. On that note, let's solve for the amount of butterflies in the conservatory. There are 450 total of them. Let's divide 450 by 100 to find the amount we will multiply by. 450/100 is 4.5. We will mutliply 36 by that amount to find the total amount of butterflies. 36 * 4.5 is 162. That's it. There are 162 butterflies in the conservatory.
Answer:
5 and 6
Step-by-step explanation:
Consider perfect square numbers either side of 29
25 < 29 < 36, thus
<
<
, that is
5 <
< 6
Answer:
a. FG ≈ 6.983 cm
b. FH = 13.16 cm
Step-by-step explanation:
<h3>a)</h3>
Corresponding sides of similar triangles are proportional. This means ...
FG/GH = CD/DE
FG = GH(CD/DE) = (9.4 cm)(2.6/3.5) . . . . . . multiply by GH; fill in values
FG ≈ 6.983 cm
__
<h3>b)</h3>
And ...
FH/GH = CE/DE
FH = GH(CE/DE) = (9.4 cm)(4.9/3.5)
FH = 13.16 cm
__
<em>Additional comment</em>
Corresponding vertices are listed in the same order in the similarity statements. This means, for example, segment FG (which names the first two vertices in the name of ΔFGH) will correspond to segment CD (which names the first two vertices of ΔCDE).
Step-by-step explanation:
The triangle is an Isosceles Right.