Answer:
CI 98 % = ( 3.332 ; 5.668 )
t(c) = 2.9979
Step-by-step explanation:
Confidence Interval CI 98 % then α = 2 % α = 0,02 α/2 = 0.01
Sample information:
Sample size n = 8
sample mean x = 4.5
standard deviation of sample s = 1.1 kg
degree of freedom df = n - 1 df = 8 - 1 df = 7
With α/2 0.01 and df = 7 from t-studente table we find t(c)
t(c) = 2.9979
CI 98 % = ( x ± t(c) * s/√n )
CI 98 % = ( 4.5 ± 2.9979 * 1.1/ √8 )
CI 98 % = ( 4.5 ± 3.2976/2.8228 )
CI 98 % = ( 4.5 ± 1.168 )
CI 98 % = ( 3.332 ; 5.668 )
Remark
Are you sure you don't mean that (x - 7) is squared? The way you have written it indicates that it is squared. I'll treat it that way and you can leave a not if I am wrong.
Solution
(x - 7)^2 - 25 = 0 Add 25 to both sides
(x - 7)^2 - 25 + 25 = 25 Combine the left
(x - 7)^2 = 25 Take the square root of both sides.
sqrt(x - 7)^2 = sqrt(25)
x - 7 = +/- 5 Add 7 to both sides
x = 7 +/- 5
=========
x1 = 7 + 5
x1 = 12
x2 = 7 - 5
x2 = 2
Smallest x = 2
Largest x = 12
First is to get the given data that we might be able to use for computation.
H = 8 inches
Area = 96
B1 = B1
B2 = B1+6
Next is to know the area of a trapezoid
Area = H x (B1 + B2)/2
96 = 8 x (B1 + B1 + 6) / 2
96 = 8 x (2B1 + 6) /2
96 = 4 x (2B1 + 6)
14 = 2B1 + 6
2B1 = 8
B1 = 4
B2 = 10
0.5x22=11. To get answers like that, all you have to do is divide 11 by anything and then that number times the number you divided 11 by will give you the answer. So like 11 divided by 4 is 2.75. So 4x2.75=11.
Answer:
15 cakes can be decorated.
Step-by-step explanation:
Given:
Total number of shapes Liu has = 140
Ratio of shape of stars and hearts = 4 : 3
According to the question:
Each cake have 5 stars and 4 hearts.
Let the number of starts be "4x" and number of hearts be "3x" from the ratio.
Now,
⇒ 
⇒ 
⇒ 
⇒ 
Number of stars = 
Number of hearts = 
Each cake have 5 stars and 4 hearts .
How many cakes can be decorated with 80 stars.
⇒ No.of cakes = Total number of stars / 5
⇒ 
⇒ 
How many cakes can be decorated with 60 hearts.
⇒ 
⇒ 
But both shapes are in combination so only 15 cakes can be decorated with the combination of 5 stars and 4 hearts.
Liu can decorate 15 cakes and only.
