Answer: Fourth option is correct.
Step-by-step explanation:
Since we have given that
Mean of sample = 65.3
Standard deviation = 5.2
We need to find the 90% confidence interval for the mean.
So, z = 1.64
And the interval would be
Hence, Fourth option is correct.
Answer:
16pi or 50.2
Step-by-step explanation:
formula for area of a circle is pi * radius squared. Since the diameter is 8 you divide that by 2 to get 4 and you square it so it becomes 16. Then you multiply it by pi or 3.14 to get 50.24 and then you round.
Answer:
When selecting subsets of a larger set in which order is not important, you are finding the number of combination of n elements taken r at a time.
Step-by-step explanation:
We have to fill the blank.
When selecting subsets of a larger set in which order is not important, you are finding the number of combination of n elements taken r at a time.
Combination:
- A combination is a selection of all or part of a set of objects from a larger set such that the order of selection is not important.
- This is given by the formula:
where n is the number of objects in consideration or the larger set from which we have to choose r with no repetition.
Answer:
<h2><em>
2ft by 2ft by 1 ft</em></h2>
Step-by-step explanation:
Total surface of the cardboard box is expressed as S = 2LW + 2WH + 2LH where L is the length of the box, W is the width and H is the height of the box. Since the cardboard box is without a lid, then the total surface area will be expressed as;
S = lw+2wh+2lh ... 1
Given the volume V = lwh = 4ft³ ... 2
From equation 2;
h = 4/lw
Substituting into r[equation 1;
S = lw + 2w(4/lw)+ 2l(4/lw)
S = lw+8/l+8/w
Differentiating the resulting equation with respect to w and l will give;
dS/dw = l + (-8w⁻²)
dS/dw = l - 8/w²
Similarly,
dS/dl = w + (-8l⁻²)
dS/dw = w - 8/l²
At turning point, ds/dw = 0 and ds/dl = 0
l - 8/w² = 0 and w - 8/l² = 0
l = 8/w² and w =8/l²
l = 8/(8/l² )²
l = 8/(64/I⁴)
l = 8*l⁴/64
l = l⁴/8
8l = l⁴
l³ = 8
l = ∛8
l = 2
Hence the length of the box is 2 feet
Substituting l = 2 into the function l = 8/w² to get the eidth w
2 = 8/w²
1 = 4/w²
w² = 4
w = 2 ft
width of the cardboard is 2 ft
Since Volume = lwh
4 = 2(2)h
4 = 4h
h = 1 ft
Height of the cardboard is 1 ft
<em>The dimensions of the box that requires the least amount of cardboard is 2ft by 2ft by 1 ft</em>
Your slope would be -1/4x. If you look at the y-intercept on your graph, which is -2, you would start to count up one box and over 4 boxes to the left. We call this rise/run. So knowing what the slope is now, your entire equation would be y= -1/4x - 2. (Also, if the line is going up towards the left it is a negative slope, if it's to the right it is positive.) I hope this helps love! :)