<span>The <u>correct answer</u> is:
A) 60% ± 18%.
Explanation:
In a confidence interval, the margin of error is given by z*(</span>σ/√n<span>), where </span>σ<span> is the standard deviation and n is the sample size.
First we <u>find the value of z</u>:
We want a 95% confidence level; 95% = 95/100 = 0.95.
To find the z-score, we first subtract this from 1:
1-0.95 = 0.05.
Divide by 2:
0.05/2 = 0.025.
Subtract from 1 again:
1-0.025 = 0.975.
Using a z-table, we find this value in the middle of the table. The z-score that is associated with this value is 1.96.
Back to our formula for margin of error, we have 1.96(</span>σ<span>/</span>√n<span>). The larger n, the sample size, is, the larger its square root is. When we divide by a larger number, our answer is smaller; this gives us a smaller margin of error.
This means that if we had a small sample size, we would divide by a smaller number, making our margin of error larger. The largest margin of error we have in this question is 18%, so this is our correct answer.</span>
Answer:
A- 7.4 ⋅ 10−4 mm
Step-by-step explanation:
Well, to solve this problem, we must convert the number and / or the units in a more imaginable one.
We are given two choices:
a. 7.4 x 10^-4 mm
b. 7.4 x 10^4 mm
Converting the units and numbers into meters and general form, respectively. (What is meant by general form is not to write it in scientific notation).
a. 7.4 x 10^-4 mm (1 m / 1000 mm) = 0.00000074 m
b. 7.4 x 10^4 mm (1 m / 1000 mm) = 74 m
Now comparing the two values above, what do you think is the distance between the tracks on a DVD? Definitely NOT 74 m or else the DVD is extremely big. Therefore the correct is the smaller one.
The area of a triangle in determined by the formula:
where b is the base of the triangle and h is it's height
You just have to replace the b and h with their values in the formula (b=9.9ft and h=5.5ft)
The answer is 27.225 ft^2
Answer:
1/2
Step-by-step explanation:
The above statement is true meaning cos(π/₂-x)=sin(x)
Step-by-step explanation:
We know that sine and cosine function are mutual cofunctions.
Hence this would mean that these two functions are complimentary of each other meaning cos(π/₂-x) = sin(x)
This can be verified mathematically by assuming “x” as 30°
Hence Cos (π/₂-30°) = cos 60°= 0.5 (from trigonometric table values)
Similarly Sin 30°= 0.5 (from trigonometric table values)
This can be proved through using the formula
Cos(A-B)= Cos A.Cos B + Sin A.Sin B
Here A=90° and b=x°
Putting the values we get (it is to be remembered that cos 90°=0 and sin 90°=1)
Cos 90°.cos x+ sin 90.sin x
0+sinx= sinx
Hence it is proved that cos(π/₂-x)=sin(x)
