Answer:
Step-by-step explanation:
We want to determine a 95% confidence interval for the mean salary of all graduates from the English department.
Number of sample, n = 400
Mean, u = $25,000
Standard deviation, s = $2,500
For a confidence level of 95%, the corresponding z value is 1.96. This is determined from the normal distribution table.
We will apply the formula
Confidence interval
= mean ± z × standard deviation/√n
It becomes
25000 ± 1.96 × 2500/√400
= 25000 ± 1.96 × 125
= 25000 ± 245
The lower end of the confidence interval is 25000 - 245 =24755
The upper end of the confidence interval is 25000 + 245 = 25245
Therefore, with 95% confidence interval, the mean salary of all graduates from the English department is between $24755 and $25245
9514 1404 393
Answer:
164π cm²
Step-by-step explanation:
The area of a circle is given by the formula ...
A = πr²
The radius (r) is half the diameter (d), so the area of a semicircle in terms of its diameter is ...
1/2A = (1/2)(π)(d/2)² = (π/8)d²
The given shape is the combination of three (3) semicircles. The smallest has a diameter of 6 cm; the middle-sized one has a diameter of (32 cm -6 cm -8 cm) = 18 cm. The largest has a diameter of 32 cm.
The total area will be ...
area of largest + area of middle-size - area of smallest
= (π/8)(32² +18² -6²) = (π/8)(1312) . . . . cm²
The area of the shape is 164π cm².
Answer:
Amplitude increases and the period decreases
Step-by-step explanation:
Here, we are to compare amplitude change and period change
The first equation is;
y = sin x
The second is
y = 3 sine (2/3)x
Generally, the equation of a sine graph can be written as;
y = a sin (bx + c)
where a represents the amplitude and b refers to the period
In the first equation , a = 1 while in the second , a = 3 ; This shows an amplitude increase
In the first equation, b = 1 while in the second equation b = 2/3; this shows a period decrease
