Answer:
1.7 × 10⁻⁴
Step-by-step explanation:
The question relates to a two sample z-test for the comparison between the means of the two samples
The null hypothesis is H₀: μ₁ ≤ μ₂
The alternative hypothesis is Hₐ: μ₁ > μ₂
Where;
= 13.5
= 12
σ₁ = 2.5
σ₂ = 1.5
We set our α level at 0.05
Therefore, our critical z = ± 1.96
For n₁ = n₂ = 23, we have;
We reject the null hypothesis at α = 0.05, as our z-value, 3.5969 is larger than the critical z, 1.96 or mathematically, since 3.5969 > 1.96
Therefore, there is enough statistical evidence to suggest that Alyse time is larger than Jocelyn in a 1 mile race on a randomly select day and the probability that Alyse has a larger time than Jocelyn is 0.99983
Therefore;
The probability that Alyse has a smaller time than Jocelyn is 1 - 0.99983 = 0.00017 = 1.7 × 10⁻⁴.
Total tax due Answer: $27,000.
Step-by-step explanation:
x - 12 < 15
x < 15 + 12
x < 27
For x < 27 , i will add a number smaller than 27.
x = {26,25,24,23, etc}
Answer:
<em>The shaded region has an area of 1400 square units</em>
Step-by-step explanation:
<u>Area of Compound Shapes</u>
We are given a shape and it's required to calculate its area. The shape can be divided into three rectangles as shown in the figure attached below.
The lengths of these rectangles are x, y, and z.
The value of x can be calculated as:
x = 60 - 15 - 10 = 35
Similarly:
y = 60 - 15 = 45
z = y = 45
The first rectangle has dimensions of x by 10, thus its area is:
A1 = 35*10 = 350
The second rectangle has dimensions of 60 by 10:
A2 = 60*10 = 600
The third rectangle has dimensions y by 10:
A3 = 55*10 = 450
The shaded area is:
A = 350 + 600 + 450 = 1400
The shaded region has an area of 1400 square units
