Anna bought a sofa set which cost $380 excluding GST.

The question appears to be incomplete. Here’s the complete inquiry:

Samir is quite skilled with the gun. When he targets a specific aim at the shooting range, he has a 0.95 probability of striking it. On one occasion, Samir sets out to shoot 10 targets consecutively.

If he has the same chance of hitting each of the 10 targets, what is the likelihood that he will miss at least one?

Response:

40.13%

Step-by-step breakdown:

Let 'A' represent the event of successfully hitting all targets in 10 trials.

The complement of 'A' is

Now, since Samir has a consistent probability of hitting each target at 0.95.

Now,

We know that the combined probability of an event and its complement equals 1.

<pThus,

Consequently, the probability that he misses at least one target among 10 attempts is 40.13%.

To tackle this problem, we first need to ascertain the commission taken by the pizza shop and how much money belongs to Mindy. We know that Mindy sells her artwork for $15, and the pizza shop retains a 15% commission. Therefore, the commission is calculated as (15/100) * 15, which equals 2.25 dollars. This means the pizza shop deducts $2.25 from each art sale made by Mindy. Consequently, the amount Mindy receives is (15 - 2.25), resulting in $12.75. Since Mindy opts not for cash but instead chooses a pizza valued at $12, including a 5% sales tax, it seems she benefits by $0.75 plus the pizza worth $12. Therefore, this arrangement appears fair for Mindy. Meanwhile, the pizza shop also makes an additional $2.25 from this transaction, making it equitable for both Mindy and the shop owner.

<span>15000 feet The height of Mt. Whitney is listed as 14,505 feet. To round this figure to the closest thousand, we examine the hundreds digit, which is 5. According to the rounding rule, "5 or above, round up, 4 or below, round down". Given that the digit is 5, we round up to yield 15000 feet</span>

To determine the values of b that fulfill 3(2b+3)^2 = 36

we start with
3(2b+3)^2 = 36
Divide both sides by 3
(2b+3)^2 = 12
Next, take the square root of both sides
(2b+3)} = (+ /-) \sqrt{12} \\ 2b=(+ /-) \sqrt{12}-3

b1=\frac{\sqrt{12}}{2} -\frac{3}{2}
b1=\sqrt{3} -\frac{3}{2}

b2=\frac{-\sqrt{12}}{2} -\frac{3}{2}
b2=-\sqrt{3} -\frac{3}{2}
Thus,

the solutions for b are
b1=\sqrt{3} -\frac{3}{2}
b2=-\sqrt{3} -\frac{3}{2}

Response:

Null hypothesis = H₀ = σ₁² ≤ σ₂²

Alternative hypothesis = Ha = σ₁² > σ₂²

Calculated statistic = 1.9

p-value = 0.206

Given that the p-value exceeds α, we do not reject the null hypothesis.

Thus, we conclude that night shift workers do not exhibit higher variability in their output levels compared to day workers.

Step-by-step elaboration:

Let σ₁² represent the variance for night shift workers

Let σ₂² represent the variance for day shift workers

State the null and alternative hypotheses:

The null hypothesis suggests that the variance of night shift workers does not exceed that of day shift workers.

Null hypothesis = H₀ = σ₁² ≤ σ₂²

The alternative hypothesis posits that the variance for night shift workers surpasses that of day shift workers.

Alternative hypothesis = Ha = σ₁² > σ₂²

Calculated statistic:

The test statistic, or F-value, is derived using

Test statistic = Larger sample variance/Smaller sample variance

The larger sample variance is σ₁² = 38

The smaller sample variance is σ₂² = 20

Test statistic = σ₁²/σ₂²

Test statistic = 38/20

Calculated statistic = 1.9

p-value:

The corresponding degrees of freedom for night shift workers is[1]

df₁ = n - 1

df₁ = 9 - 1

df₁ = 8

The corresponding degrees of freedom for day shift workers is[1]

df₂ = n - 1

df₂ = 8 - 1

df₂ = 7

We can obtain the p-value using the F-table or Excel.

To determine the p-value in Excel, we use

p-value = FDIST(F-value, df₁, df₂)

p-value = FDIST(1.9, 8, 7)

p-value = 0.206

Conclusion:

p-value > α    

0.206 > 0.05   ( α = 0.05)As the

p-value is larger than α, we do not reject the null hypothesis with a confidence level of 95%

[[TAG_101]]This leads us to conclude that night shift workers do not demonstrate more variability in their output levels in comparison to day workers.[[TAG_102]]