Select the sequence of transformations that will carry rectangle A onto rectangle A'. A) reflect over y-axis, rotate 90° clockwi
2 answers:
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Answer:
The P-value ranges between 2.5% and 5% according to the t-table.
Step-by-step explanation:
A random sample of 16 students from a large university showed an average age of 25 years with a standard deviation of 2 years.
Let = true average age of all students at the university.
So, the Null Hypothesis, :
24 years {indicating the average age is less than or equal to 24 years}
Alternate Hypothesis, :
> 24 years {indicating the average age is significantly greater than 24 years}
Here we employ the One-sample t-test statistics as the population's standard deviation is unknown;
T.S. = ~
where, = sample average age = 25 years
s = sample standard deviation = 2 years
n = sample size = 16
This gives us the test statistics = ~
= 2
The value of the t-test statistics is 2.
Moreover, the P-value of the test-statistics can be found as follows;
P-value = P( > 2) = 0.034 {as per the t-table}
Thus, the P-value lies between 2.5% and 5% based on the t-table.
Answer:
The ratio corresponds to the tangent of ∠I.
Step-by-step explanation:
Let’s revisit the trigonometric ratios:
- sin Ф =
- cos Ф =
- tan Ф =
For triangle HIJ
∵ m∠J = 90°
- The hypotenuse is the side opposite the right angle.
So, HI is the hypotenuse.
∵ HJ = 3 units
∵ IH = 5 units
- We’ll apply the Pythagorean Theorem to solve for HJ.
∵ (HJ)² + (IJ)² = (IH)²
∴ 3² + (IJ)² = 5²
∴ 9 + (IJ)² = 25
- Subtract 9 from both sides.
∴ (IJ)² = 16
- Taking the square root on both sides gives:
∴ IJ = 4 units
To determine the tangent of ∠I, identify the sides that are opposite and adjacent to it.
∵ HJ is opposite to ∠I
∵ IJ is adjacent to ∠I
- Utilizing the rule of tan above:
∴ tan(∠I) =
∴ tan(∠I) =
The ratio indicates the tangent of ∠I.