The weight of a USB flash drive is 30 grams and is normally distributed. Periodically, quality control inspectors at Dallas Flas
1 answer:
Answer:
The critical t values are -1.746 and 1.746.
Step-by-step explanation:
Given information:
The weight of a USB flash drive is 30 grams and is normally distributed.
Population mean = 30
Sample size = 17
Sample mean= 31.9
Standard deviation = 1.8
Significance level, α=0.10
Null hypothesis:
Alternative hypothesis:
It is a two tailed test.
The t-critical values for a two-tailed test, for a significance level of α=0.1 are -1.746 and 1.746.
Therefore the critical t values are -1.746 and 1.746.
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The percentage of change in the area of the rectangle is -25% ⇒ B
Step-by-step explanation:
The given is:
- Sides AB and DC of the rectangle are increased in length by 50%
- Sides AD and BC are decreased in length by 50%
We need to find the percentage change in the <em>AREA</em> of the rectangle
Assume that the length of AB ans DC is x units, and the length of AD and BC is y units
∵ The length of the sides AB and DC increased by 50%
∵ The length of AB and CD = x
- That means x will increase by 50% of x
∵ 50% of x = (50 ÷ 100) × x = 0.5 x
∴ The length is increased by 0.5 x
∴ The new length of AB and CD = x + 0.5 x = 1.5 x units
∵ The length of the sides BC and AD decreased by 50%
∵ The length of BC and AD = y
- That means y will decrease by 50% of y
∵ 50% of y = (50 ÷ 100) × y = 0.5 y
∴ The length is decreased by 0.5 y
∴ The new length of BC and AD = y - 0.5 y = 0.5 y units
∵ The area before the change = x × y = xy units²
∵ The area after the change = 1.5 x × 0.5 y = 0.75 xy units²
∵ The new area is less than the old area
∴ The area is decreased
- To find the the percentage of change in the area subtract the
new area from the old area and divide the difference by the
old area and then multiply the quotient by 100%
∴ The percentage of the change = × 100%
∴ The percentage of the change = × 100%
∴ The percentage of the change = 0.25 × 100%
∴ The percentage of the change = 25%
∴ The area of the rectangle is decreased by 25% ⇒ (-25%)
The percentage of change in the area of the rectangle is -25%
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Answer:
A. Hypotenuse-leg (HL) congruence.
HL, when you have 2 right triangles and their hypotenuses are congruent you are able to say HL
Step-by-step explanation:
We know that the hypotenuse-leg theorem states that if the hypotenuse and one leg of a right triangle are congruent to hypotenuse and corresponding leg of another right triangle, then the triangles are congruent.
hypotenuse(AB) of △BDA equals to hypotenuse (CD) of △DBC.
BDA and DBC share a common side DB.
Using Pythagorean theorem we will get,
We have been given that CD=AB, Upon using this information we will get,
Upon subtracting from both sides of our equation we will get,