Answer:
25π
Step-by-step explanation:
5² · π = 25π
The system of solution is at the point (-6,24)
Answer:
Tom has 70 cards, and Harry has 28 cards.
Step-by-step explanation:
Let h = number of cards Harry has.
Then the number of cards Tom has is 2 1/2 * h = 2.5h.
Together they have 2.5h + h = 3.5h number of cards.
Together they have 98 cards.
3.5h = 98
h = 98/3.5
h = 28
Harry has 28 cards.
Tom has 2.5h = 2.5 * 28 = 70
Answer: Tom has 70 cards, and Harry has 28 cards.
Answer:
Step-by-step explanation:
Hello!
The objective of this experiment is to test if the presence of toxaphene in the diet reduces the gain of weight. For these two random samples of female rats were made, one was fed with a diet that contained a low dose of toxaphene and the other, called the control group, was fed with the same type of food but without toxaphene. The weight of the rats was registered in both groups obtaining:
Sample 1 (with toxaphene)
n₁= 19 female rats
S₁= 58g
Sample 2 (control group)
n₂= 21
S₂= 30g
The hypothesis is that the presence of low-dose insecticide in the diet increases the variability in weight gain. Symbolically: σ₁² > σ₂²
The hypothesis is:
H₀: σ₁² ≤ σ₂²
H₁: σ₁² > σ₂²
α: 0.05
This hypothesis test is for the variance ratio, the statistic to use is:
F= (S₁²/S₂²)*( σ₁²/σ₂²)~F
This test is one-tailed (right) and the critical value is:
If F ≥ 2.19, you reject the null hypothesis.
If F < 2.19, you support the null hypothesis.
F= (S₁²/S₂²)*( σ₁²/σ₂²) = (3364/900)*1 = 3.737
Since the calculated value is greater than the critical value, the decision is to reject the null hypothesis. The variability of the weight gain of rats fed with a low dose of insecticide is greater than the variability of the control group.
I hope it helps!
Answer:
√446 ≈ 21.12 cm
Step-by-step explanation:
The longest dimension of a rectangular prism is the length of the space diagonal from one corner to the opposite corner through the center of the prism. The Pythagorean theorm tells you the square of its length is the sum of the squares of the dimensions of the prism:
d² = (15 cm)² +(11 cm)² +(10 cm)² = (225 +121 +100) cm² = 446 cm²
d = √446 cm ≈ 21.12 cm
The longest line segment that can be drawn in a right rectangular prism is about 21.12 cm.
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<em>Additional comment</em>
The square of the face diagonal is the sum of the squares of the dimensions of that face. The square of the space diagonal will be the sum of that square and the square of the remaining prism dimenaion, hence the sum of squares of all three prism dimensions.