Answer:
64/3 cc or 64/3 cm³
Step-by-step explanation:
The formula for the volume of a triangular pyramid is
V = (1/3)(area of base)(height)
Here we have a square prism (actually, a cube), whose square base is 4 cm by 4 cm (4 cm is the cube root of 64 cc). The height of this cube is also 4 cm.
The volume of a triangular pyramid of base area (4 cm)² and height 4 cm is
V = (1/3)(base area)(height)
= (1/3)(16 cm²)(4 cm) = 64/3 cc
A) Angle A has to be congruent to Angle D
Answer:
here are a few that are equivalent
8:6
28:21
48:36
68:51
Answer:
The calculated χ² = 0.57 does not fall in the critical region χ² ≥ 12.59 so we fail to reject the null hypothesis and conclude the proportion of fatal bicycle accidents in 2015 was the same for all days of the week.
Step-by-step explanation:
1) We set up our null and alternative hypothesis as
H0: proportion of fatal bicycle accidents in 2015 was the same for all days of the week
against the claim
Ha: proportion of fatal bicycle accidents in 2015 was not the same for all days of the week
2) the significance level alpha is set at 0.05
3) the test statistic under H0 is
χ²= ∑ (ni - npi)²/ npi
which has an approximate chi square distribution with ( n-1)=7-1= 6 d.f
4) The critical region is χ² ≥ χ² (0.05)6 = 12.59
5) Calculations:
χ²= ∑ (16- 14.28)²/14.28 + (12- 14.28)²/14.28 + (12- 14.28)²/14.28 + (13- 14.28)²/14.28 + (14- 14.28)²/14.28 + (15- 14.28)²/14.28 + (18- 14.28)²/14.28
χ²= 1/14.28 [ 2.938+ 5.1984 +5.1984+1.6384+0.0784 +1.6384+13.84]
χ²= 1/14.28[8.1364]
χ²= 0.569= 0.57
6) Conclusion:
The calculated χ² = 0.57 does not fall in the critical region χ² ≥ 12.59 so we fail to reject the null hypothesis and conclude the proportion of fatal bicycle accidents in 2015 was the same for all days of the week.
b.<u> It is r</u>easonable to conclude that the proportion of fatal bicycle accidents in 2015 was the same for all days of the week
Answer:
5. x = -1
6. x = 2
Step-by-step explanation:
5. AB = 5
BC = 2x + 6
AC = x + 10
AB + BC = AC (segment addition postulate)
5 + 2x + 6 = x + 10 (substitution)
Collect like terms
5 + 6 + 2x = x + 10
11 + 2x = x + 10
2x - x = - 11 + 10
x = -1
6. AB = 9x + 7
BC = -3x + 20
AC = 39
AB + BC = AC (segment addition postulate)
(9x + 7) + (-3x + 20) = 39 (substitution)
Solve for x
9x + 7 - 3x + 20 = 39
Collect like terms
9x - 3x + 7 + 20 = 39
6x + 27 = 39
Subtract 27 from both sides
6x + 27 - 27 = 39 - 27
6x = 12
Divided both sides by 6
6x/6 = 12/6
x = 2
