Answer:
14.85
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh where b is the base and h is the height
A =1/2 ( 6.6)(4.5)
A = 14.85
Let x = cost of the dishwasher.
The amounts the children are paying are:
Mark =20% = 1/5, so 1/5x
Sorin = 75
Raymond = 1/4x
Stephanie = 75
Kristin = 1/3x
Add them together:
x = 1/5x + 1/4x + 1/3x + 75 + 75
x - ( 1/5x + 1/4x + 1/3x ) = 150
Rewrite fractions with common denominator:
x - ( 12/60x + 15/60x + 20/60x ) = 150
60/60x - 47/60x = 150
13/60x = 150
x = 150/1 • 60/13
x = 9000/13
x = 692.31
The total cost of the dishwasher is $692.31
Now calculate the amount each child pays:
Mark = 1/5 x = 692.31/ 5 = $138.46
Sorin = $75.00
Raymond = 1/4 x = 692.31 / 4 = $173.08
Stephanie = $75.00
Kristin = 1/3 x = 692.31 / 3 = $230.77
Answer:
Step-by-step explanation:
6x - 2y = -4
y= 3x + 2
We see that y = 3x + 2 so we can use that value of Y everytime we see i in the other equation.
6x - 2(3x +2) = -4
Now usually we'd we simply solve for X.
6x - 6x -4 = -4
This clearly does not work as we cannot get rid of X
Therefore, this system of equations has no solution we can find through substitution
171 / 7.6 = 22.5 miles per gallon
22.5 x 12.5 = 281.25 miles she can drive
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
