Answer:
4
Step-by-step explanation:
5 times 4 is 20, which leaves 4
(a) Let h and d represent the numbers of packages of Hamburger and hotDog buns, respsectively.
.. h +d = 12 . . . . . . . . . . . . the family brought 12 packages of buns
.. 2.00h +1.50d = 20 . . . . each family contributed $20
(b) Double the first equation and subtract the second one
.. 2(h +d) -(2h +1.5d) = 2(12) -(20)
.. 0.5d = 4 . . . . . . . . . . . . . . . . . . . . . simplify
.. d = 8 . . . . . . . . . . . . . . . . . . . . . . . . multiply by 2
.. h = 12 -d = 4
They brought 4 packages of hamburger buns and 8 packages of hotdog buns.
(c) The number of hotdog bun packages cannot exceed 20/1.5 = 13.3 or the budget will be exceeded.
(d) It depends on the relationship of the variables to the ordered pair.
.. (h, d) = (5, 7) would mean 5 hamburger bun packages and 7 hotdog bun packages
.. (d, h) = (5, 7) would mean 7 hamburger bun packages and 5 hotdog bun packages
(e) Their cost for that purchase would be 7*2.00 +4*1.50 = 14.00 +6.00 = 20. That purchase meets the cost constraint, so is fair from a cost contribution point of view. Whether it is fair from a menu point of view depends on the number of hamburgers and hotdogs that need buns.
Answer:
D
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
To calculate m use the slope formula
m = ( y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (3, 6) and (x₂, y₂ ) = (8, 4)
m = 
= - 
, hence
y = - x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (8, 4), then
4 = - 
+ c ⇒ c = 4 + = 
y = - x + ← equation of line
Answer:
- (x + 10)² + (y + 4)² = 232
Step-by-step explanation:
<h3>Given </h3>
- Center = (-10, -4)
- Point on circle = (4, 2)
<h3>To find </h3>
<h3>Solution</h3>
<u>Remember the standard equation of circle:</u>
- (x - h)² + (y - k)² = r², where (h, k) is the center and r is radius
<u>We have</u>
Use distance formula (Pythagorean theorem) to work out the length of the radius. We know that radius is the distance from the center to any point on the circle.
<u>Here we are finding the distance between points (-10, -4) and (4, 2)</u>
- r² = (-10 - 4)² + (-4 - 2)²
- r² = 14² + 6²
- r² = 232
<u>So the equation is:</u>
- (x + 10)² + (y + 4)² = 232
Answer:
a) 2.9%
b) Option B is correct.
The prisoners must be independent with regard to recidivism.
Step-by-step explanation:
Probability that one prisoner goes back to prison = 17% = 0.17
a) The probability that two prisoners released both go back to prison = 0.17 × 0.17 = 0.0289 = 2.89% = 2.9% to 1 d.p
b) The only assumption taken during the calculation is that probability of one of the prisoners going back to prison has no effect whatsoever in the probability that another prisoner goes back to prison. That is the probability that theses two events occur are totally independent of each other.
If they weren't, we wouldn't be able to use 0.17 as the probability that the other prisoner goes back to prison too.
