Answer:
168 km
Step-by-step explanation:
Let x represent the distance Tyler drives at the slower speed, and let y represent the distance at the higher speed. Using time = distance/speed, we can write equations for the total travel time:
x/42 +y/105 = 2.5
x/28 +y/60 = 4.0 . . . . . 1.5 hours more than the usual 2.5 hours
Multiplying the first equation by 210, we have ...
5x +2y = 525
Multiplying the second equation by 420, we get ...
15x +7y = 1680
Subtracting 3 times the first of these equations from the second, we have ...
(15x +7y) -3(5x +2y) = (1680) -3(525)
y = 105
Putting this into the very first equation, we get ...
x/42 + 105/105 = 2.5
x/42 = 1.5 . . . . . . subtract 1
x = 63 . . . . . . . . .multiply by 42.
The total distance to Tyler's parents' house is ...
63 km + 105 km = 168 km
Answer:
Step-by-step explanation:
From the first receipt:
2 pounds of grapes + 4 pounds of oranges = 10.70 which, in an algebraic equation, looks like this:
2g + 4o = 10.70
From the second receipt:
3 pounds of grapes + 2 pounds of oranges = 9.65 which, in an algebraic equation, looks like this:
3g + 2o = 9.65
Putting those together into a system and solving using the elimination method:
2g + 4o = 10.7
3g + 2o = 9.65
I am going to eliminate the oranges first since it's easier to do that. I will multiply the second equation by -2 to get a new system:
2g + 4o = 10.7
-6g - 4o = -19.3
As you can see, the oranges are eliminated because 4o - 4o = 0o. That leaves us with only the grapes:
-4g = -8.6 so
g = 2.15
Grapes cost $2.15 per pound. Now sub that into either one of the original equations to solve for the cost per pound of oranges:
2(2.15) + 4o = 10.7 and
4.3 + 4o = 10.7 and
4o = 6.4 so
o = 1.60
Oranges cost $1.60 per pound. That is choice D from your list.
The domain is the value of x. In this case, -3≤x≤7
the range is the value of y. in this case, -1≤y≤9
this is not a function, because the same x value has two corresponding y values. For example, when x=5, y=0 or y=8
It IS a function if every x value has only one corresponding y value.
<u>Answer:</u>
<u>Null hypothesis: Policy B remains more effective than policy A.</u>
<u>Alternate hypothesis: Policy A is more effective than policy B.</u>
<u>Step-by-step explanation:</u>
Remember, a hypothesis is a usually tentative (temporary until tested) assumption about two variables– independent and the dependent variable.
We have two types of hypothesis errors:
1. A type I error occurs when the null hypothesis (H0) is wrongly rejected.
That is, rejecting the assumption that policy B remains more effective than policy A when it is <em>actually true.</em>
2. A type II error occurs when the null hypothesis H0, is not rejected when it is actually false. That is, accepting the assumption that policy B remains more effective than policy A when it is <em>actually false.</em>
Answer:
x = 
Step-by-step explanation:
Given
y = 4x - 10 ( add 10 to both sides )
y + 10 = 4x ( divide both sides by 4 )
= x
