Answer:
120
Step-by-step explanation:
16.2 miles.
Since she paid a $5 tip, the cost for her fare was $23.50. Let x be the number of 0.2-mile increments in the trip:
23.50 = 2.50 + 1 + 0.25(x-1)
This equation comes from the 2.50 home pick-up fee; $1 for the first 0.2-mile increment; and 0.25 for each other 0.2-mile increment.
Using the distributive property, we have:
23.50 = 2.50 + 1 + 0.25*x - 0.25*1
23.50 = 2.50 + 1 + 0.25x - 0.25
Combining like terms,
23.50 = 0.25x + 2.75
Subtracting 2.75 from both sides, we have:
23.50 - 2.75 = 0.25x + 2.75 - 2.75
20.25 = 0.25x
Dividing both sides by 0.25, we have:
20.25/0.25 = 0.25x/0.25
81 = x
This means there are 81 0.2-mile increments in her trip. 81(0.2) = 16.2 miles
Answer:
0.95988 (Accuracy of the test )
Step-by-step explanation:
To determine the accuracy of this test we have to list out the given values
Prevalence rate of the disease = 0.3% = 0.003
sensitivity rate of the disease = 92% = 0.92
specificity rate for the test = 96% = 0.96
The accuracy of the test can be found using this equation
Accuracy = sensitivity * prevalence + specificity ( 1 - prevalence )
= 0.92 * 0.003 + 0.96 ( 1 - 0.003 )
= 0.00276 + 0.95712
= 0.95988
Answer:
Mid point is: (2.8;4.9)
Step-by-step explanation:
To find midpoint of a line segment we can use the general equation:
Where the point of the line are: (x₁;y₁) and (x₂;y₂).
In the problem, x₁ = 2.6, y₁ = 5.1 and x₂ = 3 and y₂ = 4.7. Replacing in the equation:
<h3>Mid point is: (2.8;4.9)</h3>
<h2><em>y
2
+
6
y
−
16
=
(
y
+
8
)
(
y
−
2
)
</em></h2><h2 /><h2><em>Explanation:
</em></h2><h2><em>Note that in general:
</em></h2><h2 /><h2><em>(
y
+
a
)
(y
−
b
)
=
y
2
+
(
a
−
b
)
y
−
a
b
</em></h2><h2 /><h2><em>So we want to find a pair of factors a and b of 16 which differ by 6
. </em></h2><h2><em>The pair 8
,
2 works in that 8−
2
=
6 and 8
⋅
2=
16
.
</em></h2><h2 /><h2><em>Hence:
</em></h2><h2><em>
y
2
+
6
y
−
16
=
(
y+
8
)
(
y
−
2
)</em></h2><h2><em>y=2,-8</em></h2>
