Answer:
y = 1/2 - 3/2
Step-by-step explanation:
All we need to do is find the y-intercept of the line using the formula for slope intercept form [ y = mx + b ].
-3 = 1/2(-3) + b
-3 = -1.5 + b
-1.5 = b
We can put all the information we know/solved for into the formula.
y = 1/2 - 1.5
Best of Luck!
Answer:
16/31, 51.612903225807%
Step-by-step explanation:
Let Z be the reading on thermometer. Z follows Standard Normal distribution with mean μ =0 and standard deviation σ=1
The probability that randomly selected thermometer reads greater than 2.07 is
P(z > 2.07) = 1 -P(z < 2.07)
Using z score table to find probability below z=2.07
P(Z < 2.07) = 0.9808
P(z > 2.07) = 1- 0.9808
P(z > 2.07) = 0.0192
The probability that a randomly selected thermometer reads greater than 2.07 is 0.0192
Answer: 30 m ; (or, write as: "30 meters") .
______________________________________________
Explanation:
____________________
Area of a trapezoid, "A" = (1/2) ( b₁ + b₂) h ;
______________________________________________
or, write as: A = ( b₁ + b₂) h / 2 ;
___________________________________
in which: A = area;
b₁ = length of "base 1" (choose either one of the 2 (two bases);
b₂ = length of "base 2" (use the base that is remaining);
h = height of trapezoid;
____________________________________________
From the information given:
___________________________
A = 100 m² ;
h = 5 m
b₁ = 10 m
b₂ = x
___________________________
Find "x", which is: "b₂" ;
__________________________
A = ( b₁ + b₂) h / 2 ;
_____________________________
Plug in our known values; and plug in "x" for "b₂" ; and solve for "x" ;
_________________________________________________________
100 m² = [(10m + x) (5m)] / 2 ; Solve for "x" ;
_________________________________________________________
(10m + x) (5m) = (2)* (100m²) ;
_________________________________________________________
(5m) (10m + x) = 200 m² ;
___________________________________________
Note: The distributive property of multiplication:
____________________________________________
a(b+c) = ab + ac ;
a(b−c) = ab <span>− ac ;
</span>____________________________________________
We have: (5m) (10m + x) = 200 m² ;
____________________________________________
So: (5m) (10m + x) = (5m*10m) + (5m * x) ;
= 50m² + (5m)x ;
_______________________________________________
→ 50m² + (5m)x = 200m² ;
_______________________________________________
Divide the ENTIRE equation by "5m" ;
_______________________________________________
→ { 50m² + (5m)x } / 5m = (200m² / 5m) ;
_______________________________________________
→ 10m + x = 40m ;
________________________________________________
Now, subtract "10m" from EACH side of the equation; to isolate "x" on one side of the equation; and to solve for "x" ;
_______________________________________
→ 10m + x − 10m = 40m − 10m ;
to get:
→ x = 30 m ; which is our answer.
___________________________________________________
Answer: 30 m ; (or, write as: "30 meters") .
_____________________________________________________
Answer:
Step-by-step explanation:
4). This is an exponential function.
5). Let the equation of this function is,
f(x) = a(b)ˣ
Since, two points (-1, 4) and (0, 6) are lying on the graph of the function,
For (-1, 4),
4 = a(b)⁻¹
4 =
--------(1)
For (0, 6),
6 = a(b)⁰
a = 6
From equation (1),
4 = 
b =
= 1.5
Therefore, equation of the function will be,
f(x) = 6(1.5)ˣ
6). Now the value of f(-4) will be,
f(-4) = 6(1.5)⁻⁴
= 1.185