Answer:
The translation is left 4 units
Step-by-step explanation:
we know that
Is a vertical parabola open upward with vertex at (15,3)
Is a vertical parabola open upward with vertex at (11,3)
so
The rule of the translation of (15,3) ----> (11,3) is equal to
(x,y) ----> (x-4,y)
That means ----> The translation is left 4 units
Answer:
a2 =14
a4 = 22
a11 = 50
Step-by-step explanation:
an = 10 + (n-1) *4
n is the term number
Let n =2
a2 = 10 +(2-1)*4 =10 +(1)*4 = 14
Let n =4
a4= 10 + (4-1)*4 = 10 *3*4 = 10+12 = 22
Let n = 11
a11 = 10 +(11-1)*4 = 10 *10*4 = 10+40 = 50
Answer:
Step-by-step explanation:
x = 4
=> y = 3
x = 8
=> y = -2
x = 12
=> y = -5
Answer:
Step-by-step explanation:
Since the heights of women are normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = heights of women.
µ = mean height
σ = standard deviation
From the information given,
µ = 65 inches
σ = 2.5 inches
The probability that a woman is taller than 70 inches is expressed as
P(x > 70) = 1 - P(x ≤ 70)
For x = 70
z = (70 - 65)/2.5 = 2
Looking at the normal distribution table, the probability corresponding to the z score is 0.977
Therefore,
P(x > 70) = 1 - 0.977 = 0.023
The percent of women that are taller than a man of average height is 0.023 × 100 = 2.3℅
Answer:
the home is
5.83 blocks 31° North of west of the school
Step-by-step explanation:
Resolving the displacement to vertical and horizontal axis
Let north and south represent positive and negative vertical axis, also east and west represent positive and negative horizontal axis;
Vertical axis; , 2 blocks south to visit her aunt, then 5 blocks north to go home
Ry = -2 + 5
Ry = +3
Horizontal axis; 5 blocks west to the grocery store
Rx = -5
Resultant distance = R = √(Rx^2 + Ry^2)
R =√(-5^2 + 3^2)
R = √34
R = 5.83 blocks
For the direction;
∅ = arctan(Ry/Rx) = arctan(3/5)
∅ = 31°
Therefore, the home is
5.83 blocks 31° North of west of the school.