A.
the starting point is where t=0
d(0)=-16(0)^2+96(0)+112
D(0)=112
started from 112 feet
b. max height is vertex
for
y=ax^2+bx+c
the x value of the vertex is -b/2a
so
D(t)=-16t^2+96t+112
t value of vertex is -96/(2*-16)=3
it reaches after 3 seconds
C. simpliy evaluate D(t) for t=3
D(3)=-16(3)^2+96(3)+112
D(3)=-16(9)+288+112
D(3)=-144+400
D(3)=256
max height is 256ft
Answer:
8 hours
Step-by-step explanation:
Its is on the chart and is at the top
<span>Equation:
0.15x + 0.10(5-x) = 0.11*5
---
Multiply thru by 100:
15x + 10*5 - 10x = 11*5
---
5x = 5
x = 1 liter (amt. 15% oj needed)
----
5-x = 4 liters (amt of 10% oj needed)
======</span>
The new mean and standard deviation is 26 and 15, when each score in data set is multiplied by 5 and then 7 is added.
According to the question,
Original mean is 10 and original standard deviation is 5 . In order to find to new mean and standard deviation when each score in data set is multiplied by 5 and then 7 is added.
First "change of scale" when every score in a data set is multiplied by a constant, its mean and standard deviation is multiplied by a same constant.
Mean: 10*3 = 30
Standard deviation: 5*3 = 15
Secondly "change of origin" when every score in a data set by a constant, its mean get added or subtracted by the same constant and standard deviation remains constant.
Applying change of origin in the above mean and standard deviation
Mean: 30 - 4 = 26
Standard deviation: Remains same = 15
Hence, the new mean and standard deviation is 26 and 15, when each score in data set is multiplied by 5 and then 7 is added.
Learn more about Mean and standard deviation here
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Answer:
25 girls
Step-by-step explanation:
Let
x denote number of boys
and
y denote number of girls
According to the statement that total 45 people came,
x+y = 45 => Eqn 1
And total paid amount was 175
So,
5x + 3y = 175 => Eqn 2
For solving, We will use the substitution method
So, from eqn 1
x = 45-y
Putting value of x in eqn 2
5(45-y) +3y = 175
225 - 5y + 3y = 175
-2y+225 = 175
-2y = 175-225
-2y = -50
2y = 50
y = 25
Putting y =25 in eqn 1
x+25 = 45
x = 45 - 25
x = 20
As y= 25
So, 25 girls came to the dance ..