Work done on cart
:
W
=
6000
J
Kinetic energy of cart
:
E
K
=
6000
J
Explanation:
Work done
W
is defined as the product of force
F
and distance
s
:
⇒
W
=
F
⋅
s
Let's substitute the values of
F
and
s
into the equation:
⇒
W
=
300
N
⋅
20
m
⇒
W
=
300
kg
⋅
m s
−
2
⋅
20
m
⇒
W
=
300
⋅
20
kg
⋅
m
2
s
−
2
⇒
W
=
6000
kg
⋅
m
2
s
−
2
∴
W
=
6000
J
The gain in kinetic energy
E
K
is the same amount as the work done moving the cart:
∴
E
K
=
6000
Using the z-distribution, it is found that the 90% confidence interval is given by: (0.6350, 0.6984).
<h3>What is a confidence interval of proportions?</h3>
A confidence interval of proportions is given by:

In which:
is the sample proportion.
In this problem, we have a 90% confidence level, hence
, z is the value of Z that has a p-value of
, so the critical value is z = 1.645.
The sample size and the estimate are given by:

Hence, the bounds of the interval are given by:


The 90% confidence interval is given by: (0.6350, 0.6984).
More can be learned about the z-distribution at brainly.com/question/25890103
#SPJ1
Answer: of each shape? 3 & 4?
Step-by-step explanation:
Answer:
do its ??
Step-by-step explanation:
Answer:
Given the equation: 
A quadratic equation is in the form:
where a, b ,c are the coefficient and a≠0 then the solution is given by :
......[1]
On comparing with given equation we get;
a =3 , b = 10
then, substitute these in equation [1] to solve for c;

Simplify:

Also, it is given that the difference of two roots of the given equation is
i.e,

Here,
, ......[2]
.....[3]
then;

simplify:

or

Squaring both sides we get;

Subtract 100 from both sides, we get

Simplify:
-12c = -96
Divide both sides by -12 we get;
c = 8
Substitute the value of c in equation [2] and [3]; to solve 

or
or

Simplify:

Now, to solve for
;

or
or

Simplify:

therefore, the solution for the given equation is:
and -2.