Answer:
2/3
Step-by-step explanation:
If we have 'x' students who like math and 'y' students that like science, we can formulate that:
Half of x likes math and science, and also one third of y likes math and science, so:
(1/2) * x = (1/3) * y
x / y = (1/3) / (1/2)
x / y = (1/3) * 2 = 2/3
So the ratio of the number of students who like math to the number of students who like science is 2/3
Answer:
6.51 cm
Step-by-step explanation:
Since the sphere causes the water level in the cylindrical container to rise and thus increase by its own volume, the volume of the sphere is V = 4πr³/3 where r = radius of sphere. The volume rise of the container is thus V' = πR²h where R = radius of base of cylinder = 7 cm and h = height of water level = 7.5 cm.
Since V = V',
4πr³/3 = πR²h
dividing through by π, we have
4r³/3 = R²h
multiplying both sides by 3/4, we have
r³ = 3R²h/4
taking cube-root of both sides, we have
r = ∛(3R²h/4)
Substituting the values of the variables into the equation, we have
r = ∛(3(7 cm)² × 7.5 cm/4)
r = ∛(3 × 49 cm² × 7.5 cm/4)
r = ∛(1102.5cm³/4)
r = ∛(275.625 cm³)
r = 6.508 cm
r ≅ 6.51 cm to 2 decimal places
Answer:
The given equation will have value less than 100 whenever the value of b is greater than 12.89
Step-by-step explanation:
For the given equation, p(b) = 520 × 
to have a value less than 100 we can establish inequality as:
p(b) < 100
or, 520 × < 100
or, 
× < 
or, < 
or, ㏒ ( ) < ㏒ ()
or, b× ㏒ 0.88 < ㏒ ()
or, 
< b
or, 12.89 < b
Hence for the equation to have value less than 100, b must be greater than 12.89.
95% of red lights last between 2.5 and 3.5 minutes.
<u>Step-by-step explanation:</u>
In this case,
- The mean M is 3 and
- The standard deviation SD is given as 0.25
Assume the bell shaped graph of normal distribution,
The center of the graph is mean which is 3 minutes.
We move one space to the right side of mean ⇒ M + SD
⇒ 3+0.25 = 3.25 minutes.
Again we move one more space to the right of mean ⇒ M + 2SD
⇒ 3 + (0.25×2) = 3.5 minutes.
Similarly,
Move one space to the left side of mean ⇒ M - SD
⇒ 3-0.25 = 2.75 minutes.
Again we move one more space to the left of mean ⇒ M - 2SD
⇒ 3 - (0.25×2) =2.5 minutes.
The questions asks to approximately what percent of red lights last between 2.5 and 3.5 minutes.
Notice 2.5 and 3.5 fall within 2 standard deviations, and that 95% of the data is within 2 standard deviations. (Refer to bell-shaped graph)
Therefore, the percent of red lights that last between 2.5 and 3.5 minutes is 95%
Answer:
Step-by-step explanation:
Width=(Length-2) units
W=(L-2) units
Area of the rectangle= 35 square units
Area = length* Width
Subtracting 35 both sides:
Solving the quadratic equation for 'L' ;
Using factorization:
Taking common from the equation :
OR
The length cannot be negative, therefore Length(L)= 7
