1.
a) metres to centimetres :
multiply length by 100
b) metres to millimetres:
multiply length by 1000
c) kilograms to grams:
multiply the mass value by 1000
d) litres to millilitres :
multiply volume by 1000
2.
a) 3 m = 3× 100 = 300 cm
b) 28 cm = 28 × 10 = 280 mm
c) 2.4 km = 2.4 × 1000
= 24 × 10^-1 × 10^3
= 24 × 10^2 =2400 m
d) 485 mm =485 / 10
= 485 / 10 ^1
= 485 × 10 ^-1
= 48.5 cm
e) 35 cm = 35 / 100
= 35 /10^2
= 35 × 10 ^ -2
= 0.35 m
f) 2.4 m = 2.4 / 1000
= 24 × 10 ^-1 / 10^3
= 24 × 10^-1 × 10 ^-3
= 24 × 10 ^ -4
= 0.0024 km
g) 2495 mm = 2495 /1000
= 2495 /10^ 3
= 2495 × 10 ^-3
=2.495 m
Answer:
a. E(x) = 3.730
b. c = 3.8475
c. 0.4308
Step-by-step explanation:
a.
Given
0 x < 3
F(x) = (x-3)/1.13, 3 < x < 4.13
1 x > 4.13
Calculating E(x)
First, we'll calculate the pdf, f(x).
f(x) is the derivative of F(x)
So, if F(x) = (x-3)/1.13
f(x) = F'(x) = 1/1.13, 3 < x < 4.13
E(x) is the integral of xf(x)
xf(x) = x * 1/1.3 = x/1.3
Integrating x/1.3
E(x) = x²/(2*1.13)
E(x) = x²/2.26 , 3 < x < 4.13
E(x) = (4.13²-3²)/2.16
E(x) = 3.730046296296296
E(x) = 3.730 (approximated)
b.
What is the value c such that P(X < c) = 0.75
First, we'll solve F(c)
F(c) = P(x<c)
F(c) = (c-3)/1.13= 0.75
c - 3 = 1.13 * 0.75
c - 3 = 0.8475
c = 3 + 0.8475
c = 3.8475
c.
What is the probability that X falls within 0.28 minutes of its mean?
Here we'll solve for
P(3.73 - 0.28 < X < 3.73 + 0.28)
= F(3.73 + 0.28) - F(3.73 + 0.28)
= 2*0.28/1.3 = 0.430769
= 0.4308 -- Approximated
Answer:
diameter of the pizza = 21.88 centimeters
Step-by-step explanation:
Given:
C = d^2 – 2d + 447
where
C = cost of the pizza
d = diameter of the pizza
If the pizza costs $12.00, then what is a reasonable estimate for the diameter of the pizza?
12 = d^2 – 2d + 447
d^2 - 2d = 447 - 12
d^2 - 2d = 435
d^2 - 2d - 435 = 0
Solve the quadratic equation using formula
a = 1
b = -2
c = -435
d = -b +or- √b^2 - 4ac / 2a
= -(-2) +or- √(-2)^2 - (4)(1)(-435) / 2(1)
= 2 +or- √4 - (-1740) / 2
= 2 +or- √4 + 1740 / 2
= 2 +or- √1744 / 2
= 2 +or- 4√109 / 2
= 2/2 +or- 4√109/2
= 1 +or- 2√109
d = 1 + 2√109 or d = 1 - 2√109
= 1 + 2(10.44) or d = 1 - 2(10.44)
= 1 + 20.88 or d = 1 - 20.88
d = 21.88 or -19.88
diameter of the pizza = 21.88 centimeters
Therefore, the estimated diameter of the pizza can not be negative. So, diameter of the pizza = 21.88 cm
Answer:
and 
Step-by-step explanation:
Options
Required
Select the unit rates
Unit rate involve two items where the first item being measured can be any positive number, but the second item must be measured in units (i.e. 1)
For clarity:
If 
represents unit rate, then 
Having said that:
Only and satisfy the condition of unit rates; others are not because they have a denominator other than 1
Answer:6
Step-by-step explanation:
In a circle, a radius perpendicular to a chord bisects the chord. So BC = CA BC = 6 (given) x (or AC) = 6 Answer = 6. Tell me if I was right. Thanks.
