Dimensions of the rectangle (width and length) are 19 cm and 31 cm respectively.
Step-by-step explanation:
- Step 1: Given that the perimeter = 100 cm, let width be x cm and then length = 12 + x.
Perimeter of a rectangle = 2(length + width)
100 = 2(x + 12 + x)
100 = 4x + 24
4x = 100 - 24 = 76
∴ x = 76/4 = 19 cm
∴ Length = 19 + 12 = 31 cm
Answer:
mArc A B = 120° (C)
Step-by-step explanation:
Question:
In circle O, AC and BD are diameters.
Circle O is shown. Line segments B D and A C are diameters. A radius is drawn to cut angle D O C into 2 equal angle measures of x. Angles A O D and B O C also have angle measure x.
What is mArc A B?
a)72°
b) 108°
c) 120°
d) 144°
Solution:
Find attached the diagram of the question.
Let P be the radius drawn to cut angle D O C into 2 equal angle measures of x
From the diagram,
m Arc AOC = 180° (sum of angle in a semicircle)
∠AOD + ∠DOP + ∠COP = 180° (sum of angles on a straight line)
x° +x° + x° =180°
3x = 180
x = 180/3
x = 60°
m Arc DOB = 180° (sum of angle in a semicircle)
∠AOB + ∠AOD = 180° (sum of angles on a straight line)
∠AOB + x° = 180
∠AOB + 60° = 180°
∠AOB = 180°-60°
∠AOB = 120°
mArc A B = 120°
Given:
Principal = <span>£100
Interest rate = 6%
Interest = </span><span>£12
Simple Interest is computed by multiplying the principal by its interest rate and term
Interest = Principal * rate * term
12 = 100 * 0.06 * term
12 = 6 * term
12/6 = term
2 = term
It will take 2 years for </span>£100 to earn <span>£12 at 6%</span>
There are 12 months in a year, and 15 years to pay the mortgage.
Therefore you are simply doing 12 multiplied by 15.
12 × 15
= 180
So your answer is C. 180
Answer:
c. binomial distribution with n = 5 and p = 1/33.
Step-by-step explanation:
For each birth, there are only two possible outcomes. Either it results in a defect, or it does not. The probability of a birth resulting in a defect is independent of other births. So we use the binomial probability distrbution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which
is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.
The proportion of American births that result in a birth defect is approximately 1/33 according to the Centers for Disease Control and Prevention (CDC).
This means that the probability of a birth resulting in a defect is 
A local hospital randomly selects five births.
This means that 
So the correct answer is:
c. binomial distribution with n = 5 and p = 1/33.