MATHEMATICS
HIGH SCHOOL

Answer:

Answer:

The nth term of the series is 5-9n.

Step-by-step explanation:

Given : Series 14, 23, 32, 41,..

To find : The nth term of the series ?

Solution :

The given series 14, 23, 32, 41,.. is an arithmetic series as the difference between term is common.

Where, first term is a=14 and common difference d=23-14=9

The nth term of the arithmetic series is

Therefore, The nth term of the series is 5-9n.

Answer: 1.14

2.23

3.32

4.41

5.50

6.59

7.68

8.77

9.86

2.23

3.32

4.41

5.50

6.59

7.68

8.77

9.86

MIDDLE SCHOOL

the statue of liberty is 305.5 feet tall from the foundation of its pedestal to the top of its torch. Isla is building a model of the statue. the model will be one hundredth times as tall as the actual statue, how tall will the model be?

Answer: 3.055 feet

Step-by-step explanation:

Given : The statue of liberty is 305.5 feet tall from the foundation of its pedestal to the top of its torch.

Its model will be one hundredth times as tall as the actual statue.

Now , One hundredth =

According to the statement,

The height of the model will be =

Hence, the height of the model will be 3.055 feet.

The model will be 3.055 feet

HIGH SCHOOL

Round 87,298 to the nearest thousand

The answer is 90,000

MIDDLE SCHOOL

A certain medicine is given in an amount proportion to a patient’s body weight. Suppose a patient weighing 132 pounds requires 143 milligrams of medicine. What is the amount of medicine required by a patient weighing 156 pounds?

Answer:

169 mg

Step-by-step explanation:

The ratio of medicine quantity to body weight is the same for both patients, so ...

amount/(156 lb) = (143 mg)/(132 lb)

Multiply by 156 lb:

amount = (143 mg)(156/132) = 169 mg

The patient requires 169 mg of medicine.

Answer:

160 milligrams......

HIGH SCHOOL

a. Show that the following statement forms are all logically equivalent. p → q ∨ r, p ∧ ∼q → r, and p ∧ ∼r → q b. Use the logical equivalences established in part (a) to rewrite the following sentence in two different ways. (Assume that n represents a fixed integer.) If n is prime, then n is odd or n is 2.

Answer:

(a) if n is prime, then n is odd or n is 2

(b) if n is prime and n is not odd, then n is 2

(c) if n is prime and n is not 2, then n is odd

Step-by-step explanation:

a) p → q ∨ r

b) p ∧ ∼q → r

c) p ∧ ∼r → q

Lets show that (a) implies (b) and (c). (a) says that if property p is true, then either q or r is true, thus, if p is true we have:

- If the condition of (b) applies (thus q is not true), we need r to be true because either q or r were true because we are assuming (a) and p. Hence (b) is true
- If the condition of (c) applies (r is not true), since either r or q were true due to what (a) says, then q neccesarily is true, hence (c) is also true.

Now, lets prove that (b) implies (a)

- If p is true and property (b) is true, then if q is true, then either q or r are true thus (a) is correct. If q is not true, then property (b) claims that, since p is true and q not, r has to be true, therefore (a) is valid in this case as well, hence (a) is also true.

(c) implies (a) can be proven with similar argument, changing (b) for (c), q for r and r for q.

With this we prove that the 3 properties are equivalent.

For the rest of the exercise, we have

- property p: n is prime
- property q: n is odd
- property r: n is 2

Translating this, we obtain (a), (b) and (c)

(a) if n is prime, then n is odd or n is 2

(b) if n is prime and n is not odd, then n is 2

(c) if n is prime and n is not 2, then n is odd