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2 years ago

14

1.9n−14=5n+58

1 answer:

elena-s [515]2 years ago

8 0

1. n=18
2. n=18
3. x=4
4. a= -12
5. x=3

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Given that A and B are true and X and Y are false, determine the truth value of the following proposition: ~[(A ⊃ Y) v ~(X ⊃ B)]

Anni [7]

Answer:

The value of the proposition is FALSE

Step-by-step explanation:

~[(A ⊃ Y) v ~(X ⊃ B)] ⋅ [~(A ≡ ~X) v (B ⊃ X)]

Let's start with the smallest part: ~X. The symbol ~ is negation when X is true with the negation is false and vice-versa. In this case, ~X is true (T)

~[(A ⊃ Y) v ~(X ⊃ B)] ⋅ [~(A ≡ T) v (B ⊃ X)]

Now the parts inside parenthesis: (A ⊃ Y),(X ⊃ B),(A ≡ T) and (B ⊃ X). The symbol ⊃ is the conditional and A ⊃ Y is false when Y is false and A is true, in any other case is true. The symbol ≡ is the biconditional and A ≡ Y is true when both A and Y are true or when both are false.

(A ⊃ Y) is False (F)

(X ⊃ B) is True (T)

(A ≡ T) is True (T)

(B ⊃ X) is False (F)

~[(F) v ~(T)] ⋅ [~(T) v (F)]

The two negations inside the brackets must be taken into account:

~[(F) v F] ⋅ [F v (F)]

The symbol left inside the brackets v is the disjunction, and A v Y is false only with both are false. F v (F) is False.

~[F] ⋅ [F]

Again considerating the negation:

T⋅ [F]

Finally, the symbol ⋅ is the conjunction, and A v Y is true only with both are true.

T⋅ [F] is False.

5 0

2 years ago

The SAT Reasoning Test (formerly called the Scholastic Aptitude Test) is perhaps the most widely used standardized test for coll

slamgirl [31]

Answer:

The score is $x = 1884$

Step-by-step explanation:

From the question we are told that

The population mean is $\mu = 1500$

The standard deviation is $\sigma = 300$

From the question we are told that the score follow a normal distribution

i.e $X \~ \ N( 1500 , 300)$

The proportion of score in the top 10% is mathematically

$P(X > x ) = P( \frac{X - \mu}{\sigma } > \frac{x - \mu}{\sigma } ) = 0.10$

Where x is the minimum score required to be in the top 10%

Now the $\frac{X - \mu}{\sigma } = Z (The \ Standardized \ value \ of \ X)$

So

$P(X > x ) = P( Z > \frac{x - \mu}{\sigma } ) = 0.10$

So

$P(X > x ) = P( Z > \frac{x - 1500}{300} ) = 0.10$

So the critical value of 0.10 from the normal distribution table is $Z_{0.10} = 1.28$

So

$\frac{x - 1500}{300} = 1.28$

$x = 1884$

6 0

3 years ago

An angle between 180’ and 360’

stealth61 [152]

Step-by-step explanation:

you start with 90 then 180 then270 then 360

3 0

3 years ago

Read 2 more answers

Prove this conjecture

steposvetlana [31]

Answer:

See explanation

Step-by-step explanation:

Consider the natural number $n(n+1)(n+2).$

If $n$ is the natural number, then $n+1, \ n+2$ are next two natural numbers, so numbers $n,\ n+1$ and $n+2$ are three consecutive numbers.

Given three consecutive natural numbers, one of them is always even number and one of them is always multiple of 3, so the product

$n(n+1)(n+2)$

is divisible by 6.

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3 years ago

Find the area and circumference of the circle. Use 3.14 for A.

Kaylis [27]

Answer:

A = 63.59

C = 28.26

Step-by-step explanation:

r = 4.5

Area of a circle:

A = πr²

A = 3.14(4.5²)

A = 3.14(20.25)

A = 63.59

Circumference:

C = 2πr

C = 2(3.14)(4.5)

C = 28.26

8 0

3 years ago