What are the angle measures of the triangle? (Answer choices in picture)

Mathematics

1 answer:

antiseptic1488 [7]2 years ago

4 0

I would go with 45,45, 90 because first you can eliminate C and D.
C because it is not an equilateral triangle and D because you can figure it out.

Now you have A and B. A 30, 60 90 Degree Triangle would mean that none of the sides are equal (or the legs don't equal the hypotenuse when you put it in Pythagorean form [a²+b²=c²]). However if you translate the problem to answers that are easier to understand: {(7√3 = 12.124)² + 21² = 587.8944 = 14√3} Then you can see, two angles are equal to each other. So the answer is B.

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1. Consider the following hypotheses:

Andrej [43]

Answer:

See deductions below

Step-by-step explanation:

a) p(y)∧q(y) for some y (Existencial instantiation to H1)

b) q(y) for some y (Simplification of a))

c) q(y) → r(y) for all y (Universal instatiation to H2)

d) r(y) for some y (Modus Ponens using b and c)

e) p(y) for some y (Simplification of a)

f) p(y)∧r(y) for some y (Conjunction of d) and e))

g) ∃x (p(x) ∧ r(x)) (Existencial generalization of f)

a) ¬C(x) → ¬A(x) for all x (Universal instatiation of H1)

b) A(x) for some x (Existencial instatiation of H3)

c) ¬(¬C(x)) for some x (Modus Tollens using a and b)

d) C(x) for some x (Double negation of c)

e) A(x) → ∀y B(y) for all x (Universal instantiation of H2)

f) ∀y B(y) (Modus ponens using b and e)

g) B(y) for all y (Universal instantiation of f)

h) B(x)∧C(x) for some x (Conjunction of g and d, selecting y=x on g)

i) ∃x (B(x) ∧ C(x)) (Existencial generalization of h)

3) We will prove that this formula leads to a contradiction.

a) ∀y (P (x, y) ↔ ¬P (y, y)) for some x (Existencial instatiation of hypothesis)

b) P (x, y) ↔ ¬P (y, y) for some x, and for all y (Universal instantiation of a)

c) P (x, x) ↔ ¬P (x, x) (Take y=x in b)

But c) is a contradiction (for example, using truth tables). Hence the formula is not satisfiable.

7 0

2 years ago

The average breaking strength of a certain brand of steel cable is 2000 pounds, with a standard deviation of 100 pounds. A sampl

Westkost [7]

Answer:

1963.2 pounds (lbs.)

Step-by-step explanation:

Things to understand before solving:

- <u>Normal Probability Distribution</u>

The z-score formula can be used to solve normal distribution problems. In a set with mean ц and standard deviation б, the z-score of a measure X is given by: $Z=\frac{X-u}{a}$

The Z-score reflects how far the measure deviates from the mean. After determining the Z-score, we examine the z-score table to determine the p-value associated with this z-score. This p-value represents the likelihood that the measure's value is less than X, or the percentile of X. Subtracting 1 from the p-value yields the likelihood that the measure's value is larger than X.

- <u>Central Limit Theorem</u>

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean ц and standard deviation б , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean ц and standard deviation $s=\frac{a}{\sqrt{n} }$

As long as n is more than 30, the Central Limit Theorem may be applied to a skewed variable. A specific kind of steel cable has an average breaking strength of 2000 pounds, with a standard variation of 100 pounds.

This means, ц = 2000 and б = 100.

A random sample of 20 cables is chosen and tested.

This means that n = 20, $s=\frac{100}{\sqrt{120} } =22.361$