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valina [46]
3 years ago
15

1 What is the simplified value of the exponential expression 27'? © malo 03​

Mathematics
2 answers:
LenaWriter [7]3 years ago
8 0

Answer: 3

Step-by-step explanation:

Anon25 [30]3 years ago
4 0

Answer:

{27}^{ \frac{1}{3} }  =  \sqrt[3]{27}  =  \sqrt[3]{3 \times 3 \times 3}  = \boxed{ 3}✓

<h3>3. <em><u>3</u></em> is the right answer.</h3>
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The lighthouse was moved 230 feet inland at a rate of 40 feet per hour. How many hours did it take to move the lighthouse? What
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Answer:

5.75

Step-by-step explanation:

4) 230 ÷ 40 = 5.75

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Helen is choosing a main course and a dessert in a restaurant.
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3 years ago
Let f(x) be a quartic polynomial with integer coefficients and four integer roots. Suppose the constant term of f(x) is 6.(a) Is
frez [133]

Answer:

  (a) yes

  (b) no; see below

Step-by-step explanation:

(a) Integer roots of the quartic will be integer divisors of 6. One of the divisors of 6 is 3, so 3 is a possible root.

(b) In order for 3 to be a double root, it would have to be a double factor of 6. The only integer factors of 6 are 1, 2, 3, 6. (3² = 9 is not one.)

___

The quartic can be written as ...

  k(x -a)(x -b)(x -c)(x -d) . . . . . where a, b, c, d, k are integers

The constant term will be kabcd, of which each of the roots is a factor. If the constant is 6 and one root is d=3, then we must have

  kabcd = 3kabc = 6

  kabc = 6/3 = 2

Among these four integer factors, there must be an even number of minus signs, and one that has the value ±2. Another root whose value is 3 will not satisfy the requirements.

3 0
3 years ago
Mary is rolling a standard six-sided die and spinning on a spinner with the number 1-8.
Readme [11.4K]

Answer:

a) Dice and spinner are different objects, with no relation between themselves, and thus her dice rolls and spinning outcomes are independent.

b) \frac{1}{48} probability of her rolling a 4 and spinning an 8.

c) \frac{1}{8} probability of her rolling an even number and spinning a number less than 3.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

A) Are her dice rolls and spinning outcomes independent or dependent?

Dice and spinner are different objects, with no relation between themselves, and thus her dice rolls and spinning outcomes are independent.

B) What is the probability of her rolling a 4 and spinning an 8?

Since the events are independent, we find each separate probability and multiply them.

Probability of rolling a 4:

One side out of 6 on the dice. So

P(A) = \frac{1}{6}

Probability of spinning an 8:

One side out of 8 on the spinner. So

P(B) = \frac{1}{8}

Probability of rolling a 4 and spinning an 8:

P(A \cap B) = P(A)P(B) = \frac{1}{6} \times \frac{1}{8} = \frac{1}{48}

\frac{1}{48} probability of her rolling a 4 and spinning an 8.

C) What is the probability of her rolling an even number and spinning a number less than 3?

Since the events are independent, we find each separate probability and multiply them.

Probability of rolling an even number:

2, 4 or 6(3 sides out of 6). So

P(A) = \frac{3}{6} = \frac{1}{2}

Probability of spinning a number less than 3:

Two numbers(1 or 2) out of 8 on the spinner. So

P(B) = \frac{2}{8} = \frac{1}{4}

Probability of rolling an even number and spinning a number less than 3:

P(A \cap B) = P(A)P(B) = \frac{1}{2} \times \frac{1}{4} = \frac{1}{8}

\frac{1}{8} probability of her rolling an even number and spinning a number less than 3.

8 0
2 years ago
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