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arlik [135]
3 years ago
10

How many two-digit positive integers can be formed the digits 1,5,6, and 8 if no digit is repeated?

Mathematics
1 answer:
IgorLugansk [536]3 years ago
5 0

Answer:

12

Step-by-step explanation:

There are 4 different digits to choose from. Since we want 2-digit number, we will see what digits can we put in place of 1st digit and what digit can we place in place of 2nd digit.

Hence, <u><em>how many digits (from 1,5,6 and 8) can be placed in the 1st digit of the number we want?</em></u>

Any one of the four digits (1,5,6, or 8).

Now, <em><u>How many digits (from 1,5,6 and 8) can be placed as the 2nd digit of the number we want?</u></em>

Any one of the THREE digits (since repetition is not allowed, we disregard the initial digit).

Thus the number of two-digit positive integers is 4 * 3 = 12

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MA_775_DIABLO [31]

Answer:

The fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. The roots are x=1\pm i\sqrt{7}.

Step-by-step explanation:

Consider the provided information.

Algebra's fundamental theorem states that: Every polynomial equation of degree n with complex coefficients has n roots in the complex numbers.

Now consider the provided equation.

2x^2-4x+16=0

The degree of the polynomial equation is 2, therefore according to Algebra's fundamental theorem the equation have two complex roots.

Now find the root of the equation.

For the quadratic equation of the form ax^2+bx+c=0 the solutions are: x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}

Substitute a=2,\:b=-4,\:\ and \ c=16 in above formula.

x_{1,\:2}=\frac{-\left(-4\right)\pm \sqrt{\left(-4\right)^2-4\cdot \:2\cdot \:16}}{2\cdot \:2}

x_{1,\:2}=\frac{4\pm \sqrt{16-128}}{4}

x_{1,\:2}=\frac{4\pm \sqrt{-112}}{4}

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Hence, the fundamental theorem of algebra tells you that the equation will have two complex roots since the degree of the polynomial is 2. The roots are x=1\pm i\sqrt{7}.

4 0
3 years ago
To estimate the mean of a population with unknown distribution shape and unknown standard deviation, we take a random sample of
Naddika [18.5K]

Answer:

t_{critical} = \pm 1.7793                        

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 64

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92% Confidence interval:  

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Putting the values, we get,

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Answer:

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Step-by-step explanation:

Given

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To start with;

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To convert from feet to yard;

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This implies that;

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Answer:

x = 2

Step-by-step explanation:

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