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Elan Coil [88]
4 years ago
11

6. Calculate the value of tan (48°19'23").

Mathematics
1 answer:
lisov135 [29]4 years ago
4 0

Answer:

C. 1.12

Step-by-step explanation:

There are 60' (minutes) in a degree and 60" in a minute meaning that we have (60×60) seconds in a degree.

Therefore to convert seconds to degrees we divide by 3600. and minutes to degrees we divide by 60.

The angle 48°19'23'' can be converted into a decimal as follows

48°+(19/60+23/3600)°

=48.323°

Tan 48.323= 1.12

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Which of these rational numbers is also an integer?
dexar [7]

Answer:

6/3

Step-by-step explanation:

An integer is a whole number, that is not a fraction. All of the numbers are fractions, but if you simplify them, you see that 6/3=2. 2 is a whole number, and therefore an integer.

3 0
3 years ago
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A doctor wants to estimate the mean HDL cholesterol of all​ 20- to​ 29-year-old females. How many subjects are needed to estimat
REY [17]

(a) 404 subjects are needed to estimate the mean HDL cholesterol within 2 points with 99% confidence.

(b) When the confidence level decreases to 95%, the number of subjects decreases from 404 to 234.

<u>Explanation:</u>

Given:

σ = 15.6

Let the number of subjects be n

(a)

When the confidence level is 99%, then z = 2.576

E = 2

We know:

n = [\frac{z X s}{E}]^2

On substituting the value, we get:

n = [\frac{2.576 X 15.6}{2} ]^2\\\\n = 403.7

Thus, 404 subjects are needed to estimate the mean HDL cholesterol within 2 points with 99% confidence.

(b)

When the confidence level is 95%, then z = 1.96

E = 2

We know:

n = [\frac{z X s}{E}]^2

On substituting the value, we get:

n = [\frac{1.96 X 15.6}{2} ]^2\\\\n = 233.7

n = 234

Thus, when the confidence level decreases to 95%, the number of subjects decreases from 404 to 234.

8 0
3 years ago
Find a polynomial function of degree 3 with 2, i, -i as zeros.
sergiy2304 [10]

Answer:

p(x)= x^3-2x^2+x-2

Step-by-step explanation:

Here we are given that a polynomial has zeros as 2 , i and -i . We need to find out the cubic polynomial . In general we know that if \alpha , \ \beta \ \& \ \gamma are the zeros of the cubic polynomial , then ,

\sf \longrightarrow p(x)= (x -\alpha )(x-\beta)(x-\gamma)

Here in place of the Greek letters , substitute 2,i and -i , we get ,

\sf\longrightarrow p(x)= (x -2 )(x-i)(x+i)

Now multiply (x-i) and (x+i ) using the identity (a+b)(a-b)=a² - b² , we have ,

\sf  \longrightarrow p(x)= (x-2)\{ x^2 - (i)^2\}

Simplify using i = √-1 ,

\sf \longrightarrow p(x)= (x-2)( x^2 + 1 )

Multiply by distribution ,

\sf \longrightarrow p(x)= x(x^2+1) -2(x^2+1)

Simplify by opening the brackets ,

\sf\longrightarrow p(x)= x^3+x-2x^2-2

Rearrange ,

\sf\longrightarrow \underline{\boxed{\blue{\sf p(x)= x^3-2x^2+x-2}}}

4 0
3 years ago
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xeze [42]

Step-by-step explanation:

x² + 2x - 63 = 0

(x+9)(x-7)=0

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7 0
1 year ago
The population of a country was 6 million in the year 2000 and has grown continually since then. The function P(t)= 6e^0.016t, m
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