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Ahat [919]
3 years ago
8

Cos30° cos45°-sin30° sin 45°​

Mathematics
1 answer:
sammy [17]3 years ago
4 0

Answer:

(√6 - √2)/4

Step-by-step explanation:

cos30°cos45° - sin30°sin45°

= cos (30 + 45)°

= cos 75°

= (√6 - √2)/4

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What are the domain and range of the function f(x)= negative squared x+3 negative 2
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Answer:

  1. Domain = R\ (\text{All real numbers})
  2. Range = f\ \epsilon\ R\ :\ f\le -2}

Step-by-step explanation:

The given function is,

f\left(x\right)=-\left(x+3\right)^2-2

f(x) is a quadratic function. As this is a polynomial function, so its domain is the entire real number set.

As its leading coefficient will be negative, so it will open downward. Hence, its range will be all real numbers below its vertex.

The general vertex form of quadratic function or parabola is,

f(x)=a(x-h)^2+k

where (h, k) is the vertex.

Comparing the given function with this we get the vertex at (-3,-2)

The y coordinate of the vertex is -2, so the range of the given quadratic function is,

f\ \epsilon\ R\ :\ f\le -2}

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A gallup survey indicated that 72% of 18- to 29-year-olds, if given choice, would prefer to start their own business rather than
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We are given that a Gallup survey indicated that 72% of 18- to 29-year-olds, if given choice, would prefer to start their own business rather than work for someone else.

Let \hat p = <u><em>sample proportion of people who prefer to start their own business</em></u>

The z-score probability distribution for the sample proportion is given by;

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Now, the probability that no more than 70% would prefer to start their own business is given by = P( \hat p \leq 70%)

       P( \hat p \leq 70%) = P( \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } } \leq \frac{0.70-0.72}{\sqrt{\frac{0.70(1-0.70)}{600} } } ) = P(Z \leq -1.07) = 1 - P(Z < 1.07)

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The above probability is calculated by looking at the value of x = 1.07 in the z table which has an area of 0.8577.

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