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3 years ago

8

What is the solution set of {x | x < -3} ∩ {x | x > 5}

1 answer:

lozanna [386]3 years ago

7 0

Any $x$ in this set will be real numbers that are both less than $-3$ and greater than $5$ . But that's not possible, so this set is empty.

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A tutor gives John 5 assignments and asks him to complete 5. How many possible combinations? Pls answer ASAP

Fittoniya [83]

Answer:

There is 1 possible combination

Step-by-step explanation:

There are 5 assignments and they must be completed. 5. We want to find the number of combinations, then we use the formula of combinations.

$nCr =\frac{n!}{r!(n-r)!}$

Where n is the total number of objects and you choose r from them

Then

$n= 5\\\\r = 5$

$5C5 =\frac{5!}{5!(5-5)!}$

$5C5 =\frac{5!}{5!(0)!}$

$5C5 =\frac{5!}{5!}$

$5C5 =1$

7 0

3 years ago

If cos() = − 2 3 and is in Quadrant III, find tan() cot() + csc(). Incorrect: Your answer is incorrect.

nydimaria [60]

Answer:

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \frac{5 - 3\sqrt 5}{5}$

Step-by-step explanation:

Given

$\cos(\theta) = -\frac{2}{3}$

$\theta \to$ Quadrant III

Required

Determine $\tan(\theta) \cdot \cot(\theta) + \csc(\theta)$

We have:

$\cos(\theta) = -\frac{2}{3}$

We know that:

$\sin^2(\theta) + \cos^2(\theta) = 1$

This gives:

$\sin^2(\theta) + (-\frac{2}{3})^2 = 1$

$\sin^2(\theta) + (\frac{4}{9}) = 1$

Collect like terms

$\sin^2(\theta) = 1 - \frac{4}{9}$

Take LCM and solve

$\sin^2(\theta) = \frac{9 -4}{9}$

$\sin^2(\theta) = \frac{5}{9}$

Take the square roots of both sides

$\sin(\theta) = \±\frac{\sqrt 5}{3}$

Sin is negative in quadrant III. So:

$\sin(\theta) = -\frac{\sqrt 5}{3}$

Calculate $\csc(\theta)$

$\csc(\theta) = \frac{1}{\sin(\theta)}$

We have: $\sin(\theta) = -\frac{\sqrt 5}{3}$

So:

$\csc(\theta) = \frac{1}{-\frac{\sqrt 5}{3}}$

$\csc(\theta) = \frac{-3}{\sqrt 5}$

Rationalize

$\csc(\theta) = \frac{-3}{\sqrt 5}*\frac{\sqrt 5}{\sqrt 5}$

$\csc(\theta) = \frac{-3\sqrt 5}{5}$

So, we have:

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta)$

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \tan(\theta) \cdot \frac{1}{\tan(\theta)} + \csc(\theta)$

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = 1 + \csc(\theta)$

Substitute: $\csc(\theta) = \frac{-3\sqrt 5}{5}$

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = 1 -\frac{3\sqrt 5}{5}$

Take LCM

$\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \frac{5 - 3\sqrt 5}{5}$

6 0

3 years ago

What is -10 degrees Celsius equal to in Fahrenheit

hjlf

the formula is f=(c*20)+30 so 14 degrees farhenhight

3 0

3 years ago

Select the graphs that have an equation with a < 0.

Eddi Din [679]

Answer:

Second graph only.

Step-by-step explanation:

The standard equation of a parabola is ax^2+bx+c where a,b and c are coefficients.

If the coefficient of (a) is positive then the parabola is concave upwards (as in picture 1)

If the coefficient of (a) is negative then the parabola is concave downwards as in picture 2.

7 0

3 years ago

Read 2 more answers

Anne has worn a black shirt on 6 of the last 20 days. Considering this

Stels [109]

Answer:

3

Step-by-step explanation:

Considering she wore a black shirt 6 times in 20 days will give you the statistic of 3/10. If the question is about the next 10 days then she will wear 3 black shirts. (It's also 1/2 of the original question.)

7 0

3 years ago