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3 years ago

What is the simplest form of the expression below?

Mathematics

2 answers:

ivann1987 [24]3 years ago

6 0

Answer:

Step-by-step explanation:

cot theta

sineoko [7]3 years ago

3 0

Answer:

(B) cot Theta

Step-by-step explanation:

We want to simplify the expression:

$\dfrac{cot\theta cos\theta}{sin\theta } X\dfrac{tan\theta}{\frac{sin\theta}{cos\theta tan \theta} }$

Now:

$\dfrac{ cos\theta}{sin\theta } =cot\theta\\\dfrac{ sin\theta}{cos\theta }=tan \theta\\$Substituting these into the expression\\\dfrac{cot\theta cos\theta}{sin\theta } X\dfrac{tan\theta}{\frac{sin\theta}{cos\theta tan \theta} }=cot\theta cot\theta X\dfrac{tan\theta}{\frac{tan\theta}{ tan \theta} }\\=cot\theta cot\theta X tan\theta$ (Since cot\theta X tan\theta =1) \\$Therefore our result:\\=cot\theta$

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4 years ago

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How to determine whether the given function is even,odd, or neither?<br>f(x) = x^3 + x^2 + 3

Gnom [1K]

f(x) = x^3 + x^2 + 3x^0 is neither even nor odd. Why? Because we have a mixture of even and odd powers of x here: x^3 (odd) and x^2 and x^0 (even).

Even functions: all component functions are even (e. g., x^2 and x^0).

Odd functions: all component functions are odd (e. g., x^5 and x^3.

Neither: There's a mixture of even ad odd functions.

Another way to test for even, odd or neither:

Even functions: f(-x) = f(x). Changing the sign of the input (x) doesn't change the sign of the output.

Odd functions: f(-x) = -f(x). Changing the sign of the input changes the sign of the output.

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3 years ago

A triangular bandana has an area of 90 square inches. The height of the triangle is 5 5/8 inches. Enter and solve an equation to

Mandarinka [93]

B = 2 · A/h
b = 2 / 1 x 90 / 5 5/8 top times top, bottom times bottom (2 x 90, 1 x 5 5/8)
b = 180 / 5 5/8
b = 32

CHECK ANSWER BY INPUTTING AREA EQUATION AND FILL IN NUMBERS

A = height x base
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3 years ago

an outdoor swimming pool costs $9 per day to visit during the summer. there is also a $25 yearly registration fee. is the total

jolli1 [7]

Answer:

Step-by-step explanation:

cost=25+8d

To be proportional you'd have to have no flat fee: cost=8d

1 day = $8

2 days = $16

5 days = $40

10 days = $80, etc.

I hope I helped.

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3 years ago

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After an extensive advertising campaign, the manager of a company expects the proportion of potential customers that recognize a

lina2011 [118]

Answer:

Step-by-step explanation:

Hello!

The study variable is:

X: number of customers that recognize a new product out of 120.

There are two possible recordable outcomes for this variable, the customer can either "recognize the new product" or " don't recognize the new product". The number of trials is fixed, assuming that each customer is independent of the others and the probability of success is the same for all customers, p= 0.6, then we can say this variable has a binomial distribution.

The sample proportion obtained is:

p'= 54/120= 0.45

Considering that the sample size is large enough (n≥30) you can apply the Central Limit Theorem and approximate the distribution of the sample proportion to normal: p' ≈ N(p; $\sqrt{\frac{p(1-p)}{n} }$ )

The other conditions for this approximation are also met: (n*p)≥5 and (n*q)≥5

The probability of getting the calculated sample proportion, or lower is:

P(X≤0.45)= P(Z≤ $\frac{0.45-0.6}{\sqrt{\frac{0.6*0.4}{120} } }$ )= P(Z≤-3.35)= 0.000

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