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3 years ago

Which expression is equivalent to cot t sec t?

1 answer:

3 0

$\bf cot(\theta)=\cfrac{cos(\theta)}{sin(\theta)}
\qquad 
% cosecant
csc(\theta)=\cfrac{1}{sin(\theta)}
\qquad 
% secant
sec(\theta)=\cfrac{1}{cos(\theta)}\\\\
-------------------------------\\\\
cot(t)sec(t)\implies \cfrac{\underline{cos(t)}}{sin(t)}\cdot \cfrac{1}{\underline{cos(t)}}\implies \cfrac{1}{sin(t)}\implies ?$

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What is the x value ?????

Lady bird [3.3K]

I got x=2.64 or x=1.32 i don't know if i done it right

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3 years ago

if the area of a square is 144 feet and the perimeter of the triangle is 28 feet, what is the perimeter of the room's floor?

FinnZ [79.3K]

Answer:

$52+12\pi$

Step-by-step explanation:

The diagram for the question is attached below

perimeter of the triangle is 28 feet

area of a square is 144 feet

Area of the square is side^2

$side ^2= 144$

take square root on both sides

side = 12

side of the square = 12

side is the diameter of the semicircle

Diameter = 12 , so radius = 12 divide 2 = 6

circumference of semicircle = $2\pi r=2\pi (6)=12\pi$

one side of the rectangle is calculated in the perimeter of triangle and other side is calculated using circumference

perimeter of other two side = 2(12)= 24

Total perimeter = $28+24+12\pi =52+12\pi$

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3 years ago

Marine scientists categorize signature whistles of bottlenose dolphins by typelong dash—type a, type b, type c, etc. In one s

r-ruslan [8.4K]

Answer:

The 95% confidence interval for the true proportion of bottlenose dolphin signature whistles that are type a whistles is (0.4687, 0.6123).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

$n = 185, \pi = \frac{100}{185} = 0.5405$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5405 - 1.96\sqrt{\frac{0.5405*0.4595}{185}} = 0.4687$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5405 + 1.96\sqrt{\frac{0.5405*0.4595}{185}} = 0.6123$

The 95% confidence interval for the true proportion of bottlenose dolphin signature whistles that are type a whistles is (0.4687, 0.6123).

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3 years ago

Solve each given equation and show your work.

Eduardwww [97]

Answer:

(a) x = 3

(b) y = 6

(d) x = 5

Step-by-step explanation:

(A) 2 + x = 5 You would subtract the 2 from both sides which gives you x = 3

(B) 8y = 48 You would divide 8 from both sides which is 6 so y = 6

(D) -7x - 3x + 2 = -8x - 8 First simplify the equation; -10x + 2 = -8x - 8. Next, you want to subtract 2 from both sides which gives us -10x = -8x - 10. Now you want to add 8x to both sides which is -2x = -10. And now you just divide -2 on both sides which gives us the answer 5. So, x = 5. I hope this helps. Let me know if one of the answers are incorrect.

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2 years ago

What is the weight of a square if a triangle weighs 4 grams? Explain your reasoning

stellarik [79]

Answer:

8 grams

Step-by-step explanation:

The balance is in equilibrium, so the weights of the two sides are equal.

Let the weight of a square be s.

Left side: 2s + 4

Right side: s + 3(4) = s + 12

The weights are equal, so we set the two expressions equal.

2s + 4 = s + 12

s = 8

Answer: The weight of a square is 8 grams.

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3 years ago