All categories

3 years ago

Evaluate 11p4 and 9c5

1 answer:

7 0

$\bf _{n}P_{r}=\cfrac{n!}{(n-r)!}\qquad \qquad _{11}P_4=\cfrac{11!}{(11-4)!}
\\\\\\
_nC_r=\cfrac{n!}{r!(n-r)!}\qquad \qquad _9C_5=\cfrac{9!}{5!(9-5)!}
$

check your calculator on the factorial(!) button.

You might be interested in

Which molecule activates light reactions

natta225 [31]

Answer:

Step-by-step explanation:

The light-dependent reactions use light energy to make two molecules needed for the next stage of photosynthesis: the energy storage molecule ATP and the reduced electron carrier NADPH. In plants, the light reactions take place in the thylakoid membranes of organelles called chloroplasts.

5 0

3 years ago

Please help me out :P

Veseljchak [2.6K]

cos θ = $\frac{-4\sqrt{65} }{65}$ , sin θ = $\frac{-7\sqrt{65} }{65}$ , cot θ = 4/7, sec θ = $\frac{-\sqrt{65} }{4}$ , cosec θ = $\frac{-\sqrt{65} }{7}$

<h3>What are trigonometric ratios?</h3>

Trigonometric Ratios are values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

Sin θ: Opposite Side to θ/Hypotenuse

Tan θ: Opposite Side/Adjacent Side & Sin θ/Cos

Cos θ: Adjacent Side to θ/Hypotenuse

Sec θ: Hypotenuse/Adjacent Side & 1/cos θ

Analysis:

tan θ = opposite/adjacent = 7/4

opposite = 7, adjacent = 4.

we now look for the hypotenuse of the right angled triangle

hypotenuse = $\sqrt{7^{2} + 4^{2} }$ = $\sqrt{49+16}$ = $\sqrt{65}$

sin θ = opposite/ hyp = $\frac{7}{\sqrt{65} }$

Rationalize, $\frac{7}{\sqrt{65} }$ x $\frac{\sqrt{65} }{\sqrt{65} }$ = $\frac{7\sqrt{65} }{65}$

But θ is in the third quadrant(180 - 270) and in the third quadrant only tan and cot are positive others are negative.

Therefore, sin θ = - $\frac{7\sqrt{65} }{65}$

cos θ = adj/hyp = $\frac{4}{\sqrt{65} }$

By rationalizing and knowing that cos θ is negative, cos θ = - $\frac{-4\sqrt{65} }{65}$

cot θ = 1/tan θ = 1/7/4 = 4/7

sec θ = 1/cos θ = 1/ $\frac{4}{\sqrt{65} }$ = - $\frac{-\sqrt{65} }{4}$

cosec θ = 1/sin θ = 1/ $\frac{\sqrt{65} }{7}$ = $\frac{-\sqrt{65} }{7}$

Learn more about trigonometric ratios: brainly.com/question/24349828

#SPJ1

5 0

1 year ago

A rug maker is using a patter that is a rectangle with a length of 96 inches and a width of 60 inches. the rug maker wants to in

dexar [7]

Recall that the formula for the perimeter of a rectangle is: 2Length+2Width
With this in mind, we have that the original design is 96×60, where 90 is length and 60 is width, so it would simply be:
2(96+l) + 2 (60+w) = New Perimeter
Or simplified, it'd be:
2l + 2w + 312 = New Perimeter

8 0

3 years ago

Carlos has been given a list of 5 bands and asked to place a vote. His vote must have the names of his favorite, second favorite

Alex_Xolod [135]

Answer:

Step-by-step explanation:

8 0

3 years ago

Using 45-in. fabric, Regan needs 2 and one fourth yd for a dress, one fourth yd of contrasting fabric for the band at the bot

Arte-miy333 [17]

Answer:

$7\dfrac14$ yards$