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3 years ago

Use the binomial expression (p+q)n

Mathematics

1 answer:

zvonat [6]3 years ago

3 0

Answer:

{0.16807, 0.36015, 0.3087, 0.1323, 0.02835, 0.00243}

Step-by-step explanation:

The expansion of (p+q)^n for n = 5 is ...

(p+q)^5 = p^5 +5·p^4·q +10·p^3·q^2 +10·p^2·q^3 +5·p·q^4 +q^5

When the probability p=0.3 and q = 1-p = 0.7 the terms of this series correspond to the probabilities of 5, 4, 3, 2, 1, and 0 favorable outcomes out of 5 trials.

For example, p^5 = 0.3^5 = 0.00243 is the probability of 5 favorable outcomes in 5 trials where the probability of each favorable outcome is 0.3.

___

The attachment shows the calculation of these numbers using a graphing calculator. It lists them in reverse order of the expansion of (p+q)^5 shown above, so that they are the probabilities of 0–5 favorable outcomes in the order 0–5.

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The height of a golfball hit off a 128-foot hill is modeled by the function h(t) = −16t2 + 32t + 128, where h is height in feet

taurus [48]

The time taken for the golf ball to reach the ground is 1 s.

<h3>Motion of the golf ball</h3>

The path of motion of the golf ball can be described as parabolic because it is projectile.

When the golf ball reaches the ground, the final velocity will be zero.

Velocity of the golf ball is change in height with time.

v = dh/dt

h(t) = -16t² + 32t + 128

dh/dt = -32t + 32

0 = -32t + 32

32t = 32

t = 1 s

Thus, the time taken for the golf ball to reach the ground is 1 s.

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2 years ago

Triangle P Q R is shown. Angle Q R P is a right angle. Angle R P Q is 30 degrees and angle P Q R is 60 degrees. Given right tria

mote1985 [20]

Answer:

The correct option is option (c).

$Sin \ P= \frac {RQ}{PQ}$

Step-by-step explanation:

Right angled triangle:

One angle must be 90° and other two angles are acute angle.
The hypotenuses is the longest side of the triangle and opposite right angle.
It follows the Pythagorean Theorem.

Given that,

∠QRP= 90°, ∠RPQ= 30°, ∠PQR = 60°

we know that,

$sin \theta =\frac{Opposite }{Hypotenuse}$

for sin P , the opposite is QR.

The hypotenuse is PQ.

Therefore,

$Sin \ P= \frac {RQ}{PQ}$

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3 years ago

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Answer:

I think answer is B or C or D

Step-by-step explanation:

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3 years ago

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Answer:

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2 years ago

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Which statements are true about ΔJKL and ΔLMN? Select all that apply.

svp [43]

Answer:

A. ΔJKL and ΔLMN have only one pair of angles that are congruent

C. ΔJKL has angles that measure $50^o,60^o,70^o$

Step-by-step explanation:

step 1

Find the value of x

we know that

$m\angle KLJ=m\angle MLN$ ----> by vertical angles

substitute the given values

$(6x-2)^o=(5x+10)^o$

solve for x

$6x-5x=10+2\\x=12$

step 2

Find the measure of the interior angles of triangle JKL

we have

$m\angle KLJ=(6(12)-2)=70^o$

$m\angle KJL=(5(12))=60^o$

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

$m\angle JKL=180^o-130^o=50^o$

therefore

Triangle JKL has angles that measure $50^o,60^o,70^o$

step 3

Find the measure of the interior angles of triangle LMN

we have

$m\angle MLN=(5(12)+10)=70^o$

$m\angle LMN=(6(12)-7)=65^o$

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

$m\angle LNM=180^o-135^o=45^o$

Triangle LMN has angles that measure $45^o,65^o,70^o$

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

The corresponding angles of triangle JKL and LMN are not congruent

therefore

The triangles are not similar

<u><em>Verify each statement</em></u>

Part a) ΔJKL and ΔLMN have only one pair of angles that are congruent

The statement is true (see the explanation)

Part b) ΔJKL and ΔLMN have two pairs of angles that are congruent

The statement is false

Because have only one pair of angles that are congruent

Part c) ΔJKL has angles that measure $50^o,60^o,70^o$

The statement is true (see the explanation)

Part d) ΔLMN has angles that measure $50^o,60^o,70^o$

The statement is false

Because, Triangle LMN has angles that measure $45^o,65^o,70^o$

Part e) ΔJKL and ΔLMN are similar

The statement is false

Because, the corresponding angles are not congruent

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