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3 years ago

Help me answer the question please

Mathematics

2 answers:

Yuki888 [10]3 years ago

8 0

Answer:

see explanation

Step-by-step explanation:

(10)

(a)

The opposite sides of the rectangle are equal, then perimeter P is

P = 2(4p - 6) + 2(p + 13) ← distribute parenthesis and simplify

= 8p - 12 + 2p + 26

= 10p + 14

Given P = 84 , then

10p + 14 = 84 ( subtract 14 from both sides )

10p = 70 ( divide both sides by 10 )

p = 7

---------------------------------------------

(b)

The area (A) of the shaded region is calculated as

A = area of rectangle - area of triangle

area of rectangle = (4p - 6)(p + 13) ← expand using FOIL

= 4p² + 46p - 78 ← substitute p = 7

= 4(7)² + 46(7) - 78

= 4(49) + 322 - 78

= 196 + 244

= 440 cm²

area of triangle = $\frac{1}{2}$ bh

= $\frac{1}{2}$ ( 3p - 3)( p + 13) ← substitute p = 7

= $\frac{1}{2}$ (3(7) - 3)(7 + 13)

= $\frac{1}{2}$ (21 - 3)(20)

= $\frac{1}{2}$ × 18 × 20 = 9 × 20 = 180 cm²

Then

A = 440 - 180 = 260 cm²

(11)

pole B = $\frac{1}{2}$ × 72 = 36

pole A = $\frac{5}{6}$ × 36 = 5 × 6 = 30 m

jok3333 [9.3K]3 years ago

3 0

Answer:

ok it is very hard question

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a) Let the random variable X= "number of these tracks where SBIRS detects the object." in order to use the binomial probability distribution we need to satisfy some conditions:

1) Independence between the trials (satisfied)

2) A value of n fixed , for this case is 20 (satisfied)

3) Probability of success p =0.2 fixed (Satisfied)

So then we have all the conditions and we can assume that:

$X \sim Bin(n =20, p=0.8)$

b) $X \sim Bin(n =20, p=0.8)$

c) $P(X=15)=(20C15)(0.8)^{15} (1-0.8)^{20-15}=0.17456$

d) $P(X \geq 15) = P(X=15)+ .....+P(X=20)$

$P(X=15)=(20C15)(0.8)^{15} (1-0.8)^{20-15}=0.17456$

$P(X=16)=(20C16)(0.8)^{16} (1-0.8)^{20-16}=0.218$

$P(X=17)=(20C17)(0.8)^{17} (1-0.8)^{20-17}=0.205$

$P(X=18)=(20C18)(0.8)^{18} (1-0.8)^{20-18}=0.137$

$P(X=19)=(20C19)(0.8)^{19} (1-0.8)^{20-19}=0.058$

$P(X=20)=(20C20)(0.8)^{20} (1-0.8)^{20-20}=0.012$

$P(X\geq 15)=0.804208$

e) $E(X) = np = 20*0.8 = 16$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

Part a

Let the random variable X= "number of these tracks where SBIRS detects the object." in order to use the binomial probability distribution we need to satisfy some conditions:

1) Independence between the trials (satisfied)

2) A value of n fixed , for this case is 20 (satisfied)

3) Probability of success p =0.2 fixed (Satisfied)

So then we have all the conditions and we can assume that:

$X \sim Bin(n =20, p=0.8)$

Part b

$X \sim Bin(n =20, p=0.8)$

Part c

For this case we just need to replace into the mass function and we got:

$P(X=15)=(20C15)(0.8)^{15} (1-0.8)^{20-15}=0.17456$

Part d

For this case we want this probability: $P(X\geq 15)$

And we can solve this using the complement rule:

$P(X \geq 15) = P(X=15)+ .....+P(X=20)$

$P(X=15)=(20C15)(0.8)^{15} (1-0.8)^{20-15}=0.17456$

$P(X=16)=(20C16)(0.8)^{16} (1-0.8)^{20-16}=0.218$

$P(X=17)=(20C17)(0.8)^{17} (1-0.8)^{20-17}=0.205$

$P(X=18)=(20C18)(0.8)^{18} (1-0.8)^{20-18}=0.137$

$P(X=19)=(20C19)(0.8)^{19} (1-0.8)^{20-19}=0.058$

$P(X=20)=(20C20)(0.8)^{20} (1-0.8)^{20-20}=0.012$

$P(X\geq 15)=0.804208$

Part e

The expected value is given by:

$E(X) = np = 20*0.8 = 16$

5 0

3 years ago

What is x-(3)/(5)=(5x)/(6)? with steps answer fast

Anettt [7]

x- 3/5 = 5x/ 6

6x - 18/5 = 5x

6x -5x = 18/5

x = 18/5

let's check : 18/5 - 3/5 = 15/5 = 3

5 * 18/5 / 6 = 18/6 = 3

result is correct.

8 0

3 years ago

Help me answer the question please ​

Help me answer the question please