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3 years ago

1. Solve the equations below.

Mathematics

1 answer:

Sergio039 [100]3 years ago

7 0

Step-by-step explanation:

A) 3x + 8 = 23

3x = 23 - 8

3x = 15

x = 15 / 3 = 5

B) 5x + 1 = 3x + 17

5x - 3x = 17 - 1

2x = 16

x = 16 /2 = 8

C) 4 (x+2) = 32

4x + 8 = 32

4x = 32 - 8

4x = 24

x = 24 / 4 = 6

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An example problem in a Statistics textbook asked to find the probability of dying when making a skydiving jump.

MArishka [77]

Answer:

(a) 0.999664

(b) 15052

Step-by-step explanation:

From the given data of recent years, there were about 3,000,000 skydiving jumps and 21 of them resulted in deaths.

So, the probability of death is $\frac{21}{3000000}==0.000007$ .

Assuming, this probability holds true for each skydiving and does not change in the present time.

So, as every skydiving is an independent event having a fixed probability of dying and there are only two possibilities, the diver will either die or survive, so, all skydiving can be regarded as is Bernoulli's trial.

Denoting the probability of dying in a single jump by $q$ .

$q=7\times 10^{-6}=0.000007$ .

So, the probability of survive, $p=1-q$

$\Rightarrow p=1-7\times 10^{-6}=0.999993.$

(a) The total number of jump he made, n=48

Using Bernoulli's equation, the probability of surviving in exactly 48 jumps (r=48) out of 48 jumps (n=48) is

$=\binom(n,r)p^rq^{n-r}$

$=\binom(48,48)(0.999993)^{48}(0.000007)^{48-48}$

$=(0.999993)^{48}=0.999664$ (approx)

So, the probability of survive in 48 skydiving is 0.999664,

(b) The given probability of surviving =90%=0.9

Let, total $n$ skydiving jumps required to meet the surviving probability of 0.9.

So, By using Bernoulli's equation,

$0.9=\binom {n }{r} p^rq^{n-r}$

Here, r=n.

$\Rightarrow 0.9=\binom{n}{n}p^nq^{n-n}$

$\Rightarrow 0.9=p^n$

$\Rightarrow 0.9=(0.999993)^n$

$\Rightarrow \ln(0.9)=n\ln(0.999993)$ [ taking $\log_e$ both sides]

$\Rightarrow n=\frac {\ln(0.9)}{\ln(0.999993)}$

$\Rightarrow n=15051.45$

The number of diving cant be a fractional value, so bound it to the upper integral value.

Hence, the total number of skydiving required to meet the 90% probability of surviving is 15052.

3 0

3 years ago

The area of triangle ABC is _____.

Marizza181 [45]

I FOUND YOUR COMPLETE QUESTION IN OTHER SOURCES.
SEE ATTACHED IMAGE.
Using Heron's Formula we can find the area of the triangle.
A = root (s (s-a) * (s-b) * (s-c))
s = (a + b + c) / 2
Where,
s: semi-perimeter
a, b, c: sides of the triangle
Substituting values:
s = (15 + 16 + 20) / 2
s = 25.5
s = 26
The area will be:
A = root (26 * (26-15) * (26-16) * (26-20))
A = 130.9961832
A = 130 u ^ 2
Answer:
The area of triangle ABC is:
C.
130 u ^ 2

5 0

4 years ago

What could be concluded if the relative frequency of an event is equal to 1?

liubo4ka [24]

What could be concluded if the relative frequency of an event is equal to 1?

8 0

3 years ago

I need the answer if you know write with explination if you don't know don't answer

yarga [219]

Answer:

ABD ≅ ACD and PQS ≅ PRS

Step-by-step explanation:

For ABD ≅ ACD;

AB = AC = 3.5

BD = CD = 2.5

AD ≅ AD by reflexive

Since all 3 sides are congruent, SSS can be used

For PQS ≅ PRS

PQ≅PR by given

QS≅RS by given

PS≅PS by reflexive property

Since all 3 sides are congruent, SSS can be used and they are congruent

8 0

3 years ago

Which one is the answer for these qution 4x=5(9x+2)<br> A)5/2<br> B)41/10<br> C)-10/41<br> D)10/41

stealth61 [152]

C. -10/41

First use the distributive property to get 4x = 45x + 10
Use subtraction on both sides by 10
Again use subtraction of 4x on both sides
You now have -10 = 41x
Use division to get x alone and you now have -10/41 = x

5 0

4 years ago