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3 years ago

X-y=6 2x-3z=16 2y+z=4 Solve the systems of equations.

Mathematics

1 answer:

Neko [114]3 years ago

5 0

Answer:

Given System of equation:

x-y =6 .....,[1]

2x-3z = 16 ......[2]

2y+z = 4 .......[3]

Rewrite the equation [1] as

y = x - 6 .......[4]

Substitute the value of [4] in [3], we get

$2(x-6)+z = 4$

Using distributive property on LHS ( i.e, $a \cdot (b+c) =a \cdot b+ b \cdot c$ )

then, we have

2x - 12 +z =4

Add 12 to both sides of an equation:

2x-12+z+12=4+12

Simplify:

2x +z = 16 .......[5]

On substituting equation [2] in [5] we get;

2x+z=2x -3z

z = -3z

Add 3z both sides of an equation:

z+3z = -3z+3z

4z = 0

Simplify:

z = 0

Substitute the value of z = 0 in [2] to solve for x;

$2x-3(0) = 16$

2x = 16

Divide by 2 both sides of an equation:

$\frac{2x}{2} =\frac{16}{2}$

Simplify:

x= 8

Substitute the value of x =8 in equation [4] to solve for y;

y = 8-6 = 2

y = 2

Therefore, the solution for the given system of equation is; x = 8 , y = 2 and z =0

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A carpenter charges $325 for 13 hours of work. She charges the same amount of money for each hour of work.

Citrus2011 [14]

Answer: She charges 25 dollars per hour.

Step-by-step explanation:

325 dollars for 13 hours means we have to divide 325 by 13 to get the amount that she charges for every hour. $325 / 13 hours = $25 per hour.

3 0

2 years ago

A company is in the business of finding addresses of long-lost friends. The company claims to have a 70% success rate. Suppose t

Galina-37 [17]

Answer:

a) Figure attached

b) $E(X) =\mu= np = 9*0.7=6.3$

$Sd(X) =\sigma= \sqrt{np(1-p)}= \sqrt{9*0.7*(1-0.7)}=1.375$

c) For the case n= 6

$P(X \leq 2) = 0.9891$

For the case n= 5

$P(X \leq 2) = 0.9692$

So then we need at least n=5 or n=6 to satisfy the condition required.

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".

Solution to the problem

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=9, p=0.7)$

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

For this case we can use the following R code:

> x <- seq(0,9,by = 1)

> y <- dbinom(x,9,0.7)

> plot(x,y,main="Histogram",type = "h")

And we can see on the figure attached the solution.

We see that the higher probabilities are from 4 to 9

Part b

The expected value is given by:

$E(X) =\mu= np = 9*0.7=6.3$

The variance is given by:

$Var (X) =\sigma^2= np(1-p) = 9*0.7*(1-0.7)= 1.89$

And the standard deviation is:

$Sd(X) =\sigma= \sqrt{np(1-p)}= \sqrt{9*0.7*(1-0.7)}=1.375$

Part c

First we can find the probability that at least two addresses will be found in the list of 9 that we have like this:

$P(X \geq 2)$

We can use the complement rule and we have:

$P(X \geq 2) = 1-P(X$

We find the indicidual probabilities:

$P(X=0)=(9C0)(0.7)^0 (1-0.7)^{9-0}=0.00001968$

$P(X=1)=(9C1)(0.7)^1 (1-0.7)^{9-1}=0.000413$

$P(X \geq 2) = 1-[0.00001968+0.000413]=0.9996$

If we use the case of n=8 and we find $P(X\leq 2)$ , we got:

$P(X \leq 2) = 0.9987$

For the case n= 7

$P(X \leq 2) = 0.9962$

For the case n= 6

$P(X \leq 2) = 0.9891$

For the case n= 5

$P(X \leq 2) = 0.9692$

So then we need at least n=5 or n=6 to satisfy the condition required.

5 0

2 years ago

Darius is putting tiles on the roof of his house. After working for 3 1/3 hours, he has completed 4/5 of the roof. Can Darius pu

tangare [24]

Answer:

No.

Step-by-step explanation:

It is given that Darius is putting tiles on the roof of his house.

Darius had completed = $\frac{4}{5}$ th of the work

He takes time = $3 \frac{1}{3}$ hours to complete $\frac{4}{5}$ th of the work

The remaining work = $1 -\frac{4}{5}$

$=\frac{5-4}{5}$

$=\frac{1}{5}$

∴ Darius completes $\frac{4}{5}$ th of the work in = $\frac{10}{3}$ hours

So, $\frac{1}{5}$ th of the work in = $\frac{10}{3} \times \frac{5}{4} \times \frac{1}{5}$ hours

$=\frac{10}{12}$ hours

Therefore total time taken to complete the work $=\frac{10}{3}+\frac{10}{12}$ hours

$=\frac{40+10}{12}$ hours

$=\frac{50}{12}$ hours

$=4\frac{2}{12}$ hours

$=4\frac{1}{6}$ hours

Thus, Darius continues to work at the same rate will not be able to complete the work in 4 hours.

8 0

3 years ago

Can someone help me please

Blizzard [7]

Answer:

Area=76.56 square feet

Step-by-step explanation:

area of a rectangle =base*height = 5ft*8ft= 40 square feet

area of a triangle=(base*height)/2 =(4ft*4ft)/2= 8 square feet

area of a square=base*height =4ft*4ft= 16 square feet

area of a circle = $\pi$ * r^{2}[/tex]=3.14* $2^{2}$ = 12.56 square feet

r = radius

Total area=(40+8+16+12.56)square feet

Total area=76.56square feet

3 0

2 years ago

At midnight the temperature was 30°F by 6 o'clock in the morning it was dropped 15° & by noon increased by 22° what was the

Mila [183]

Answer: 37°F

let me know if this is wrong

Step-by-step explanation:

30-15=15

15+22=37

7 0

2 years ago