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3 years ago

What is the solution to the open sentence? 3y – 4 = y + 10 a. 2 b. 3 c. 6 d. 7

Mathematics

2 answers:

Elan Coil [88]3 years ago

7 0

Answer: the correct option is

(d) 7.

Step-by-step explanation: We are given to solve the following open sentence :

$3y-4=y+10~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

To solve the given equation, we need to find the value of the unknown variable y.

The solution of equation (i) is as follows :

$3y-4=y+10\\\\\Rightarrow 3y-y=10+4\\\\\Rightarrow 2y=14\\\\\Rightarrow y=\dfrac{14}{2}\\\\\Rightarrow y=7.$

Thus, the required solution is y = 7.

Option (d) is CORRECT.

jenyasd209 [6]3 years ago

6 0

1. subtract y from both sides 3y-4=y+10
. -3 -3
2.now you have -4=-2y+10 subtract 10 to both sides
-10 -10
3. you have -14=-2y divide
4. y=7

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3 years ago

USA Today reports that about 25% of all prison parolees become repeat offenders. Alice is a social worker whose job is to counse

pychu [463]

Answer:

a) $P(X=0)=(4C0)(0.75)^0 (1-0.75)^{4-0}=0.0039$

$P(X=1)=(4C1)(0.75)^1 (1-0.75)^{4-1}=0.0469$

$P(X=2)=(4C2)(0.75)^2 (1-0.75)^{4-2}=0.211$

$P(X=3)=(4C3)(0.75)^2 (1-0.75)^{4-3}=0.422$

$P(X=4)=(4C4)(0.75)^2 (1-0.75)^{4-4}=0.316$

b) $E(X) = np = 4*0.75=3$

c) $Sd(X) =\sqrt{np(1-p)}=\sqrt{4*0.75*(1-0.75)}=0.866$

d) $P(X \geq 3) \geq 0.98$

And the dsitribution that satisfy this is $X\sim Binom(n=9,p=0.75$

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".

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

$X \sim Binom(n=4, p=1-0.25=0.75)$

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

$P(X=0)=(4C0)(0.75)^0 (1-0.75)^{4-0}=0.0039$

$P(X=1)=(4C1)(0.75)^1 (1-0.75)^{4-1}=0.0469$

$P(X=2)=(4C2)(0.75)^2 (1-0.75)^{4-2}=0.211$

$P(X=3)=(4C3)(0.75)^2 (1-0.75)^{4-3}=0.422$

$P(X=4)=(4C4)(0.75)^2 (1-0.75)^{4-4}=0.316$

Part b

The expected value is givn by:

$E(X) = np = 4*0.75=3$

Part c

For the standard deviation we have this:

$Sd(X) =\sqrt{np(1-p)}=\sqrt{4*0.75*(1-0.75)}=0.866$

Part d

For this case the sample size needs to be higher or equal to 9. Since we need a value such that:

$P(X \geq 3) \geq 0.98$

And the dsitribution that satisfy this is $X\sim Binom(n=9,p=0.75$

We can verify this using the following code:

"=1-BINOM.DIST(3,9,0.75,TRUE)" and we got 0.99 and the condition is satisfied.

4 0

3 years ago

Subtract 1.05 from a certain number. Multiply the difference by 0.8, add 2.84 to the product then divide the sum by 0.01 and get

attashe74 [19]

Just do the whole process backwards
700*0.01=7
7-2.84=4.16
4.16/0.8=5.2
5.2+1.05=6.25

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3 years ago

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Paladinen [302]

(5+1+1)*2 + 5*5*5*(1+5)*4 = 3014
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All humans legs = 7*2 = 14
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3 years ago

Hoshi walks 10 meters in 3 seconds. She walks the same at this rate for 50 seconds. How far does she walk?

svlad2 [7]

10m ----> 3 sec

x meters ----> 50 sec

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2 years ago

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