Please help! Topic: square root and cube root equations and inequalities 5.3

frosja888 [35]

We have been given an equation $gv=-3x +5$ . We are asked to solve our given equation for x.

First of all, we will separate expression with x on one side of equation. We can do it by subtracting 5 from both sides of equation.

$gv-5=-3x +5-5$

$gv-5=-3x$

Now we will switch the sides as:

$-3x=gv-5$

Now we will divide both sides by $-3$ as:

$\frac{-3x}{-3}=\frac{gv-5}{-3}$

$x=-\frac{gv-5}{3}$

Therefore, the value of x would be $-\frac{gv-5}{3}$ .

4 0

3 years ago

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A tennis player makes a successful first serve 51% of the time. If she serves 9 times, what is the probability that she gets exa

aleksley [76]

Answer:

$P(X=3)$

And we can use the probability mas function and we got:

$P(X=3)=(9C3)(0.51)^3 (1-0.51)^{9-3}=0.1542$

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:

$X \sim Binom(n=9, p=0.51)$

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:

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

And we want this probability:

$P(X=3)$

And we can use the probability mas function and we got:

$P(X=3)=(9C3)(0.51)^3 (1-0.51)^{9-3}=0.1542$

4 0

3 years ago

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Where does the normal line to the paraboloid z = x2 + y2 at the point (1, 1, 2) intersect the paraboloid a second time?

Digiron [165]

Answer:

the intersection point is ( -5/4, -5/4, -9/8)

Step-by-step explanation:

F(x,y,z) = x² +y² -z= 0

Then find differential of each terms then we have

∀f(x)=2x

∀f(y)=2y

∀f(z)=-1

The partial differential which is the director vector is at F(x,y,z)= (1,1,2)

Vf(1,1,2) = (2,2,-1)

But the given point is ( 1.1,2)

Then the parametric equation of normal line will be

x= 1+2t

y= 1+2t

z= 2 -t

The parametric equation can be formed as

(1+2t)² + (1+2t)² - (2-t)= 0

If we expand the expression above we have,

2(1+4t+4t²) - 2+t= 0

0= 8t² + 9t

t= 0 or t= -9/8

Substitute the value of t into the parametric equation above

At t=0

x= 1+2t; x= 1+2(0)=1

y= 1+2t; y= 1+2(0)=1

z=2 -t ; z= 2-(0)= 2

At =0 , we have (1,1,2)

At t= -9/8

x= 1+2t; x= 1+2(-9/8)=-5/4

y= 1+2t; y= 1+2(-9/8)=-5/4

z=2 -t ; z= 2-(-9/8)= -9/8

Therefore, the intersection point is ( -5/4, -5/4, -9/8)

4 0

3 years ago

An agar plate for counting colonies and maximizing statistical validity should ideally contain

Oxana [17]

It seems that you have missed the necessary options for us to answer this question, so I had to look for it. Anyway, here is the answer. <span>An agar plate for counting colonies and maximizing statistical validity should ideally contain 30 to 300 colonies. Hope this answers your question.</span>

4 0

3 years ago

HELP ASAP PLEASE WILL GIVE 20 POINTS

lys-0071 [83]

I believe it’s b. Hope this helps mate

5 0

3 years ago