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3 years ago

Solve 6k + 9 > k – 1.

Mathematics

2 answers:

agasfer [191]3 years ago

6 0

Answer:

k > - 2

Step-by-step explanation:

subtract k from both sides

5k + 9 > - 1 ( subtract 9 from both sides )

5k > - 10 ( divide both sides by 5 )

k > - 2

Agata [3.3K]3 years ago

6 0

$Solution, 6k+9>k-1\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x>-2\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-2,\:\infty \:\right)\end{bmatrix}$

$Steps:$ To Prove Its Not A Pic I Wrote In The Middle

$6k+9>k-1$

$\mathrm{Subtract\:}9\mathrm{\:from\:both\:sides},\\6k+9-9>k-1-9$

$\mathrm{Simplify},\\6k>k-10$

$\mathrm{Subtract\:}k\mathrm{\:from\:both\:sides},\\6k-k>k-10-k$

$\mathrm{Simplify},\\5k>-10$

$\mathrm{Divide\:both\:sides\:by\:}5,\\\frac{5k}{5}>\frac{-10}{5}$

$\mathrm{Simplify},\\k>-2$

$The\:Correct\:Answer\:Is\:k>-2$

$Hope\:This\:Helps!!!$

$-Austint1414$

More Proof In The Pic Below \/

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3 years ago

What is the equation of the line that is perpendicular to y = 3x + 3 and passes through the point (−6, 9)?

Ludmilka [50]

The equation of the line will be equal to 3y = -x + 21.

A line may be defined as the straight figure drawn which has no end points. The equation of a line can be written in slope intercept form as y = mx + c where m is the slope of line, c is y intercept an x and y are independent and dependent variables. If a point (x₁, y₁) is given then equation of line is (y - y₁) = m (x - x₁). The slope of line which is perpendicular to a given line having slope m is equal to -1/m.

Now, equation of line is y = 3x + 3. If we compare with slope intercept form then, m = 3. Now, slope of line perpendicular to this line is equal to -1/3. Now, equation of line passing through point (-6, 9) is given as

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1 year ago

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3 years ago

You have a coin that is not weighted evenly and therefore is not a fair coin. Assume the true probability of getting heads when

Alexandra [31]

Answer:

$X \sim Binom(n=157, p=0.52)$

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:

$P(X$

And we can use the following Excel code to find the exact answer:

"=BINOM.DIST(75,157,0.52,TRUE)"

And we got 0.1633

The other way to solve the problem is using the normal approximation

We need to check the conditions in order to use the normal approximation.

$np=157*0.52=81.64 \geq 10$

$n(1-p)=157*(1-0.52)=75.36 \geq 10$

So we see that we satisfy the conditions and then we can apply the approximation.

If we appply the approximation the new mean and standard deviation are:

$E(X)=np=157*0.52=81.64$

$\sigma=\sqrt{np(1-p)}=\sqrt{157*0.52(1-0.52)}=6.26$

We want this probability:

$P(X$

And using the continuity correction we have this:

$P(X$

We can use the z score given by this formula $Z=\frac{x-\mu}{\sigma}$ .

$P(X< 76.5)=P(\frac{X-\mu}{\sigma}< \frac{76.5-81.64}{6.26})=P(Z < -0.821)=0.206$

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:

$X \sim Binom(n=157, p=0.52)$

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:

$P(X$

And we can use the following Excel code to find the exact answer:

"=BINOM.DIST(75,157,0.52,TRUE)"

And we got 0.1633

The other way to solve the problem is using the normal approximation

We need to check the conditions in order to use the normal approximation.

$np=157*0.52=81.64 \geq 10$

$n(1-p)=157*(1-0.52)=75.36 \geq 10$

So we see that we satisfy the conditions and then we can apply the approximation.

If we appply the approximation the new mean and standard deviation are:

$E(X)=np=157*0.52=81.64$

$\sigma=\sqrt{np(1-p)}=\sqrt{157*0.52(1-0.52)}=6.26$

We want this probability:

$P(X$

And using the continuity correction we have this:

$P(X$

We can use the z score given by this formula $Z=\frac{x-\mu}{\sigma}$ .

$P(X< 76.5)=P(\frac{X-\mu}{\sigma}< \frac{76.5-81.64}{6.26})=P(Z < -0.821)=0.206$

4 0

4 years ago

(5x^2 - 2x - 14) - (x^2 + 4x - 10)

JulijaS [17]

Answer:

2( x - 2)(2x + 1)

Step-by-step explanation:

Dude

4 0

2 years ago

Read 2 more answers