What is y=4/5x+7 in standard form?

Expanding logarithmic Expression In Exercise,Use the properties of logarithms to rewrite the expression as a sum,difference,or m

wel

Answer:

$\frac{1}{2}ln(2x)-\frac{1}{2}ln(x^2-1)$

Step-by-step explanation:

In 2x/(x^2 - 1)1/2

$ln(\frac{2x}{x^2-1} )^\frac{1}{2}$

Apply the property of natural log

ln x^m = m ln(x) move the exponent before ln

$ln(\frac{2x}{x^2-1} )^\frac{1}{2}$

$\frac{1}{2}ln(\frac{2x}{x^2-1})$

ln(m/n)= ln m - ln n

$\frac{1}{2}(ln(2x)-ln(x^2-1))$

multiply 1/2 inside the terms

$\frac{1}{2}ln(2x)-\frac{1}{2}ln(x^2-1)$

6 0

2 years ago

Cristina financed a $799 laptop with a 7.2% interest rate on a 2-year loan. If she can afford to make a $75 payment, how quickly

KatRina [158]

Your question is missing some elements but to answer the question I have to make an assumption.

Assuming that she make a monthly payment of $75.

The value of an loan at the end of the two year is given by

$FV=PV(1+r)^n$

where PV = $799, r = 7.2% = 0.072 and n = 2 years.

Thus,

$FV=799(1+0.072)^2=799(1.072)^2=799(1.149184)=\$918.20$

If she makes a monthly payment of $75, the number of months it will take her to pay off for her laptop is given by

$\frac{\$918.20}{\$75} =12.24\, months$

Therefore, it will take her 13 months to pay off for the laptop.

7 0

2 years ago

Find the coordinates of the midpoint of the segment connecting points (-3,-6) and ( 2,5)

Pavlova-9 [17]

(x2 subtracted by x1 divided by 2, y2 subtracted by y1 divided by 2) is the midpoint formula.
(2-3/2, 5-6/2)= (-1/2, -1/2) which is the answer/

3 0

3 years ago

Convert the decimal into a reduce fraction.

Ivanshal [37]

Answer:

hey i dont really know, but look up calculator soup, it has a ton of different calculators and may be able to help u

Step-by-step explanation:

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7 0

2 years ago

A practice law exam has 100 questions, each with 5 possible choices. A student took the exam and received 13 out of 100.If the s

Cloud [144]

Answer:

$z=\frac{13-20}{4}=-1.75$

Assuming:

H0: $\mu \geq 20$

H1: $\mu$

$p_v = P(Z$

Step-by-step explanation:

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 (number of correct answers in the test), on this case we now that:

$X \sim Binom(n=100, p=0.2)$

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:

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

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

$np=100*0.2=20 \geq 10$

$n(1-p)=20*(1-0.2)=16 \geq 10$

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:

$E(X)=np=100*0.2=20$

$\sigma=\sqrt{np(1-p)}=\sqrt{100*0.2(1-0.2)}=4$

So we can approximate the random variable X like this:

$X\sim N(\mu =20, \sigma=4)$

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean". The letter $\phi(b)$ is used to denote the cumulative area for a b quantile on the normal standard distribution, or in other words: $\phi(b)=P(z$