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3 years ago

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Find the equation of the line that contains the point (-4,-1) and is perpendicular to the line 4x+5y=15. Write the line in slop

e-intercept form, if possible. Graph the lines.

1 answer:

AlexFokin [52]3 years ago

7 0

Hope this was helpful

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. Given the first term "a" and the common ratio "r", generate the next three terms in the geometric sequence: a = 12.3; r = 0.5.

IRINA_888 [86]

Answer:

i wanna say 12.8, 13.3, 13.8

im not sure though, i hope this helps

7 0

3 years ago

Tan 3( ) tan 3 lim<br> h<br> xh x<br> ® h

I am Lyosha [343]

Answer:

27

Step-by-step explanation:

know that

h = 3

h × h × h

3 × 3 × 3

= 27

4 0

3 years ago

For the following telescoping series, find a formula for the nth term of the sequence of partial sums

gtnhenbr [62]

I'm guessing the sum is supposed to be

$\displaystyle\sum_{k=1}^\infty\frac{10}{(5k-1)(5k+4)}$

Split the summand into partial fractions:

$\dfrac1{(5k-1)(5k+4)}=\dfrac a{5k-1}+\dfrac b{5k+4}$

$1=a(5k+4)+b(5k-1)$

If $k=-\frac45$ , then

$1=b(-4-1)\implies b=-\frac15$

If $k=\frac15$ , then

$1=a(1+4)\implies a=\frac15$

This means

$\dfrac{10}{(5k-1)(5k+4)}=\dfrac2{5k-1}-\dfrac2{5k+4}$

Consider the $n$ th partial sum of the series:

$S_n=2\left(\dfrac14-\dfrac19\right)+2\left(\dfrac19-\dfrac1{14}\right)+2\left(\dfrac1{14}-\dfrac1{19}\right)+\cdots+2\left(\dfrac1{5n-1}-\dfrac1{5n+4}\right)$

The sum telescopes so that

$S_n=\dfrac2{14}-\dfrac2{5n+4}$

and as $n\to\infty$ , the second term vanishes and leaves us with

$\displaystyle\sum_{k=1}^\infty\frac{10}{(5k-1)(5k+4)}=\lim_{n\to\infty}S_n=\frac17$

7 0

3 years ago

Ella and three friends run in a relay that is 14 miles long.Each person runs equal parts of the race.How many miles does each pe

sergeinik [125]

Each Person Runs: 3.5 miles.
14÷4= 3.5.

3 0

3 years ago

Read 2 more answers

Given a population with a mean of muμequals=100100 and a variance of sigma squaredσ2equals=3636, the central limit theorem appl

lakkis [162]

Answer:

a) $\bar X \sim N(100,\frac{6}{\sqrt{25}}=1.2)$

$\mu_{\bar X}=100$ $\sigma^2_{\bar X}=1$

b) $P(\bar X >101)=1-P(\bar X$

c) $P(\bar X$

Step-by-step explanation:

Previous concepts

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 central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

The complement rule is a theorem that provides a connection between the probability of an event and the probability of the complement of the event. Lat A the event of interest and A' the complement. The rule is defined by: $P(A)+P(A') =1$

Let X the random variable that represent the variable of interest on this case, and for this case we know the distribution for X is given by:

$X \sim N(\mu=100,\sigma=6)$

And let $\bar X$ represent the sample mean, by the central limit theorem, the distribution for the sample mean is given by:

$\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})$

a. What are the mean and variance of the sampling distribution for the sample means?

$\bar X \sim N(100,\frac{6}{\sqrt{25}}=1.2)$

$\mu_{\bar X}=100$ $\sigma^2_{\bar X}=1.2^2=1.44$

b. What is the probability that x overbarxgreater than>101

First we can to find the z score for the value of 101. And in order to do this we need to apply the formula for the z score given by:

$z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

If we apply this formula to our probability we got this:

$z=\frac{101-100}{\frac{6}{\sqrt{25}}}=0.833$

And we want to find this probability:

$P(\bar X >101)=1-P(\bar X$

On this last step we use the complement rule.

c. What is the probability that x bar 98less than

First we can to find the z score for the value of 98.

$z=\frac{98-100}{\frac{6}{\sqrt{25}}}=-1.67$

And we want to find this probability:

$P(\bar X$

5 0

3 years ago