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3 years ago

Write the equation of the line that is perpendicular to y = -3x +2 and passes through (3.1).

Mathematics

1 answer:

Scrat [10]3 years ago

4 0

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$y = \frac{1}{3} x \\$

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Let me know if you need explanation

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What the y-intercept in the equation y= 4x - 3?

kompoz [17]

Answer:

-3

Step-by-step explanation:

Note the parts of the equation:

y = mx + b

y = (x , y)

m = slope

x = (x , y)

b = y-intercept

In this case: y = 4x - 3

x = x

y = y

m = slope = 4

b = y-intercept = -3

3 0

4 years ago

Read 2 more answers

Write an expression that, when simplified is equivalent to 15x +7

cupoosta [38]

Answer:

2(7.5x+3.5)

Step-by-step explanation:

I can't remember what these equations are actually called, however in order to solve this you simply multiply 7.5 by 2, and then 3.5 by 2.

4 0

4 years ago

Calculate an estimate of a square root of 119 + 120i

uysha [10]

Answer:

Step-by-step explanation:

Given

z=119+120 i

Let $\sqrt{119+120 i}=p+iq$

Squaring both sides

$119+120 i=p^2-q^2+2ipq$

Comparing real and imaginary part

Re(LHS)=Re(RHS)

$119=p^2-q^2$ -----------1

comparing Im(LHS)=Im(RHS)

120=2pq

$q=\frac{60}{p}$

Substitute q in 1

$119=p^2-(\frac{60}{p})^2$

$p^4-119p^2-(68)^2=0$

Let $x=p^2$

$x^2-119x-4624=0$

$x=frac{119\pm \sqrt{119^2+4\times 4624}}{2}$

$x=\frac{119\pm 180.71}{2}$

we take only Positive value because $p^2=x$

x=149.85

$p^2=149.85$

thus $p=\pm 12.24$

$q=\mp 4.90$

thus $\sqrt{119+120 i}=\pm (12.24+i 4.90)$

6 0

4 years ago

what is the slope of the line that passes through the point (-1,-10) and (-1,-2). answer needs to be in simplest form

Mariulka [41]

Answer: m = undefined

Step-by-step explanation:

-2-(-10) = 8

-1-(-1) = 0

m = 8/0

Which is an undefined slope

7 0

3 years ago

Read 2 more answers

Of the total population of American households, including older Americans and perhaps some not so old, 17.3% receive retirement

Alex Ar [27]

Answer:

47.54% probability that more than 20 households but fewer than 35 households receive a retirement income

Step-by-step explanation:

We use the binomial aproxiation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$p = 0.173, n = 120$ . So

$\mu = E(X) = np = 120*0.173 = 20.76$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{120*0.173*0.827} = 4.14$

In a random sample of 120 households, what is the probability that more than 20 households but fewer than 35 households receive a retirement income?

We are working with discrete values, so this is the pvalue of Z when X = 35-1 = 34 subtracted by the pvalue of Z when X = 20 + 1 = 21.

X = 34

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{34 - 20.76}{4.14}$