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3 years ago

Write an equation of the line through the point (5, 3) that is perpendicular to the line –3x+7y=5.

Mathematics

2 answers:

Fed [463]3 years ago

6 0

Answer:

7x + 3y = 44

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c (m is the slope and c the y- intercept )

Rearrange - 3x + 7y = 5 into this form by adding 3x to both sides

7y = 3x + 5 ( divide all terms by 7 )

y = $\frac{3}{7}$ x + $\frac{5}{7}$ ← in slope- intercept form

with slope m = $\frac{3}{7}$

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{\frac{3}{7} }$ = - $\frac{7}{3}$ , thus

y = - $\frac{7}{3}$ x + c ← is the partial equation

To find c substitute (5, 3) into the partial equation

3 = - $\frac{35}{3}$ + c ⇒ c = 3 + $\frac{35}{3}$ = $\frac{44}{3}$

y = - $\frac{7}{3}$ x + $\frac{44}{3}$ ← in slope- intercept form

Multiply through by 3

3y = - 7x + 44 ( add 7x to both sides )

7x + 3y = 44 ← in standard form

vredina [299]3 years ago

4 0

Answer:

equation: y = -7/3x + 14 2/3

Step-by-step explanation:

–3x+7y=5

y = 3/7 x + 5

slope of perpendicular line: - 7/3

y = mx + b for (5 , 3)

b = y - mx = 3 - ((-7/3) * 5) = 3 + 35/3 = 44/3 = 14 2/3

equation: y = -7/3x + 14 2/3

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What’s 45 divided by 2

Anna35 [415]

Answer:

22.5

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

. Suppose that we want to estimate the true proportion of defectives in a very large shipment of adobe bricks, and that we want

wlad13 [49]

Answer:

A sample of 601 bricks will be needed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

How large a sample will we need?

A sample of n bricks will be needed.

n is found when M = 0.04.

We have no estimate for the proportion of defective bricks, so we work with the worst case scenario, which is $M = 0.04$

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.04 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.04\sqrt{n} = 1.96*0.5$

$\sqrt{n} = \frac{1.96*0.5}{0.04}$

$(\sqrt{n})^{2} = (\frac{1.96*0.5}{0.04})^{2}$

$n = 600.25$

Rounding up

A sample of 601 bricks will be needed.

8 0

3 years ago

24% of a certain country's voters think that it is too easy to vote in their country. You randomly select 12 likely voters. Fi

shepuryov [24]

Answer:

a) $P(X=3) = 12C3 (0.24)^3 (1-0.24)^{12-3}= 0.2573$

b) $P(X=0) = 12C0 (0.24)^0 (1-0.24)^{12-0}= 0.037$

$P(X=1) = 12C1 (0.24)^1 (1-0.24)^{12-1}= 0.1407$

$P(X=2) = 12C2 (0.24)^2 (1-0.24)^{12-2}= 0.2573$

$P(X=3) = 12C3 (0.24)^3 (1-0.24)^{12-3}= 0.1828$

And after replace we got:

$P( X \geq 4) = 1-0.6795 = 0.3205$

c) $P(X=0) = 12C0 (0.24)^0 (1-0.24)^{12-0}= 0.037$

$P(X=1) = 12C1 (0.24)^1 (1-0.24)^{12-1}= 0.1407$

$P(X=2) = 12C2 (0.24)^2 (1-0.24)^{12-2}= 0.2573$

$P(X=3) = 12C3 (0.24)^3 (1-0.24)^{12-3}= 0.1828$

$P(X=4) = 12C4 (0.24)^4 (1-0.24)^{12-4}= 0.1828$

$P(X=5) = 12C5 (0.24)^5 (1-0.24)^{12-5}= 0.092$

$P(X=6) = 12C6 (0.24)^6 (1-0.24)^{12-6}= 0.034$

$P(X=7) = 12C7 (0.24)^6 (1-0.24)^{12-7}= 0.00921$

And we got:

$P(X$

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".

Part a

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=12, p=0.24)$

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:

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

For this case we can use the mass function and we got:

$P(X=3) = 12C3 (0.24)^3 (1-0.24)^{12-3}= 0.2573$

Part b

For this case we want this probability:

$P(X \geq 4)$

And we can use the complement rule and we got:

$P(X \geq 4) = 1-P(X$

And we can find the individual probabilites and we got:

$P(X=0) = 12C0 (0.24)^0 (1-0.24)^{12-0}= 0.037$

$P(X=1) = 12C1 (0.24)^1 (1-0.24)^{12-1}= 0.1407$

$P(X=2) = 12C2 (0.24)^2 (1-0.24)^{12-2}= 0.2573$

$P(X=3) = 12C3 (0.24)^3 (1-0.24)^{12-3}= 0.1828$

And after replace we got:

$P( X \geq 4) = 1-0.6795 = 0.3205$

Part c

For this case we want this probability:

$P(X$

We can find the individual probabilites and we got:

$P(X=0) = 12C0 (0.24)^0 (1-0.24)^{12-0}= 0.037$

$P(X=1) = 12C1 (0.24)^1 (1-0.24)^{12-1}= 0.1407$

$P(X=2) = 12C2 (0.24)^2 (1-0.24)^{12-2}= 0.2573$

$P(X=3) = 12C3 (0.24)^3 (1-0.24)^{12-3}= 0.1828$

$P(X=4) = 12C4 (0.24)^4 (1-0.24)^{12-4}= 0.1828$

$P(X=5) = 12C5 (0.24)^5 (1-0.24)^{12-5}= 0.092$

$P(X=6) = 12C6 (0.24)^6 (1-0.24)^{12-6}= 0.034$

$P(X=7) = 12C7 (0.24)^6 (1-0.24)^{12-7}= 0.00921$

And we got:

$P(X$

3 0

3 years ago

Use words to explain how to solve this equation: (x-10)(x-4)=0

salantis [7]

Answer: x = 10 <em>OR</em> x = 4.

Step-by-step explanation: If x = 10 or 4 then the last step of the equation will always be multiplying by 0 which equates to 0 as well.

if x = 10

(10-10)(10-4) -> (0)(6) -> 0 x 6 = 0

if x = 4

(4-10)(4-4) -> (-6)(0) -> -6 x 0 = 0

8 0

3 years ago

Read 2 more answers

You invest AED 5000 in a saving account that earns 4% interest each year. If you do not use the account for a year, how much mon

BigorU [14]

9514 1404 393

Answer:

AED 5200

Step-by-step explanation:

The interest in the first year will be ...

I = Prt . . . . principal P invested at rate r for t years

I = 5000×0.04×1 = 200

The account will have AED 5200 in it after a year.

6 0

2 years ago