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2 years ago

Through (2, -1), perp. to y = -2x-3

Mathematics

1 answer:

kramer2 years ago

6 0

9514 1404 393

Answer:

y = 1/2x -2

Step-by-step explanation:

The given equation is in slope-intercept form, so you recognize its slope is -2. The perpendicular line will have a slope that is the opposite reciprocal of that, so is -1/-2 = 1/2.

The y-intercept can be found from ...

b = y -mx . . . . . for line of slope m through point (x, y)

b = -1 -(1/2)(2) = -1 -1 = -2

Then the slope-intercept equation of the perpendicular line is ...

y = 1/2x -2

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Consider the system:

PolarNik [594]

Answer:

An exponent value in a would make the system inconsistent because it will either gain or lose height over time.

Any real number without an exponent value will make the system consitent.

Any infintite/repeating number will make the system both consistent and inconsistent. it is consisent because it will stay at a constant rate but also inconsistent because it is repeating and will never end.

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3 years ago

Read 2 more answers

Stacy rolls a pair of six-sided fair dice.

Nutka1998 [239]

Answer:

The probability that the sum of the numbers rolled is either a multiple of 3 or an even number is 24/36 = 2/3

The two events are mutually exclusive

Step-by-step explanation:

we first need to create a table of the sample space from the experiment, the sum of the numbers rolled. Find the attached for a depiction of the possible outcomes.

The probability that the sum of the numbers rolled is either a multiple of 3 or an even number will be given by counting the numbers that are either even or multiples of 3 and then dividing by the number of possible outcomes, 36.

In our case this will be;

24/36 = 2/3

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3 years ago

write a story problem that can be solved by finding the sum of 506,211 and 424,809.then solve the problem

Rudik [331]

Jordan had 506,211 pairs of nike shoes then she bought 424,809 more. Jordan wants to find out how many pairs of nike shoes he has what is the answer Jordan is looking for? Answer: 931,020 pairs of nike shoes

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3 years ago

Read 2 more answers

There are 2,000 eligible voters in a precinct. A total of 500 voters are randomly selected and asked whether they plan to vote f

Ann [662]

Answer:

$0.7 - 2.58 \sqrt{\frac{0.7(1-0.7)}{500}}=0.647$

$0.7 + 2.58 \sqrt{\frac{0.7(1-0.7)}{500}}=0.753$

And the 99% confidence interval would be given (0.647;0.753).

So the correct answer would be:

a. 0.647 and 0.753

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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 population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

The estimated population proportion for this case is:

$\hat p = \frac{350}{500}=0.7$

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 99% confidence interval the value of $\alpha=1-0.99=0.01$ and $\alpha/2=0.005$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=2.58$

And replacing into the confidence interval formula we got:

$0.7 - 2.58 \sqrt{\frac{0.7(1-0.7)}{500}}=0.647$

$0.7 + 2.58 \sqrt{\frac{0.7(1-0.7)}{500}}=0.753$

And the 99% confidence interval would be given (0.647;0.753).

So the correct answer would be:

a. 0.647 and 0.753

7 0

3 years ago

You are at a European beach with 60 other visitors. 36 of them speak English. If you randomly meet two people on the beach, what

Kaylis [27]

Answer:

Assuming I'm one of the 36 English speakers and the other 24 speak Spanish for illustration purposes. The problem can be modeled as 59 marbles with 35 E and 24 S marbles as N = 59 possible outcomes = n(E) + n(S) = 35 + 24.

So I reach into the pile of marbles (on the beach) and the probability that it's p(E) = n(E)/N = 35/59 = 0.593220339 when I meet the one person. ANS

I assume I remember that first person; so I remove him from the marbles (by avoiding him on the beach) and now my probability is p(E and E) = n(E)/N * n(E)-1/(N - 1) = 35/59*34/58 = 0.347749854 ANS

Following the same logic p(E and E and E) = 35/59*34/58*33/57 = 0.201328863 ANS

This last one is different from the first three. This one is p(E >= 1|4 attempts). We can trace out a probability tree to identify those branches that contain at least one E event. So:

EEEE p() = 35/59 * 34/58 * 33/57 * 32/56 =

EEES p() = 35/59 * 34/58 * 33/57 * 24/56 =

EESE p() = 35/59 * 34/58 * 24/57 * 33/56 =

ESEE p() = 35/59 * 24/58 * 34/57 * 33/56 =

SEEE p() = 24/59 * 35/58 * 34/57 * 33/56 =

EESS p() = 35/59 * 34/58 * 24/57 * 23/56 =

ESES p() = 35/59 * 24/58 * 34/57 * 23/56 =

SEES

SESE

SSEE

ESSS And so on, but...a big BUT...why do all this when

SESS

SSES

SSSE

SSSS

p(E>=1|4) = 1 - p(S and S and S and S) = 1 - 24/59 * 23/58 * 22/57 * 21/56 = 0.976652619 ANS. In other words we find the probability of not meeting an Englishman and take 1 minus that value to find the probability of meeting at least one.

Step-by-step explanation:

3 0

2 years ago