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3 years ago

How do I find the value of Q in the following systems so my solution to the system is

1 answer:

4 0

Hello,

if the solution is infinite : the line x-3y=4 ,
so there is one line and not 2

==>x-3y=4 multiplied by 2
2x-6y=8=Q

Q=8

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A rectangular dartboard has an area of 648 square centimeters. The triangular part of the dartboard has an area of 162 square ce

never [62]

Answer:

The probability that the dart lands inside the triangle is 0.25

Step-by-step explanation:

* Lets explain how to find the probability of an event

- The probability of an Event = Number of favorable outcomes ÷ Total

number of possible outcomes

- P(A) = n(E) ÷ n(S) , where

# P(A) means finding the probability of an event A

# n(E) means the number of favorable outcomes of an event

# n(S) means set of all possible outcomes of an event

- P(A) < 1

* Lets solve the problem

- A rectangular dartboard has an area of 648 cm²

- The triangular part of the dartboard has an area of 162 cm²

- A dart is randomly thrown at the dartboard

- The dart lands in the rectangle

∴ The area of the rectangle is the set of all possible outcomes n(S)

- The probability P(A) that the dart lands inside the triangle

∴ The area of the triangle is set of favorable outcomes of an

event n(E)

∵ P(A) = n(E) ÷ n(S)

∴ P(T) = area of the triangle ÷ area of the rectangle

∵ Area of the rectangle is 648 cm²

∴ n(S) = 648

∵ The area of the triangle is 162 cm²

∴ n(E) = 162

∴ P(T) = 162 ÷ 648 = 1/4 = 0.25

* The probability that the dart lands inside the triangle is 0.25

5 0

3 years ago

Your state is considering raising the legal age for consumption of alcoholic beverages to 21 years old. How large a sample size

julsineya [31]

Answer:

$n=\frac{0.5(1-0.5)}{(\frac{0.01}{2.58})^2}=16641$

And rounded up we have that n=16641

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

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ . And the critical value would be given by:

$z_{\alpha/2}=-2.58, t_{1-\alpha/2}=2.58$

The margin of error for the proportion interval is given by this formula:

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

And on this case we have that $ME =\pm 0.01$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

For this case we can use as estimator for the proportion $\hat p =0.5$ , since we don't have any other previous info. And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.01}{2.58})^2}=16641$

And rounded up we have that n=16641

8 0

3 years ago

Help me plz quick only 5 mins

solniwko [45]

Answer:

line B'C' = 1

m<C'D'A' = 90 degrees (it is still a rectangle)

Step-by-step explanation:

Dilation of coordinates:

Original: d:(3,2), a:(3,4), b:(7,4), c:(7,2)

Divide all numbers by 2.

Altered: d:(1.5,1), a:(1.5,2), b:(3.5,2), c:(3.5,1)

8 0

3 years ago

When given Three points on a coordinate plane, you may be able to find a specific Quadratic equation that intersects all given p

ohaa [14]

Answer:

TRUE

Step-by-step explanation:

A quadratic equation can be found that will go through any three distinct points that ...

satisfy the requirements for a function
are not on the same line

_____

The key word here is "may." You will not be able to find a quadratic intersecting the three points if they do not meet both requirements above.

8 0

3 years ago

What is an equiangular triangle?

Sergio [31]

<span>An equiangular triangle is a triangle where all three interior angles are equal in measure.</span>

6 0

2 years ago

Read 2 more answers