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3 years ago

How are slopes and y-intercepts related to the number of solutions of a system of linear equations

Mathematics

1 answer:

Nina [5.8K]3 years ago

7 0

<h3>Explanation:</h3>

For a system of 2 equations in 2 unknowns, there are 3 cases:

slopes are different — one solution
slopes are the same and y-intercepts are different — no solutions
slopes and y-intercepts are the same — infinitely many solutions

When slopes are different, the two lines intersect at one point, the solution.

When slopes are the same, the lines may be either parallel (different y-intercepts) or the same (same y-intercepts). If the lines are parallel, there are no points of intersection, hence no solutions. If the lines are the same line, they intersect at all points, so there are infinitely many solutions.

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Use logb^2=.4307 and logb^3 - .6826 to evaluate logb18

katrin2010 [14]

Log b 18 = logb 2 * 3 * 3

When multiplying logs, they are added together so:

logb 2 * 3 * 3 = logb 2 + logb 3 + logb 3

Logb 2 is given as 0.4307 and logb 3 is 0.6826

Now we have 0.4307 + 0.6826 + 0.6826 = 1.7959

Logb 18 = 1.7959

7 0

3 years ago

A local marketing company wants to estimate the proportion of consumers in the Oconee County area who would react favorably to a

Burka [1]

Answer:

C. n=423

Step-by-step explanation:

1) Notation and important concepts

Margin of error for a proportion is defined as "percentage points your results will differ from the real population value"

Confidence=90%=0.9

$\alpha=1-0.9=0.1$ represent the significance level defined as "a measure of the strength of the evidence that must be present in your sample before you will reject the null hypothesis and conclude that the effect is statistically significant".

$\hat p=0.5$ represent the sample proportion of consumers in the Oconee County area who would react favorably to a marketing campaig. For this case since we don't have enough info we use the value of 0.5 since is equiprobable the event analyzed.

$z_{\alpha/2}$ represent a quantile of the normal standard distribution that accumulates ${\alpha/2}$ on each tail of the distribution.

2) Formulas and solution for the problem

For this case the margin of error for a proportion is given by this formula

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

For this case the confidence level is 90% or 0.9 so then the significance would be

$\alpha=1-0.9=0.1$ and $\alpha/2=0.05$

With $\alpha/2=0.05$ , we can find the value for $z_{\alpha/2}$ using the normal standard distribution table or excel.

The calculated value is $z_{\alpha/2}=1.644854$

Now from equation (1) we need to solve for n in order to answer the question.

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

Squaring both sides:

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

And solving for n we got:

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

Now we can replpace the values

$n=\frac{0.5(1-0.5)}{(\frac{0.04}{1.644854})^2}=422.739$

And rounded up to the nearest integer we got:

n=423

3 0

3 years ago

Is a − b equal to b − a?

galben [10]

Answer:

a is a 1 and then you subtraction the b is equal 0

3 0

3 years ago

The relation R is shown below as a list of ordered

Dmitrij [34]

Answer:

(1, 4) and (1,3), because they have the same x-value

Step-by-step explanation:

For a relation to be regarded as a function, there should be no two y-values assigned to an x-value. However, two different x-values can have the same y-values.

In the relation given in the equation, the ordered pairs (1,4) and (1,3), prevent the relation from being a function because, two y-values were assigned to the same x-value. x = 1, is having y = 4, and 3 respectively.

Therefore, the relation is not a function anymore if both ordered pairs are included.

The ordered pairs which make the relation not to be a function are: "(1, 4) and (1,3), because they have the same x-value".

7 0

3 years ago

A gym surveyed 100 female members. These members were chosen at random from the gym's membership database. Participants were ask

mote1985 [20]

The question is biased towards a response of preferring to use weight-lifting machines because it uses the words "hard" to describe free weights and "easy" to describe the machines, and may persuade some people to choose the machine.

The sample is not biased because it doesn't choose specific women, it includes all women who visit the gym.

6 0

3 years ago

Read 2 more answers