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4 years ago

Consider the following piece-wise function.

Mathematics

2 answers:

yKpoI14uk [10]4 years ago

4 0

The line is rising up to the left and it starts at -2,-2

If you were to continue the line to cross the y a is it would cross at (0,-3)

Find the slope

Slope = (-2 - -1) / (—2 - -4) = -1/2

It would be y= -1/2x-3 when x<-2

coldgirl [10]4 years ago

3 0

Answer:

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How many solutions exist for the given equation? 12x + 1 = 3(4x + 1) - 2

VladimirAG [237]

Answer:

Infinite

Step-by-step explanation:

3(4x + 1) - 2

= 12x + 3 - 2 (Multiply the sum in the bracket by 3)

= 12x + 1 (Simplify)

This means that:

12x + 1 = 3(4x + 1) - 2

is the same as

12x + 1 = 12x + 1

Hence, anything that is used to substitute x is correct.

4 0

3 years ago

Which phrase best describes the graph of a proportional relationship? A.a straight line passing through the origin B.a straight

Phantasy [73]

Based upon the answer choices, the answer is A;

A Straight line passing through the origin.

I hope this answer has assisted you.

3 0

3 years ago

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Which equation represents a proportional relationship? A. y = x + 1 3 y=x+13 B. y = 1 − 1 3 x y=1-13x C. y = 3 x + 1 3 y=3x+13 D

34kurt

Answer:

Option D. $y=\frac{1}{3}x$

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$ or $y=kx$

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Verify each case

case A) we have

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

Remember that

the line must pass through the origin

For x=0, y=0

In this case

For x=0

$y=0+\frac{1}{3}=\frac{1}{3}$

The line not passes through the origin

therefore

The equation A not represent a proportional relationship

case B) we have

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

Remember that

the line must pass through the origin

For x=0, y=0

In this case

For x=0

$y=1-\frac{1}{3}(0)=1$

The line not passes through the origin

therefore

The equation B not represent a proportional relationship

case C) we have

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

Remember that

the line must pass through the origin

For x=0, y=0

In this case

For x=0

$y=3(0)+\frac{1}{3}=\frac{1}{3}$

The line not passes through the origin

therefore

The equation C not represent a proportional relationship

case D) we have

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

Remember that

the line must pass through the origin

For x=0, y=0

In this case

For x=0

$y=\frac{1}{3}(0)=0$

The line passes through the origin

therefore

The equation D represent a proportional relationship

3 0

3 years ago

Lifetime of $1 Bills The average lifetime of circulated $1 bills is 18 months. A researcher believes that the average lifetime i

OLEGan [10]

<h2>Answer with explanation:</h2>

Let $\mu$ be the population mean lifetime of circulated $1 bills.

By considering the given information , we have :-

$H_0:\mu=18\\\\H_a:\mu\neq18$

Since the alternative hypotheses is two tailed so the test is a two tailed test.

We assume that the lifetime of circulated $1 bills is normally distributed.

Given : Sample size : n=50 , which is greater than 30 .

It means the sample is large so we use z-test.

Sample mean : $\overline{x}=18.8$

Standard deviation : $\sigma=2.8$

Test statistic for population mean :-

$z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

$\Rightarrow\ z=\dfrac{18.8-18}{\dfrac{2.8}{\sqrt{50}}}\approx2.02$

The p-value= $2P(z>2.02)=0.0433834$

Since the p-value (0.0433834) is greater than the significance level (0.02) , so we do not reject the null hypothesis.

Hence, we conclude that we do not have enough evidence to support the alternative hypothesis that the average lifetime of a circulated $1 bill differs from 18 months.

6 0

3 years ago

How many twelfths make one whole How many twelfths make one whole

Alenkasestr [34]

Answer:

Step-by-step explanation:

1/12x1/x

1x=12x1

x=12

3 0

3 years ago

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