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valentinak56 [21]

2 years ago

15

Below, enter x If the graph of the given equation is symmetric with respect to the x-axis, y if it is symmetric with respect to

the y axis, o (lower
case O) if it is symmetric with respect to the origin, and n (for None) if it has none of these three symmetries.
y=xt
y = x2 +1
y=x²+x
y = (1 + x2)3

1 answer:

ololo11 [35]2 years ago

5 0

Answer:

Step-by-step explanation:

You can tell by looking at the form of each equation.

y = tx

This is a straight line that passes through the origin, so it symmetric with respect to the origin.

y = x²+1

This is an up-opening parabola with vertex at (0,1), so it is symmetrical about the y-axis.

y = x²+x = (x+½)² - ¼

This is an up-opening parabola with vertex at (-½,-¼). Not symmetrical to either axis nor to the origin.

Can't tell what "y = (1 + x2)3" means. Which terms are exponents?

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Answer: (a) ( $x_{2},y_{2}$ ) = (3,2)

(b) ( $x_{2},y_{2}$ ) = (19,-7)

Step-by-step explanation: Midpoint of a segment is halfway between 2 endpoints. It is calculated using the formulas:

$x_{m}=\frac{x_{1}+x_{2}}{2}$

$y_{m}=\frac{y_{1}+y_{2}}{2}$

Isolating $x_{2}$ :

$2x_{m}=x_{1}+x_{2}$

$x_{2}=2x_{m}-x_{1}$

And $y_{2}$ :

$2y_{m}=y_{1}+y_{2}$

$y_{2}=2y_{m}-y_{1}$

(a) Replacing values and calculating $x_{2}$ :

$x_{2}=(2*2)-1$

$x_{2}=3$

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$y_{2}=[2*(-1)]-(-4)$

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3 years ago

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Suppose that scores on a knowledge test are normally distributed with a mean of 60 and a standard deviation of 4.3. Scores on an

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Question:

(c) Boris also took a logic test. His z-score on that test was +0.93 . Does this change the answer to which test Boris performed better on? Explain your answer using z-scores.

Answer:

The answers to the questions are;

(a) Based on the z score, Boris perform better on his aptitude test.

(b) Based on the z score, Callie perform better on his knowledge test .

(c) For Boris since +0.93 = $z_{logic}$ > $z_{knowledge}$ > $z_{aptitude}$

Yes as Boris now performed best on the logic test.

Step-by-step explanation:

The z-score of a score is a measurement of the score withe respect to its distance from the mean as a factor of the standard deviation.

To solve the question, we note that we are required to find the z score as follows.

z score is given by $z = \frac{x -\mu}{\sigma}$

Where:

z = Standard score

x = Score

σ = Standard deviation

μ = Mean

(a) To find out which test did Boris performed better usin z score, we have

Boris scored a

57 on the knowledge test and

106 on the aptitude test

Therefore the z sore for the knowledge test is

$z = \frac{x -\mu}{\sigma}$

Here

x = 57

μ = 60

σ = 4.3

Therefore

$z_{knowledge} = \frac{57 -60}{4.3}$ = -3/4.3 = -30/43 = -0.6977

The z sore for Boris on the aptitude test is

Here

x = 106

μ = 110

σ = 7.1

$z_{aptitude} = \frac{106 -110}{7.1}$ = -40/17 = -0.5634

Based on the z score, Boris perform better on the aptitude test as his z score is higher (on the number line), --0.5634, compared to the z score on the knowledge test , -0.6977

(b) For Callie we have

Callie scored a

63 on the knowledge test and

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Therefore the z sore for the knowledge test is

$z = \frac{x -\mu}{\sigma}$

Here

x = 63

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σ = 4.3

Therefore

$z_{knowledge} = \frac{63 -60}{4.3}$ = 3/4.3 = 30/43 = 0.6977

The z sore for Callie on the aptitude test is

Here

x = 114

μ = 110

σ = 7.1

$z_{aptitude} = \frac{114 -110}{7.1}$ = 40/17 = 0.5634

Based on the z score, Callie perform better on the knowledge test as his z score is higher (on the number line), 0.6977, compared to the z score on the aptitude test , 0.5634.

(c) If $z_{logic}$ = +0.93 then sinc for Boris $z_{knowledge}$ = -0.6977 and

$z_{aptitude}$ = - 0.5634 then

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