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nordsb [41]
3 years ago
12

Write an equation to match each graph:

Mathematics
2 answers:
morpeh [17]3 years ago
5 0

Write an equation to match each graph.

Solution:

The first graph is V shaped graph centered at origin, (0,0) and the graph is not shifted or translated. So, the equation of first graph is,

y=|x|

The second graph is V shaped graph centered at (1,0) and y=|x| is horizontally shifted right by 1 unit. So, the equation of second graph is,

y=|x-1|

The third  graph is also V shaped but, it is inverted V graph centered at (0,1) . As, the graph is inverted V So, the graph must have y=-|x|. But, as the center is (0,1). So, the graph is shifted up by 1 unit. So, the equation of the third graph is,

y=-|x|+1

The fourth graph is shifted V graph, whose center is (1,-1). So, y=|x| is shifted right by 1 unit and down by 1 unit. So, the equation of fourth graph is,

y=|x-1|-1

The center of fifth graph is (-1,0), So, y=|x| graph is shifted left by 1 unit. So, the equation of fifth graph is

y=|x+1|

Nikolay [14]3 years ago
3 0
The equation should be y=|x| BUT i am not 100%. there would be no shifts because the vertex is on the origin.
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If f(x) = 2x2 - 5 and g(x) = x2 - 4x - 8, find (f - g)(x).
oksano4ka [1.4K]

Answer:

B. ) x² + 4x + 3

Step-by-step explanation:

(f-g)(x) = f(x) - g(x) =

(2x²-5) - (x²-4x-8) =

2x² - x² + 4x + 8 - 5 =

x² + 4x + 3

8 0
3 years ago
A grinding wheel manufacturer designed a new grinding wheel. Repeated tests were conducted on wheels of approximately the same w
sergejj [24]

Answer:

a) a=225 +0.674*16.5=236.121

So the value of height that separates the bottom 75% of data from the top 25% is 236.121.  

b) P(X \geq 3) = 1-P(X

c) P(\bar X \geq 225)=1- P(\bar X

Step-by-step explanation:

Previous concepts

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 Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

2) Part a

Let X the random variable that represent the cuts of a population, and for this case we know the distribution for X is given by:

X \sim N(225,16.5)  

Where \mu=225 and \sigma=16.5

For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.25   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.674. On this case P(Z<0.674)=0.75 and P(z>0.674)=0.25

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=0.674=\frac{a-225}{16.5}

And if we solve for a we got

a=225 +0.674*16.5=236.121

So the value of height that separates the bottom 75% of data from the top 25% is 236.121.  

Part b

For this case we know that the individual probability of select one wheel with a cutting rate higher than the calculated value in part a is 0.25, and we select n =10 so then we can use the binomial distribution for this case:

X\sim Bin(n=10, p=0.25)

And we want this probability:

P(X \geq 3) = 1-P(X

We can find the individual probabilities like this:

P(X=0)=(10C0)(0.25)^0 (1-0.25)^{10-0}=0.0563

P(X=1)=(10C1)(0.25)^1 (1-0.25)^{10-1}=0.1877

P(X=2)=(10C2)(0.25)^2 (1-0.25)^{10-2}=0.2816

P(X \geq 3) = 1-P(X

Part c

For this case we know that the distribution for the sample mean is given by:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

And we want this probability:

P(\bar X \geq 225)

And for this case we can use the complement rule and the z score given by:

z= \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}

And if we replace we got:

P(\bar X \geq 225)=1- P(\bar X

4 0
3 years ago
Olve for x. 3(3x - 1) + 2(3 - x) = 0 x = 3/7 x = -3/7 x = 1/3 x = -1/3
zloy xaker [14]

<u>Answer:</u>

x = -3/7

<u>Step-by-step explanation:</u>

We are given the following equation for which we have to solve for x:

3(3x - 1) + 2(3 - x) = 0

So we will start by expanding the equation by multiplying the common factor with the brackets to get:

9x-3+6-2x=0

Arranging the like terms together (variables on one side of the equation and constants on the other side) to get:

9x-2x=3-6\\\\7x=-3\\\\x=-\frac{3}{7}

Therefore, x = -3/7.

8 0
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Find the sum.<br> 7x + 15x=
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Answer:

7x + 15x= 21x

Step-by-step explanation:

7x + 15x

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4 0
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Answer:

The most common units of distance In the metric system of measurement,  are millimeters, centimeters, meters, and kilometers.

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