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wariber [46]
3 years ago
6

F(x)=-x^2+8x+15 ...?

Mathematics
1 answer:
rusak2 [61]3 years ago
8 0
Here i how I would do it:<span>f(x)=−<span>x2</span>+8x+15</span>
set f(x) = 0 to find the points at which the graph crosses the x-axis. So<span>−<span>x2</span>+8x+15=0</span>
multiply through by -1<span><span>x2</span>−8x−15=0</span> <span>(x−4<span>)2</span>−31=0</span> <span>x=4±<span>31<span>−−</span>√</span></span>
So these are the points at which the graph crosses the x-axis. To find the point where it crosses the y-axis, set x=0 in your original equation to get 15. Now because of the negative on the x^2, your graph will be an upside down parabola, going through<span>(0,15),(4−<span>31<span>−−</span>√</span>,0)and(4+<span>31<span>−−</span>√</span>,0)</span>
To find the coordinates of the maximum (it is maximum) of the graph, you take a look at the completed square method above. Since we multiplied through by -1, we need to multiply through by it again to get:<span>f(x)=31−(x−4<span>)2</span></span><span>
Now this is maximal when x=4, because x=4 causes -(x-4)^2 to vanish. So the coordinates of the maximum are (4,y). To find the y, simply substitute x=4 into the equation f(x) to give y = 31. So it agrees with the mighty Satellite: (4,31) is the vertex.</span>
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The overhead reach distances of adult females are normally distributed with a mean of 205 cm205 cm and a standard deviation of 8
bekas [8.4K]
A) the probability is 0.123 or 12.3%.
B) the probability is 0.8589 or 85.89%.
C) the normal distribution can be used even though the sample is small because the population the sample is taken from is normally distributed.

Explanation
A) We first find the z-score that corresponds with this value.
z=\frac{X-\mu}{\sigma}&#10;\\&#10;\\=\frac{215-205}{8.6}= 1.1628

Using a z-table (http://www.z-table.com) we find 1.16; this corresponds to a probability of 0.8770.  However, This is the probability that a number will be lower than this; since we want the probability that the value is higher, we subtract from 1:

1-0.8770 = 0.123.

B) To find the probability of a sample mean, we use the formula
z=\frac{X-\mu}{\frac{\sigma}{\sqrt{n}}}&#10;\\&#10;\\=\frac{202.8-205}{\frac{8.6}{\sqrt{15}}}=-0.9908

Looking in our z-table we see that this corresponds with 0.1611.  Again, however, this is the area left of this value, which is the probability below; we want the probability above, so we subtract from 1:

1-0.1611 = 0.8589
5 0
3 years ago
When x = -3, then what does y equal?
bazaltina [42]

Answer:

y = - 6

Step-by-step explanation:

Locate x = - 3 0n the x- axis, then go vertically down until the line is met. At this point read the value of y from the y0 axis, that is

When x = - 3, y = - 6

7 0
3 years ago
Read 2 more answers
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Llana [10]
Okay. So, based off of that, if you divide 1 1/2 (3/2) by 3/4, 3/2 * 4/3 is 12/6 or 2. 1/2 cups of raspberries is needed for each fourth of the cake. 1/2 * 4 = 2. Lin will need 2 cups of raspberries for the whole cake.
6 0
3 years ago
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sattari [20]
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4 0
3 years ago
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qaws [65]

Answer:

Part A = D

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Step-by-step explanation:

Part A:

area = 5*4x = 20x

so, 100 \leq 20x \leq  1000

Part B:

to leave it only by x, you divide both sides by 20

100/20 = 5, 1000/20 = 50

which 5\leq x\leq 50

7 0
3 years ago
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