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3 years ago

hich function has a range of {y|y ≤ 5}? f(x) = (x – 4)2 + 5 f(x) = –(x – 4)2 + 5 f(x) = (x – 5)2 + 4 f(x) = –(x – 5)2 + 4

Mathematics

1 answer:

Brums [2.3K]3 years ago

6 0

Answer:

$f(x)=-(x-4)^2+5$

Step-by-step explanation:

The function $f(x)=-(x-4)^2+5$ has the vertex at $(4,5)$ .

Since $a=-1\:$ , the graph of the function is a maximum graph.

The highest y-value is the y-coordinate of the vertex which is 5.

Therefore the range is { $y|y\le 5$ }

Therefore the correct answer is B.

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Written as a simplified polynomial in standard form, what is the result when

o-na [289]

Answer:

9x^2 - 10x -4

Step-by-step explanation:

It is set up like this

9x^2 - 8x

- (x-2)2

First solve (x-2)2

the answer is (2x-4)

so now you can do this instead

9x^2 - 8x

- 2x - 4

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9x^2 - 10x +4

9x^2 minus zero is 9x^2

-8x-2x is -10x

0- -4 is 4 because that is like saying 0 + 4 because double negatives equal a positive

A simpler way is to change all the numbers to the opposite sign and then change the minus to a plus

like this

9x^2 - 8x

+ -2x + 4

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9x^2 - 10x +4

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2 years ago

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3 years ago

Darien is discounting all prices on the sales for 20%. Which expression below represents the price, p, of any item he marks down

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Step-by-step explanation:

Since Darien is discounting the prices by 20%, the new price will be 80% of the original price, or 0.8 times the original price

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2 years ago

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3 years ago

In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal dist

Tcecarenko [31]

Answer:

a. 0.7291

b. 0.9968

c. 0.7259

Step-by-step explanation:

a. np and n(1-p) can be calculated as:

$np=23\times 0.48\\\\=11.04\\\\n(1-p)=23(1-0.52)\\\\=11.96$

#Both np and np(1-p) are greater than 5, hence, normal approximation is most appropriate:

$\mu_x=11.04\\\\\sigma^2=np(1-p)=0.48\times 0.52\times 23=5.7408$

#Define Y:

Y~(11.04,5.7408)

$P(X\leq 12)\approx P(Y\leq 12.5)\\\\P(Z\leq \frac{(12.5-11.04)}{\sqrt{5.7408}})=\\\\=1-0.2709\\\\=0.7291$

Hence, the probability of 12 or fewer is 0.8291

b. The probability that 5 or more fish were caught.

#Using normal approximation:

$P(X \geq 5) \approx P(Y \geq 4.5) = P(Z \geq\frac{ (4.5-11.04)}{\sqrt{(5.7408)}})\\\\=1-0.0032\\\\=0.9968$

Hence, the probability of catching 5+ is 0.9968

c. The probability of between 5 and 12 is calculated as;

-From b above $P(X\geq 5)=0.9968$ and a , $P(X\leq 12)$ =0.7291

$P(5\leq X\leq 120\approx P(4.5\leq Y\leq 12.5)\\\\=0.7291-(1-0.9968)\\\\=0.7259$

Hence, the probability of between 5 and 12 is 0.7259

4 0

3 years ago