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3 years ago

Find the sum and product of the roots. 2x^2 + 6x - 8 = 0

1 answer:

3 0

Suppose you can factorize:

$ax^2+bx+c=a(x-r_1)(x-r_2)$

Then by expanding the right side, you have

$ax^2+bx+c=a(x^2-(r_1+r_2)x+r_1r_2)=ax^2-a(r_1+r_2)x+ar_1r_2$

which means in this case, you have to have

$\begin{cases}6=-2(r_1+r_2)\\-8=2r_1r_2\end{cases}\implies\begin{cases}r_1+r_2=-3\\r_1r_2=-4\end{cases}$

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Suppose that a basketball player can score on a particular shot with probability .3. Use the central limit theorem to find the a

Rom4ik [11]

Answer:

(a) The probability that the number of successes is at most 5 is 0.1379.

(b) The probability that the number of successes is at most 5 is 0.1379.

(d) The probability that the number of successes is at most 11 is 0.9357.

→ All the exact probabilities are more than the approximated probability.

Step-by-step explanation:

Let S = a basketball player scores a shot.

The probability that a basketball player scores a shot is, P (S) = p = 0.30.

The number of sample selected is, n = 25.

The random variable $S\sim Bin(25,0.30)$

According to the central limit theorem if the sample taken from an unknown population is large then the sampling distribution of the sample proportion ( $\hat p$ ) follows a normal distribution.

The mean of the the sampling distribution of the sample proportion is: $E(\hat p)=p=0.30$

The standard deviation of the the sampling distribution of the sample proportion is:

$SD(\hat p)=\sqrt{\frac{ p(1- p)}{n} }=\sqrt{\frac{ 0.30(1-0.30)}{25} }=0.092$

(a)

Compute the probability that the number of successes is at most 5 as follows:

The probability of 5 successes is: $p=\frac{5}{25} =0.20$

$P(\hat p\leq 0.20)=P(\frac{\hat p-E(\hat p)}{SD(\hat p)}\leq \frac{0.20-0.30}{0.092} )\\=P(Z\leq -1.087)\\=1-P(Z$

**Use the standard normal table for probability.

Thus, the probability that the number of successes is at most 5 is 0.1379.

The exact probability that the number of successes is at most 5 is:

$P(S\leq 5)={25\choose 5}(0.30)^{5}91-0.30)^{25-5}=0.1935$

The exact probability is more than the approximated probability.

(b)

Compute the probability that the number of successes is at most 7 as follows:

The probability of 5 successes is: $p=\frac{7}{25} =0.28$

$P(\hat p\leq 0.28)=P(\frac{\hat p-E(\hat p)}{SD(\hat p)}\leq \frac{0.28-0.30}{0.092} )\\=P(Z\leq -0.2174)\\=1-P(Z$

**Use the standard normal table for probability.

Thus, the probability that the number of successes is at most 7 is 0.4129.

The exact probability that the number of successes is at most 7 is:

$P(S\leq 57)={25\choose 7}(0.30)^{7}91-0.30)^{25-7}=0.5118$

The exact probability is more than the approximated probability.

(c)

Compute the probability that the number of successes is at most 9 as follows:

The probability of 5 successes is: $p=\frac{9}{25} =0.36$

$P(\hat p\leq 0.36)=P(\frac{\hat p-E(\hat p)}{SD(\hat p)}\leq \frac{0.36-0.30}{0.092} )\\=P(Z\leq 0.6522)\\=0.7422$

**Use the standard normal table for probability.

Thus, the probability that the number of successes is at most 9 is 0.7422.

The exact probability that the number of successes is at most 9 is:

$P(S\leq 9)={25\choose 9}(0.30)^{9}91-0.30)^{25-9}=0.8106$

The exact probability is more than the approximated probability.

(d)

Compute the probability that the number of successes is at most 11 as follows:

The probability of 5 successes is: $p=\frac{11}{25} =0.44$

$P(\hat p\leq 0.44)=P(\frac{\hat p-E(\hat p)}{SD(\hat p)}\leq \frac{0.44-0.30}{0.092} )\\=P(Z\leq 1.522)\\=0.9357$

**Use the standard normal table for probability.

Thus, the probability that the number of successes is at most 11 is 0.9357.

The exact probability that the number of successes is at most 11 is:

$P(S\leq 11)={25\choose 11}(0.30)^{11}91-0.30)^{25-11}=0.9558$

The exact probability is more than the approximated probability.

6 0

4 years ago

Describe the transformation from the parent function of f(x)=x2 to g(x)=(x-5)^2(Need answer in less than 2 hours!) a. a vertical

bazaltina [42]

Answer: (c) a translation 5 units to the RIGHT

Step-by-step explanation:

Consider h(x) = A(x - h)² + k

A is the vertical stretch (by factor of A)
h is the horizontal shift (positive = Right, negative = Left)
k is the vertical shift (positive = Up, negative = Down)

f(x) = x²

g(x) = (x - +5)²

↓

positive means to the RIGHT

8 0

3 years ago

PLZZ HELPP!! Water is poured from a 1.5 L water bottle into an empty glass until both the glass and the bottle are 3/4 full. Wha

Natalka [10]

Answer:

0.5 L

Step-by-step explanation:

volume of bottle: 1.5 L

amount of water = 1.5 L

volume of glass: x

3/4 full is the same as 0.75 full

vol of water in bottle + vol of water in glass = total vol of water

0.75(bottle) + 0.75(glass) = 1.5

0.75(1.5) + 0.75x = 1.5

0.75x = 0.375

x = 0.5

5 0

3 years ago

Read 2 more answers

Please help! this is an overdue assignment and i can get through this one. I WILL MARK BRAINLIEST WHOEVER ANSWERS FIRST AMD CORR

Daniel [21]

Answer:

Step-by-step explanation:

The skier would have to go skiing 15 days im pretty sure.

hope im right :)

7 0

3 years ago

The volume of the polyhedron is ______ cm3.

PSYCHO15rus [73]

Answer:

50.80 cm^3

Step-by-step explanation:

the polyhedron is a rectangular pyramid

Volume of a rectangular pyramid = 1/3 x ( width x height x length)

1/3 ( 4 x 5 x 3) = 20 inches

we need to convert inches to cm

1 in = 2.54 cm

20 x 2.54 = 50.80 cm^3

8 0

3 years ago