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3 years ago

I need answers for number 1.

Mathematics

1 answer:

kolezko [41]3 years ago

6 0

Answer:

11^9

Step-by-step explanation:

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The answer to this is. 58

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4 years ago

On the hit HGTV show Flipping the Block, Whitney and John can paint 2 walls in 30 min. At this rate, how many walls can they pai

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(1,4)(2,8)(3,12)(4,16) i think

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3 years ago

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

Find the rate of change:

AURORKA [14]

It takes 2 gallons of gas for each 50 Mike's you drive so rate of change is 25 miles per gallon

7 0

3 years ago

Can someone please help me answer these 2 questions with a full explanation so I can do the rest on my own? will give brainliest

Anton [14]

Answer:

a) ∠ABC = 54°

a) ∠ABC = 43°

Step-by-step explanation:

Trigonometric ratios

$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$

where:

$\theta$ is the angle
O is the side opposite the angle
A is the side adjacent the angle
H is the hypotenuse (the side opposite the right angle)

Part (a)

Use the cos trig ratio to find an expression for the measure of BD:

$\implies \sf \cos (38^{\circ})=\dfrac{BD}{24.3}$

$\implies \sf BD=24.3\cos (38^{\circ})$

Use the cos trig ratio and the found length of BD to find angle ABD:

$\sf \implies \cos(ABD)=\dfrac{BD}{19.9}$

$\sf \implies \angle ABD=\cos^{-1}\left(\dfrac{24.3\cos (38^{\circ})}{19.9}\right)$

$\sf \implies \angle ABD=15.79446612...^{\circ}$

Therefore:

$\sf \implies \angle ABC=\angle ADB + 38^{\circ}$

$\sf \implies \angle ABC=15.79446612...^{\circ}+ 38^{\circ}$

$\sf \implies \angle ABC=54^{\circ}\:\:(nearest\:degree)$

Part (b)

Use the tan trig ratio to find angle CAD:

$\implies \sf \tan(CAD)=\dfrac{4.9}{7.4}$

$\implies \sf \angle CAD=\tan^{-1} \left(\dfrac{4.9}{7.4}\right)$

$\implies \sf \angle CAD=33.5110188...^{\circ}$

Therefore:

$\sf \implies \angle BAD=13^{\circ}+33.5110188...^{\circ}$

$\sf \implies \angle BAD=46.5110188...^{\circ}$

∠ABC = ∠ABD

Interior angles of a triangle sum to 180°

$\sf \implies \angle ABD + \angle BAD + \angle BDA=180^{\circ}$

$\sf \implies \angle ABC + 46.5110188...^{\circ} + 90^{\circ}=180^{\circ}$

$\sf \implies \angle ABC=43^{\circ}\:\:(nearest\:degree)$

4 0

3 years ago