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Musya8 [376]
3 years ago
13

G(x)=2x-2 f(x)=x^2+3x find (g of f)(2+x)

Mathematics
1 answer:
Bumek [7]3 years ago
6 0

Answer:

Step-by-step explanation:

G(f(2+x))=g(2+x)^2+3(2+x)=2(2+x)^2+3(2+x)-2=2(4+4x+x^2)+6+3x=8+8x+2x^2+6+3x=2x^2+11x+14

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ABCD and EFII GĦ. Use the figure above to find the value of each angle.
Marta_Voda [28]

Hope these help but i wrote all of it out with all its geometrical reasons

5 0
2 years ago
What is the product of (3a + 2)(4a2 - 2a + 9)?
natka813 [3]

Answer:

12a³+2a²+23a+18

Step-by-step explanation:

(3a+2)(4a²-2a+9)=

12a³-6a²+27a+8a²-4a+18=

12a³+2a²+23a+18

If you need more explanation, reply to this answer.

4 0
3 years ago
The mean of a population is 74 and the standard deviation is 15. The shape of the population is unknown. Determine the probabili
Lena [83]

Answer:

a) 0.0548 = 5.48% probability of a random sample of size 36 yielding a sample mean of 78 or more.

b) 0.9858 = 98.58% probability of a random sample of size 150 yielding a sample mean of between 71 and 77.

c) 0.5793 = 57.93% probability of a random sample of size 219 yielding a sample mean of less than 74.2

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The mean of a population is 74 and the standard deviation is 15.

This means that \mu = 74, \sigma = 15

Question a:

Sample of 36 means that n = 36, s = \frac{15}{\sqrt{36}} = 2.5

This probability is 1 subtracted by the pvalue of Z when X = 78. So

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{78 - 74}{2.5}

Z = 1.6

Z = 1.6 has a pvalue of 0.9452

1 - 0.9452 = 0.0548

0.0548 = 5.48% probability of a random sample of size 36 yielding a sample mean of 78 or more.

Question b:

Sample of 150 means that n = 150, s = \frac{15}{\sqrt{150}} = 1.2247

This probability is the pvalue of Z when X = 77 subtracted by the pvalue of Z when X = 71. So

X = 77

Z = \frac{X - \mu}{s}

Z = \frac{77 - 74}{1.2274}

Z = 2.45

Z = 2.45 has a pvalue of 0.9929

X = 71

Z = \frac{X - \mu}{s}

Z = \frac{71 - 74}{1.2274}

Z = -2.45

Z = -2.45 has a pvalue of 0.0071

0.9929 - 0.0071 = 0.9858

0.9858 = 98.58% probability of a random sample of size 150 yielding a sample mean of between 71 and 77.

c. A random sample of size 219 yielding a sample mean of less than 74.2

Sample size of 219 means that n = 219, s = \frac{15}{\sqrt{219}} = 1.0136

This probability is the pvalue of Z when X = 74.2. So

Z = \frac{X - \mu}{s}

Z = \frac{74.2 - 74}{1.0136}

Z = 0.2

Z = 0.2 has a pvalue of 0.5793

0.5793 = 57.93% probability of a random sample of size 219 yielding a sample mean of less than 74.2

5 0
3 years ago
(Will mark brainest)If it rains tomorrow the probability is 0.6 that James will practice piano. if it doesn't rain tomorrow ther
sergiy2304 [10]

Answer:

0.64

Step-by-step explanation:

P(J / R) = P (J and R) / P(R) 

0.8 = P (J and R) / 0.6 

P (J and R) = 0.6 * 0.8 = 0.48 [Probability John practicing and it is raining] 

P(J / NR) = P (J and NR) / P(NR) 

0.4 = P (J and NR) / (1 - 0.6) = P (J and NR) / 0.4 

P (J and NR) = 0.4 * 0.4 = 0.16 [Probability John practicing and it is not raining] 

Hence; 

Probability of John practicing regardless of weather condition is 

P(John Practicing) = 0.48 + 0.16 = 0.64

HOPE THIS HELPED!!!

7 0
3 years ago
Find four consecutive even numbers whose sum is -68
melamori03 [73]
-20, -18,-16,-14 works
3 0
2 years ago
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