Whats 3(x+1)<18? i really need help with this question i've tried multiple solutions

Mathematics

1 answer:

JulijaS [17]3 years ago

7 0

Answer:

$\boxed{x$

Step-by-step explanation:

→ Expand out the brackets

3x + 3 < 18

→ Minus 3 from both sides to isolate 3x

3x < 15

→ Divide both sides by 3 to isolate x

x < 5

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Suppose that the weight of seedless watermelons is normally distributed with mean 6.1 kg. and standard deviation 1.9 kg. Let X b

horrorfan [7]

Answer:

a. $X\sim N(\mu = 6.1, \sigma = 1.9)$ b. 6.1 c. 0.6842 d. 0.4166 e. 0.1194 f. 8.5349

Step-by-step explanation:

a. The distribution of X is normal with mean 6.1 kg. and standard deviation 1.9 kg. this because X is the weight of a randomly selected seedless watermelon and we know that the set of weights of seedless watermelons is normally distributed.

b. Because for the normal distribution the mean and the median are the same, we have that the median seedless watermelong weight is 6.1 kg.

c. The z-score for a seedless watermelon weighing 7.4 kg is (7.4-6.1)/1.9 = 0.6842

d. The z-score for 6.5 kg is (6.5-6.1)/1.9 = 0.2105, and the probability we are seeking is P(Z > 0.2105) = 0.4166

e. The z-score related to 6.4 kg is $z_{1} = (6.4-6.1)/1.9 = 0.1579$ and the z-score related to 7 kg is $z_{2} = (7-6.1)/1.9 = 0.4737$ , we are seeking P(0.1579 < Z < 0.4737) = P(Z < 0.4737) - P(Z < 0.1579) = 0.6821 - 0.5627 = 0.1194

f. The 90th percentile for the standard normal distribution is 1.2815, therefore, the 90th percentile for the given distribution is 6.1 + (1.2815)(1.9) = 8.5349

7 0

3 years ago

Suppose that 44% of all Americans approve of the job the president is doing. The most recent Gallup poll consisted of a random s

PolarNik [594]

This is a typical binomial distribution since we are dealing with only two possible outcomes. For this distribution we have:
n = population = 1400
p = probability of positive answer = 0.44

A) The mean of a binomial distribution is
μ = np
= 1400 × 0.44
= 616

Hence, μ = 616

B) The standard deviation of a binomial distribution is
σ = √[np(1 - p)]
 = √[1400×0.44×(1-0.44)]
 = √(1400×0.44×0.56)
 = 18.6

Hence, σ = 18.6

C) A binomial distribution B(n, p) can be approximated by a normal distribution N(μ, σ) only when:
np ≥ 10 (we have 616 > 10)
np(1 - p) ≥ 10 (we have 344.96 > 10)

Hence, the normal approximation is N(616, 18.6)

D) We need to calculate the probability of the sample population to be within 3% of the true mean.

In order to do so, as a first thing, we need to calculate the sample standard deviation, which will be given by the formula:
$\sigma = \sqrt{ \frac{p(1-p)}{n} }$
= √[0.44 × (1 - 0.44) ÷ 1400]
= √0.000176
= 0.013

Now, we need to calculate the z-score associated with the values we want: since we want 3% from the mean, it means between 41% and 47%.
The z-score can be calculated by the formula:
z = (Y - p) / σ
z₁ = (0.41 - 0.44) / 0.013 = -2.31
z₂ = (0.47 - 0.44) / 0.013 = 2.31

Therefore, we can write
P(0.41 ≤ Y ≤ 0.47) = P(-2.31 ≤ z ≤ 2.31)
= P(z ≤ 2.31) - P(z ≤ -2.31)
= P(z ≤ 2.31) - [1 - P(z ≤ 2.31)]
= 2×P(z ≤ 2.31) - 1

From a standard normal distribution table, we find:
P(z ≤ 2.31) = 0.9896

Therefore:
2×P(z ≤ 2.31) - 1 = 2 × 0.9896 - 1
= 0.9792

Hence, the probability to find a proportion within 3% of the real mean is 97.92%

8 0

3 years ago

Write the multiplicative comparison statement as an equation. 18 is 3 times as many as 6.

likoan [24]

Answer:

18 = 3 × 6

Step-by-step explanation:

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3 years ago

Find the coordinates of the center of the following circle.

AysviL [449]

The answer is (3,7) I hope this helps!!!