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2 years ago

Express ln 32 - ln 8 as a single natural logarithm

2 answers:

8 0

$\bf \textit{Logarithm of rationals}
\\\\
log_a\left( \frac{x}{y}\right)\implies log_a(x)-log_a(y)\\\\
-------------------------------\\\\
ln(32)-ln(8)\implies ln\left( \frac{32}{8} \right)\implies ln(4)$

podryga [215]2 years ago

8 0

Answer:

its ln 4, A

Step-by-step explanation:

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A wedding website states that the average cost of a wedding is $25,809. One concerned bride hopes that the average is less than

lapo4ka [179]

Answer:

Null hypothesis H₀ : μ = 25,809

Alternative hypothesis H₁ : μ < 25,809

2) Test Statistic = -1.44

3) Conclusion:

The result is significant, there is sufficient evidence to support the bride’s hope at the 0.10 level of significance.

Step-by-step explanation:

Given the data in the question;

Sample mean x" = 24,638

sample size n = 46

standard deviation σ = 5531

level of significance ∝ = 0.10

NULL and ALTERNATIVE HYPOTHESIS

Null hypothesis H₀ : μ = 25,809

Alternative hypothesis H₁ : μ < 25,809

TEST STATISTICS

Z = (x"-μ) / σ√n

we substitute

Z = (24,638 - 25,809) / (5531/√46)

Z = -1171 / 815.5

Z = -1.44

Test Statistic = -1.44

Now, from normal z-table;

P-value = P( Z < -1.44 ) = 0.0749

P-value = 0.0749

Since P-value ( 0.0749 ) is less than level of significance ( 0.10 ), we reject H₀.

Conclusion:

The result is significant, there is sufficient evidence to support the bride’s hope at the 0.10 level of significance.

6 0

2 years ago

Given triangle GHJ, the measure of angle G equals 110°, the measure of angle J equals 40°, and the measure of angle H equals 30°

stiv31 [10]

Answer:

Since angle G is the largest angle, the opposite side, JH, is the longest. The order of the side lengths from longest to shortest is JH, HG, GJ

8 0

2 years ago

Read 2 more answers

Suppose that 20% of the adult women in the United States dye or highlight their hair. We would like to know the probability that

Rasek [7]

Answer:

71.08% probability that pˆ takes a value between 0.17 and 0.23.

Step-by-step explanation:

We use the binomial approxiation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$p = 0.2, n = 200$ . So

$\mu = E(X) = np = 200*0.2 = 40$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{200*0.2*0.8} = 5.66$

In other words, find probability that pˆ takes a value between 0.17 and 0.23.

This probability is the pvalue of Z when X = 200*0.23 = 46 subtracted by the pvalue of Z when X = 200*0.17 = 34. So

X = 46

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

$Z = \frac{46 - 40}{5.66}$

$Z = 1.06$

$Z = 1.06$ has a pvalue of 0.8554

X = 34

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

$Z = \frac{34 - 40}{5.66}$

$Z = -1.06$

$Z = -1.06$ has a pvalue of 0.1446

0.8554 - 0.1446 = 0.7108

71.08% probability that pˆ takes a value between 0.17 and 0.23.

6 0

2 years ago

High levels of cholesterol in the blood are not healthy in either humans or dogs. Because a diet rich in saturated fats raises t

VLD [36.1K]

The experiment is comparing veterinary and pets, and that pets are more vulnerable to cardiovascular disease than its counterpart.

Hypothesis is a education claim that is based on observation. Moreover, it is tested to check whether it is supported by the reality of the situation or not. Now, the hypothesis for this can be: there is a significant difference between the blood cholesterol levels among dogs and humans and how it affects cardiovascular disease.
Thank you for your question. Please don't hesitate to ask in Brainly your queries

8 0

2 years ago

After painting his porch, Jamil has \dfrac14 4 1 start fraction, 1, divided by, 4, end fractionof a can of paint remaining. Th

Nadya [2.5K]

The height of the smaller can would need to be 12.8 cm.

First find the volume of the larger can of paint. The volume of a cylinder is given by the formula
V=πr²h

Using the dimensions of the larger can, we have
V = 3.14(8²)(20) = 4019.2

Since he has 1/4 of this can, divide the volume by 4:
4019.2/4 = 1004.8

We will use this as the volume of the smaller can. Substituting this in along with the radius of the smaller can (using the same volume formula), we have:
1004.8 = 3.14(5²)h
1004.8 = 78.5h

Divide both sides by 78.5:
1004.8/78.5 = 78.5h/78.5
12.8 = h

5 0

1 year ago