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3 years ago

The expression below shows the population of butterflies in a forest after 4x years.

Mathematics

2 answers:

weeeeeb [17]3 years ago

7 0

Answer:

The equivalent expression is: $40(1.1699)^x$

Hence, option c is correct.

Step-by-step explanation:

We have been given the function:

$f(x)=40(1.04)^{4x}$

Using:

$x^{ny}=(x^n)^y$

Here, n=4 and x=y

$f(x)=40(1.04^4)^x$

On simplification of $1.04^4=1.1698\approx1.1699$ so we get:

$40(1.1699)^x$

Therefore, the equivalent expression is: $40(1.1699)^x$

Hence, option c is correct.

MrRissso [65]3 years ago

6 0

Th equivalent fraction of this expression is determined by just mutiplying the constants in the original expression and see if anything fits to the new form. We multiply 1.04 by 4 to equal to 4.16 and retain the 40. Hence the answer is f(x) = 40(4.1600)x.

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1. The data given below includes data from 42 candies, and 7 of them are red. The company that makes the candy claims that 33%

jeyben [28]

Answer:

The 95% confidence interval for true proportion of red candies is (5%, 27%).

The true proportion of red candies made by the company is different from 33%.

Step-by-step explanation:

The hypothesis to determine whether the claim made by the candy company is correct or not is:

H₀: The true proportion of red candies made by the company is 33%, i.e. p = 0.33.

Hₐ: The true proportion of red candies made by the company is different from 33%, i.e. p ≠ 0.33.

A (1 - α)% confidence interval can be constructed to check this claim.

The decision rule is:

If the confidence interval consists the null value then the null hypothesis will not be rejected. Otherwise it will be rejected.

The (1 - α)% confidence interval for population proportion is:

$CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

The information provided is:

n = 42

X = number of red candies = 7

Compute the sample proportion of candies that are red as follows:

$\hat p=\frac{X}{n}=\frac{7}{42}=0.167$

The critical value of z for 95% confidence level is:

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

*Use a z-table for the critical value.

Compute the 95% confidence interval for true proportion of red candies as follows:

$CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\\=0.167\pm 1.96\times \sqrt{\frac{0.167(1-0.167)}{42}}\\=0.16\pm0.1137\\=(0.0463, 0.2737)\\\approx(0.05, 0.27)$