If their perimeters are equal, we can add up all the side lengths of each triangle, and set the perimeters equal to each other to find the value of x that satisfies the equation:

x - 2 + x + 3x + 1 = 2x - 5 + x + 4 + 6x - 7

Combine like terms:

5x - 1 = 9x - 8

And finally, solve for x:

7 = 4x

x = $\frac{7}{4}$

Therefore, x is equal to $\frac{7}{4}$ .

<em>Hope this helps! :)</em>

6 0

3 years ago

A local bank needs information concerning the savings account balances of its customers. A random sample of 15 accounts was chec

PSYCHO15rus [73]

Answer:

(513.14, 860.36) is a 98% confidence interval for the true mean

Step-by-step explanation:

We have a small sample size of n = 15, the mean balance was $\bar{x} = 686.75$ with a standard deviation of s = 256.20. The confidence interval is given by $\bar{x}\pm t_{\alpha/2}(\frac{s}{\sqrt{n}})$ where $t_{\alpha/2}$ is the 100 $(\alpha/2)$ th quantile of the t distribution with n-1=15-1=14 degrees of freedom. As we want a $100(1-\alpha)$ % = 98% confidence interval, we have that $\alpha = 0.02$ and the confidence interval is $686.75\pm t_{0.01}(\frac{256.20}{\sqrt{15}})$ where $t_{0.01}$ is the 1st quantile of the t distribution with 14 df, i.e., $t_{0.01} = -2.6245$ . Then, we have $686.75\pm (-2.6245)(\frac{256.20}{\sqrt{15}})$ and the 98% confidence interval is given by (513.1379, 860.3621)