Answer:
Length of side of rhombus is
Step-by-step explanation:
Given Rhombus ADEF is inscribed into a triangle ABC so that they share angle A and the vertex E lies on the side BC. We have to find the length of side of rhombus.
It is also given that AB=a and AC=b
Let side of rhombus is x.
In ΔCEF and ΔCBA
∠CEF=∠CBA (∵Corresponding angles)
∠CFE=∠CAB (∵Corresponding angles)
By AA similarity rule, ΔCEF~ΔCBA
∴ their sides are in proportion
⇒
⇒
⇒
⇒
Hence, length of side of rhombus is
Answer:
Yes, this provide enough evidence to show a difference in the proportion of households that own a desktop.
Step-by-step explanation:
We are given that National data indicates that 35% of households own a desktop computer.
In a random sample of 570 households, 40% owned a desktop computer.
<em><u>Let p = population proportion of households who own a desktop computer</u></em>
SO, Null Hypothesis, : p = 25% {means that 35% of households own a desktop computer}
Alternate Hypothesis, : p
25% {means that % of households who own a desktop computer is different from 35%}
The test statistics that will be used here is <u>One-sample z proportion</u> <u>statistics</u>;
T.S. = ~ N(0,1)
where, = sample proportion of 570 households who owned a desktop computer = 40%
n = sample of households = 570
So, <u><em>test statistics</em></u> =
= 2.437
<em>Since, in the question we are not given with the level of significance at which to test out hypothesis so we assume it to be 5%. Now at 5% significance level, the z table gives critical values of -1.96 and 1.96 for two-tailed test. Since our test statistics doesn't lies within the range of critical values of z so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.</em>
Therefore, we conclude that % of households who own a desktop computer is different from 35%.