Answer:
Their sides must be in the same ratio and their angles must be equal.
Step-by-step explanation:
If two polygons are similar their sides must be in the same ratio and their angles must be equal.
e. g. -
If ABCDEF and GHIJKL be the two polygons,
then,
and,
∠ABC = ∠GHI ; ∠BCD =∠HIJ ; ∠CDE = ∠IJK ; ∠DEF =∠JKL ; ∠EFA =∠KLG;
∠FAB = ∠LGH .
Given : In a restaurant, the proportion of people who order coffee with their dinner is p.
Sample size : n= 144
x= 120
The null and the alternative hypotheses if you want to test if p is greater than or equal to 0.85 will be :-
Null hypothesis : [ it takes equality (=, ≤, ≥) ]
Alternative hypothesis : [its exactly opposite of null hypothesis]
∵Alternative hypothesis is left tailed, so the test is a left tailed test.
Test statistic :
Using z-vale table ,
Critical value for 0.05 significance ( left-tailed test)=-1.645
Since the calculated value of test statistic is greater than the critical value , so we failed to reject the null hypothesis.
Conclusion : We have enough evidence to support the claim that p is greater than or equal to 0.85.
Answer:
4r² - 5r - 15 / r(r+3)
Step-by-step explanation:
To solve this problem, we will proceed the following way, writing down the common multiple of the denominators.
Thus, the answer is 4r² - 5r - 15 / r(r+3)
Answer:
25 one-dollar coins, 16 half-dollar coins, and 164 quarters
Step-by-step explanation:
First, set up equations based on the information given:
Then, substitute <em>q</em> in the first equation with the expression from the third equation:
Next, substitute <em>h</em> in that equation with the expression from the second equation:
Solve for <em>d</em>, the number of one-dollar coins:
Substitute 25 for <em>d</em> in the second equation to find <em>h</em>, the number of half-dollar coins:
Substitute 25 for <em>d</em> and 16 for <em>h</em> in the third equation to find <em>q</em>, the number of quarters:
Then, verify that the coins total $74:
Next, verify that the number of half-dollar coins is one more than three-fifths of the number of one-dollar coins:
Finally, verify that the number of quarters is four times the number one-dollar and half-dollar coins together:
