Answer:
45
Step-by-step explanation:
Given that the number of savory dishes is 9 and the number of sweet dished is 5.
Denoting all the 9 savory dishes by
, and all the sweet dishes by
.
The possible different mix-and-match plates consisting of two savory dishes are as follows:
There are 9 plates with
from sweet plates which are 
There are 9 plates with
from sweet plates which are 
Similarly, there are 9 plated for each
and 
Hence, the total number of the different mix-and-match plates consisting of two savory dishes

Answer: The mat is 4.33 ft high off the ground.
Step-by-step explanation:
Since we have given that
Angle of elevation with the first triangle = 30°
Angle of elevation with the second triangle = 60°
Length at which gymnastics mat extends across the floor = 5 feet
so, As shown in the figure:
We need to find the height of the mat off the ground.
If CD = 5 ft,
Let, AB = y, DC = x.
In Δ ABC,

Similarly, in Δ ACD,

Hence, the mat is 4.33 ft high off the ground.
As it has been given that
,
.
We need to find the value of the following:
(i)
, substituting the value of 'x' and 'y' in the expression, we get:


So, 
(ii)
, substituting the value of 'x' and 'y' in the expression, we get:


So, 
(iii)
, we need to substitute the value of 'x' and 'y' in the expression, for this, we can use distributive property of multiplication that says,

Using the distributive property of multiplication:


Now, we know that 
We get, 

Therefore,
=
.
(iv) We have,
, we need to substitute the value of 'x' and 'y' in the expression, we get:

Again, we can use distributive property of multiplication that says,

So,



since, 
we get,


Therefore,

Answer:
d) -8 × 3 = -24
Step-by-step explanation:
a) -18 ÷ 6 = -3
b) 30 ÷ 3 = 10
c) -7 × -7 = 49
d) -8 × 3 = -24
Above from all, option d is done correctly.
Note: when negatives are multiplied together or divided they cancel out to being positive. For example: -1 × -1 = 1
Step-by-step explanation:
individual is telling the truth," to answer the following questions.
a. What is the probability of a Type I error? (Round your answer to 3 decimal places.)
b. What is the probability of a Type II error? (Round your answer to 2 decimal places.)